I would suggest we remove the object here for the variable name. I hear that it makes them practice object, but I feel it's confusing to introduce here("data", "raw") and then suddenly ask them to do here(path_data_raw, "msf_linelist_moissala_2023-09-24.xlsx"). The variable does not add much here and is only truly important with long automated scripts ...

I think side notes are distracting, I have not even noticed them until now. I would suggest we move this type of information (definitions/deeper concept) to the tooltips

Test of a comment here - what happens if I render ?

cool

waht

Elon aligns up with Trump on immigratoin

I can't really put my thumb on it. But this situation seems very similar to a certain someone...

This is so funny to me for some reason. Did his being popular already solidify him becoming president?

Mexican rights isn't something I learned during High school. The deepest we went into is how the U.s intercepted a message from Germany to betray the U.S but less on the rights of the people.

I think with how the election was nobody would have won against jfk. He has that spokeperson look, member of congress, and served.

The command line might seem intimidating at first, but it’s a lifesaver for doing tasks quickly. Plus, it’s super useful for automating things you’d hate doing manually

The evilness that is racism is something that has changed so much over decades. When things like segeration is talked about it's best to know that racial discrimination like this isn't even 100 years old, (1953)

What have our allies done to help? The U.S does give money for humanitarian aid and other neccecities but I always hear how T.G.D was unlivable but not how other countries helped us.

Una sabiduría que va más allá del conocimiento intelectual

despite its unfunny nature the first thing thing that they should have done was make a treaty. after this Russia and the U.S relations were strained

This shows how American felt during the red scare perfectly. When i was growing up I was taught that Russian's were spies and dangerous just some properganda but an important quote nontheless.

This formatting is odd

?

This could work nicely as a table of contents style? But only when anchors are specific steps

Use a textbox with header stlye?

Left/right align images to save vertical scrolling

Left/right align images to save vertical scrolling

Space between textbox and end of list/column above

Left/right align images to save vertical scrolling

Left/right align images to save vertical scrolling

Spacing above and below textbox

I'll fix space between

Something doesn't seem right here

Do we want internal table of contents? If yes, what style?

Not all QGs have Use cases

I'll fix spacing below

Use the disclaimer textbox with the shield ! icon?

Accordion? Note: not ever quick guide has additional resources and links

?

Align image right?

Accordion?

I'll fix spacing below

Accordion?

Accordion?

Accordion?

HTML accordion?

Change below to HTML accordion?

This is the only one not indented? Also, do the need to be (numbered) lists as they are only one step (except for 4?)

"Learn how"

Remove "Learn how" from linked text

Russian Language Notes

See Link for a proof with transfinite induction.

I don't see how anyone wouldn't have a problem with this happening. Soldiers die for their countries and this grotesque show of power isn't sane. Plus bro isn't even German doing this in Germany.

Learning about war is always tragic. 85 million lives were lost. 1 life lost is a tradgey but many more becomes a statistic.

At a time like this i dont understand why American farmers weren't supported more. And with other times where monopolies took over and they were tossed aside.

This is a very risky thing to do. And i see now by reading this how the great depression happened. But a plus was how much money some people made before America turned for the worse.

reply to u/Rocky__1927 at https://old.reddit.com/r/typewriters/comments/1hirzo5/remington_premier/

As Ted Munk has commented on these before, rare is a reach. They're uncommon primarily because they didn't manufacture as many of these as they did of the American Quiet-Riters (or Office- or Letter-Riters). I would suspect it's stamped as made in Great Britain (though actually made in Scotland) after American manufacture moved there in the late 50s/early 60s where they only made them for a short time before switching over to more plastic bodied machines. Probably has a serial number starting with ERP on the frame near the ribbon cup. It's essentially a Quiet-Riter made in Scotland with smooth paint rather than crinkle. Surely some of the manufacturing process and materials will be slightly different/cheaper.

There may be a completist Remington collector who might pay over $100 for it, but I wouldn't think you'd have an easy time getting over $75 for this unless it's in excellent/serviced condition, particularly when ubiquitous QRs with sturdier cases can be had for $10-25 in similar condition.

OK, good introduction to this imortant painter. What is missing is a more penetrating interpretation of the painter and place...the part the deals with architectural imagery is very interesting, I wonder if this might have been the oportunity for comparisons of actual Timurid and Safavid architecture....or something along these lines. As it is , the StoryMap appears to be too much of a mere listing of important facts with not enough of a "driving thesis"

THESIS?

Ok, an interesting subject and you touch upon some important issues in regard to the sale of art on the marketplace. Much revision of the text would be very helpful as would would a better structure of the format...for instance: a clear thesis statement would be the best way to improve the sructure..." This story map will utilize The Nativity with the Prophets Isaiah and Ezekiel to cast a vignette " is rather vague... The conclusion raises additional questions without really nailing down the defense of a well formed thesis. But, this could make for a truly excellent StoryMap with a thorough re-working!

for - Medium article - Nyams I have known and loved - Alexander Vezhnevets, 2022, Apr 28

for - key insight / adjacency- Indra's net metaphor - emptiness and form - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

key insight / adjacency - between - Indra's net metaphor - emptiness and form - new relationship - Of course! Indra's net! - Every specific form we encounter in reality - is like a node, a jewel in Indra's net - Any form is related to all forms

for - key insight / adjacency- Dzogchen practice - the experience of spaciousness and emptiness of phenomena - neuroscientist Gerald Edelman's question about the newborn classifying the world - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

key insight / adjacency - between - Dzogchen practice - the shi-ne experience of spaciousness and emptiness of phenomena - Neuroscientist Gerald Edelman's question - how does a newborn learn to classify an undivided world of phenomena? - new relationship - As the mind lets go of our habitual tendency to reify and create artificial independent things - phenomena begin to appear to arise as continuously interconnected, interdependent, yet without ground in essence - This gives us a sense of space where every phenomena is arising inter-relatedly. - This is related to Gerald Edelman's question of - how a newborn is able to start classifying a world that is undivided - Does shi-ne training take us back to our first experience of reality as a newborn, when - there was not even any inter-relationships because there were no separate objects to be in relation with each other

for - description of phenomenology of nyam ne-pa - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

description of phenomenology of nyam ne-pa - openness - stillness - inter-relatedness - clarity - expanse - spaciousness - no sense of boundaries between senses of internal and external experiences - body feels transparent and weightless

for - shi-ne practice - metaphor - The mind is like the surface of a lake and phenomena are like stones that drop into it. - The water then breaks and warps around it - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

for - definition - nyam ne-pa - the state of quiet presence - the goal of Dzogchen meditation practice - going from form to emptiness - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

for - definition - nyam-nyi - when form ad emptiness are both experienced as one taste (nonduality) - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

for - definition gYo-Wa - going from emptiness to form - from Medium article - Heart Sutra and the nyams of Dzogchen - Aleander Vezhnevets - 2022, Sept 7

Ok, A very big lift to take on...too big! Most of the interpretation relies on basic introductory information....wikipedia level material...and the text rerads too much like a mere listing of basic ideas. There is also a fair amount of redundancy....The Michelangelo scholarship is of course very extensive, the bibliography thus cited is hard to evaluate...maybe more specific publications on Michelangelo's travels might have been warranted.

This might be the best thesis...it should be right at the beginning of the text

This reminds me of when in school we were taught about the scientific revolution. Galileo being bound to his house for proposing an idea that others disagreed with.

The first time i've heard of vigilantism from lynching mobs has to be to kill a mockingbird. I remember seeing the hate from the towns folk and reading now real instances of this happening is why keeping these kinds of books in schools and not banned is important. Disgusting.

This is a good quote both in this context and in future ones. With Syria's freedom I think this quote is strong. He doesn't talk about how he'll be a hero but help heal.

It's because people in hard times want to go back. So with this promise and after the war with the loss the people wanted it to be real.

Das ist ein klares Argument für Degrowth. Der Bearf nach Wasserstoff würde sonst die Hälfte der Kapazitäten für erneuerbare Energien verschlucken.

Das ist die entscheidende Aussage in diesem Bericht.

Der sogenannte Übergang zu einer Wasserstoff-Wirtschaft ist also engstens mit den Problemen der globalen Ungleichheit und der material flows verbunden. Es geht um den Transfer von Kapital, und zwar nicht nur der finanziellen Mittel, sondern auch der Produktions-Infrastruktur.

Das heisst, dass es für die industrielle Produktion interessanter wird, sich dorthin zu bewegen, wo viel elektrische Energie produziert werden kann.

Very good! Well researched , ocumented, and written.

Excellent thesis

what is the box on the bottom right in A? Presumably it is the camera? A label would be helpful.

how does this compare to just using standard brightfield imaging or other label-free techniques (e.g. DIC)? are there any features that quantitative phase picks up that other techniques miss?

Is it possible to determine computationally whether the drop in RI is only attributed to density change or something else?

What was the motivation for the value 10,420? Is the ability to extract features pretty consistent (no the actual weights obviously but the behavior of being able to extract meaningful features) as long as the space is large enough?

There is a lot of good research in this project...there is a sense that Van Eyck benefitted significantly from observations experienced along the scenes of his travels. But it also seems that accurate depictions of actual places was not a feature in his work...comparisons of van Eyck's pictures with period depictions of Jerusalem, for example, might be instructive...perhaps even comparisons of interior scenes by other hands, Netherlandish and otherwise, would be interesting...but there is no doubt that the symbolic nature of his paintings was perhaps more to the point.

Some of the writing and format could do with a thorough revisioning, but the idea is strong.

eLife Assessment

This valuable study combines evolution experiments with molecular and genetic techniques to study how a genetic lesion in MreB that causes rod-shape cells to become spherical, with concomitant deleterious fitness effects, can be rescued by natural selection. The results are convincing, although further improvement of the statistical analyses and figure presentation, and further clarification of the concrete contribution of the paper and how it relates to previous literature, would be welcome.

Reviewer #1 (Public review):

Summary:

The authors performed experimental evolution of MreB mutants that have a slow growing round phenotype and studied the subsequent evolutionary trajectory using analysis tool from molecular biology. It was remarkable and interesting that they found that the original phenotype was not restored (most common in these studies) but that the round phenotype was maintained.

Strengths:

The finding that the round phenotype was maintained during evolution rather than that the original phenotype, rod shape cells, was recovered is interesting. The paper extensively investigates what happens during adaptation with various different techniques. Also the extensive discussion of the findings at the end of the paper is well thought through and insightful.

Weaknesses:

I find there are three general weaknesses<br /> (1) Although the paper states in the abstract that it emphasizes "new knowledge to be gained" it remains unclear what this concretely is. At page 4 they state 3 three research questions, these could be more extensively discussed in the abstract. Also these questions read more like genetics questions while the paper is a lot about cell biological findings.<br /> (2) It is not clear to me from the text what we already know about restoration of MreB loss from suppressors studies (in the literature). Are there supressor screens in the literature and which part of the findings is consistent with suppressor screens and which parts are new knowledge?<br /> (3) The clarity of the figures, captions and data quantification need to be improved.

Reviewer #3 (Public review):

This paper addresses a long-standing problem in microbiology: the evolution of bacterial cell shape. Bacterial cells can take a range of forms, among the most common being rods and spheres. The consensus view is that rods are the ancestral form and spheres the derived form. The molecular machinery governing these different shapes is fairly well understood but the evolutionary drivers responsible for the transition between rods and spheres is not. Enter Yulo et al.'s work. The authors start by noting that deletion of a highly conserved gene called MreB in the Gram-negative bacterium Pseudomonas fluorescens reduces fitness but does not kill the cell (as happens in other species like E. coli and B. subtilis) and causes cells to become spherical rather than their normal rod shape. They then ask whether evolution for 1000 generations restores the rod shape of these cells when propagated in a rich, benign medium.

The answer is no. The evolved lineages recovered fitness by the end of the experiment, growing just as well as the unevolved rod-shaped ancestor, but remained spherical. The authors provide an impressively detailed investigation of the genetic and molecular changes that evolved. Their leading results are:

(1) the loss of fitness associated with MreB deletion causes high variation in cell volume among sibling cells after cell division;<br /> (2) fitness recovery is largely driven by a single, loss-of-function point mutation that evolves within the first ~250 generations that reduces the variability in cell volume among siblings;<br /> (3) the main route to restoring fitness and reducing variability involves loss of function mutations causing a reduction of TPase and peptidoglycan cross-linking, leading to a disorganized cell wall architecture characteristic of spherical cells.

The inferences made in this paper are on the whole well supported by the data. The authors provide a uniquely comprehensive account of how a key genetic change leads to gains in fitness and the spectrum of phenotypes that are impacted and provide insight into the molecular mechanisms underlying models of cell shape.

Suggested improvements and clarifications include:<br /> (1) A schematic of the molecular interactions governing cell wall formation could be useful in the introduction to help orient readers less familiar with the current state of knowledge and key molecular players;<br /> (2) It remains unclear whether corrections for multiple comparisons are needed when more than one construct or strain is compared to the common ancestor, as in Supp Fig 19A (relative PG density of different constructs versus the SBW25 ancestor). The author's response did not clarify matters: was data for the WT obtained independently alongside each each strain/construct (justifying a paired t-test) or was a single set of data for the WT obtained and used to compare against all other strains/constructs (which would demand a correction for multiple comparisons)?<br /> (3) The authors refrain from making strong claims about the nature of selection on cell shape, perhaps because their main interest is the molecular mechanisms responsible. They identify sources of stabilizing selection favouring an intermediate cell size (lack of DNA in small cells and disorganized DNA in large cells). Their interpretation of stabilizing selection in the review is correct and entirely consistent with the mechanistic causes identified here. I think this is valuable and interesting, although I recognize it is not the focus of the paper.

Comments on revisions:

Please further clarify the experimental design and replication for the contrast between mutants and WT to address the issue of multiple comparisons.

Author response:

The following is the authors’ response to the original reviews.

Public Reviews: 

Reviewer #1 (Public Review): 

Summary: 

The authors performed experimental evolution of MreB mutants that have a slow-growing round phenotype and studied the subsequent evolutionary trajectory using analysis tools from molecular biology. It was remarkable and interesting that they found that the original phenotype was not restored (most common in these studies) but that the round phenotype was maintained. 

Strengths: 

The finding that the round phenotype was maintained during evolution rather than that the original phenotype, rod-shaped cells, was recovered is interesting. The paper extensively investigates what happens during adaptation with various different techniques. Also, the extensive discussion of the findings at the end of the paper is well thought through and insighXul. 

Weaknesses: 

I find there are three general weaknesses: 

(1) Although the paper states in the abstract that it emphasizes "new knowledge to be gained" it remains unclear what this concretely is. On page 4 they state 3 three research questions, these could be more extensively discussed in the abstract. Also, these questions read more like genetics questions while the paper is a lot about cell biological findings. 

Thank you for drawing attention to the unnecessary and gratuitous nature of the last sentence of the Abstract. We are in agreement. It has been modified, and we have taken  advantage of additional word space to draw attention to the importance of the two competing (testable) hypotheses laid out in the Discussion. 

As to new knowledge, please see the Results and particularly the Discussion. But beyond this, and as recognised by others, there is real value for cell biology in seeing how (and whether) selection can compensate for effects that are deleterious to fitness. The results will very o_en depart from those delivered from, for example, suppressor analyses, or bottom up engineering. 

In the work recounted in our paper, we chose to focus – by way of proof-of principle – on the most commonly observed mutations, namely, those within pbp1A.  But beyond this gene, we detected mutations  in other components of the cell shape / division machinery whose connections are not yet understood and which are the focus of on-going investigation.  

As to the three questions posed at the end of the Introduction, the first concerns whether selection can compensate for deleterious effects of deleting mreB (a question that pertains to evolutionary aspects); the second seeks understanding of genetic factors; the third aims to shed light on the genotype-to-phenotype map (which is where the cell biology comes into play).  Given space restrictions, we cannot see how we could usefully expand, let alone discuss, the three questions raised at the end of the Introduction in restrictive space available in the Abstract.   

(2) It is not clear to me from the text what we already know about the restoration of MreB loss from suppressors studies (in the literature). Are there suppressor screens in the literature and which part of the findings is consistent with suppressor screens and which parts are new knowledge?  

As stated in the Introduction, a previous study with B. subtilis (which harbours three MreB isoforms and where the isoform named “MreB” is essential for growth under normal conditions), suppressors of MreB lethality were found to occur in ponA, a class A penicillin binding protein (Kawai et al., 2009). This led to recognition that MreB plays a role in recruiting Pbp1A to the lateral cell wall. On the other hand, Patel et al. (2020) have shown that deletion of classA PBPs leads to an up-regulation of rod complex activity. Although there is a connection between rod complex and class A PBPs, a further study has shown that the two systems work semi-autonomously (Cho et al., 2016). 

Our work confirms a connection between MreB and Pbp1A, and has shed new light on how this interaction is established by means of natural selection, which targets the integrity of cell wall. Indeed, the Rod complex and class A PBPs have complementary activities in the building of the cell wall with each of the two systems able to compensate for the other in order to maintain cell wall integrity. Please see the major part of the Discussion. In terms of specifics, the connection between mreB and pbp1A (shown by Kawai et al (2009)) is indirect because it is based on extragenic transposon insertions. In our study, the genetic connection is mechanistically demonstrated.  In addition, we capture that the evolutionary dynamics is rapid and we finally enriched understanding of the genotype-to-phenotype map.

(3) The clarity of the figures, captions, and data quantification need to be improved.  

Modifications have been implemented. Please see responses to specific queries listed below.

Reviewer #2 (Public Review): 

Yulo et al. show that deletion of MreB causes reduced fitness in P. fluorescens SBW25 and that this reduction in fitness may be primarily caused by alterations in cell volume. To understand the effect of cell volume on proliferation, they performed an evolution experiment through which they predominantly obtained mutations in pbp1A that decreased cell volume and increased viability. Furthermore, they provide evidence to propose that the pbp1A mutants may have decreased PG cross-linking which might have helped in restoring the fitness by rectifying the disorganised PG synthesis caused by the absence of MreB. Overall this is an interesting study. 

Queries: 

Do the small cells of mreB null background indeed have have no DNA? It is not apparent from the DAPI images presented in Supplementary Figure 17. A more detailed analysis will help to support this claim. 

It is entirely possible that small cells have no DNA, because if cell division is aberrant then division can occur prior to DNA segregation resulting in cells with no DNA. It is clear from microscopic observation that both small and large cells do not divide. It is, however, true, that we are unable to state – given our measures of DNA content – that small cells have no DNA. We have made this clear on page 13, paragraph 2.

What happens to viability and cell morphology when pbp1A is removed in the mreB null background? If it is actually a decrease in pbp1A activity that leads to the rescue, then pbp1A- mreB- cells should have better viability, reduced cell volume and organised PG synthesis. Especially as the PG cross-linking is almost at the same level as the T362 or D484 mutant.  

Please see fitness data in Supp. Fig. 13. Fitness of ∆mreB ∆pbp1A is no different to that caused by a point mutation. Cells remain round.  

What is the status of PG cross-linking in ΔmreB Δpflu4921-4925 (Line 7)? 

This was not analysed as the focus of this experiment was PBPs. A priori, there is no obvious reason to suspect that ∆4921-25 (which lacks oprD) would be affected in PBP activity.

What is the morphology of the cells in Line 2 and Line 5? It may be interesting to see if PG cross-linking and cell wall synthesis is also altered in the cells from these lines. 

The focus of investigation was restricted to L1, L4 and L7. Indeed, it would be interesting to look at the mutants harbouring mutations in :sZ, but this is beyond scope of the present investigation (but is on-going). The morphology of L2 and L5 are shown in Supp. Fig. 9.

The data presented in 4B should be quantified with appropriate input controls. 

Band intensity has now been quantified (see new Supp. Fig .20). The controls are SBW25, SBW25∆pbp1A, SBW25 ∆mreB and SBW25 ∆mreBpbp1A as explained in the paper.

What are the statistical analyses used in 4A and what is the significance value? 

Our oversight. These were reported in Supp. Fig. 19, but should also have been presented in Fig. 4A. Data are means of three biological replicates. The statistical tests are comparisons between each mutant and SBW25, and assessed by paired t-tests.  

A more rigorous statistical analysis indicating the number of replicates should be done throughout. 

We have checked and made additions where necessary and where previously lacking. In particular, details are provided in Fig. 1E, Fig. 4A and Fig. 4B. For Fig. 4C we have produced quantitative measures of heterogeneity in new cell wall insertion. These are reported in Supp. Fig. 21 (and referred to in the text and figure caption) and show that patterns of cell wall insertion in ∆mreB are highly heterogeneous.

Reviewer #3 (Public Review): 

This paper addresses an understudied problem in microbiology: the evolution of bacterial cell shape. Bacterial cells can take a range of forms, among the most common being rods and spheres. The consensus view is that rods are the ancestral form and spheres the derived form. The molecular machinery governing these different shapes is fairly well understood but the evolutionary drivers responsible for the transition between rods and spheres are not. Enter Yulo et al.'s work. The authors start by noting that deletion of a highly conserved gene called MreB in the Gram-negative bacterium Pseudomonas fluorescens reduces fitness but does not kill the cell (as happens in other species like E. coli and B. subtilis) and causes cells to become spherical rather than their normal rod shape. They then ask whether evolution for 1000 generations restores the rod shape of these cells when propagated in a rich, benign medium. 

The answer is no. The evolved lineages recovered fitness by the end of the experiment, growing just as well as the unevolved rod-shaped ancestor, but remained spherical. The authors provide an impressively detailed investigation of the genetic and molecular changes that evolved. Their leading results are: 

(1) The loss of fitness associated with MreB deletion causes high variation in cell volume among sibling cells a_er cell division. 

(2) Fitness recovery is largely driven by a single, loss-of-function point mutation that evolves within the first ~250 generations that reduces the variability in cell volume among siblings. 

(3) The main route to restoring fitness and reducing variability involves loss of function mutations causing a reduction of TPase and peptidoglycan cross-linking, leading to a disorganized cell wall architecture characteristic of spherical cells. 

The inferences made in this paper are on the whole well supported by the data. The authors provide a uniquely comprehensive account of how a key genetic change leads to gains in fitness and the spectrum of phenotypes that are impacted and provide insight into the molecular mechanisms underlying models of cell shape. 

Suggested improvements and clarifications include: 

(1) A schematic of the molecular interactions governing cell wall formation could be useful in the introduction to help orient readers less familiar with the current state of knowledge and key molecular players. 

We understand that this would be desirable, but there are numerous recent reviews with detailed schematics that we think the interested reader would be better consulting. These are referenced in the text.

(2) More detail on the bioinformatics approaches to assembling genomes and identifying the key compensatory mutations are needed, particularly in the methods section. This whole subject remains something of an art, with many different tools used. Specifying these tools, and the parameter sesngs used, will improve transparency and reproducibility, should it be needed. 

We overlooked providing this detail, which has now been corrected by provision of more information in the Materials and Methods. In short we used Breseq, the clonal option, with default parameters. Additional analyses were conducted using Genieous. The BreSeq output files are provided https://doi.org/10.17617/3.CU5SX1 (which include all read data).

(3) Corrections for multiple comparisons should be used and reported whenever more than one construct or strain is compared to the common ancestor, as in Supplementary Figure 19A (relative PG density of different constructs versus the SBW25 ancestor). 

The data presented in Supp Fig 19A (and Fig 4A) do not involve multiple comparisons. In each instance the comparison is between SBW25 and each of the different mutants. A paired t-test is thus appropriate.

(4) The authors refrain from making strong claims about the nature of selection on cell shape, perhaps because their main interest is the molecular mechanisms responsible. However, I think more can be said on the evolutionary side, along two lines. First, they have good evidence that cell volume is a trait under strong stabilizing selection, with cells of intermediate volume having the highest fitness. This is notable because there are rather few examples of stabilizing selection where the underlying mechanisms responsible are so well characterized. Second, this paper succeeds in providing an explanation for how spherical cells can readily evolve from a rod-shaped ancestor but leaves open how rods evolved in the first place. Can the authors speculate as to how the complex, coordinated system leading to rods first evolved? Or why not all cells have lost rod shape and become spherical, if it is so easy to achieve? These are important evolutionary questions that remain unaddressed. The manuscript could be improved by at least flagging these as unanswered questions deserving of further attention. 

These are interesting points, but our capacity to comment is entirely speculative. Nonetheless, we have added an additional paragraph to the Discussion that expresses an opinion that has yet to receive attention:

“Given the complexity of the cell wall synthesis machinery that defines rod-shape in bacteria, it is hard to imagine how rods could have evolved prior to cocci. However, the cylindrical shape offers a number of advantages. For a given biomass (or cell volume), shape determines surface area of the cell envelope, which is the smallest surface area associated with the spherical shape. As shape sets the surface/volume ratio, it also determines the ratio between supply (proportional to the surface) and demand (proportional to cell volume). From this point of view, it is more efficient to be cylindrical (Young 2006). This also holds for surface attachment and biofilm formation (Young 2006). But above all, for growing cells, the ratio between supply and demand is constant in rod shaped bacteria, whereas it decreases for cocci. This requires that spherical cells evolve complex regulatory networks capable of maintaining the correct concentration of cellular proteins despite changes in surface/volume ratio. From this point of view, rod-shaped bacteria offer opportunities to develop unsophisticated regulatory networks.”

why not all cells have lost rod shape and become spherical.

Please see Kevin Young’s 2006 review on the adaptive significance of cell shape

The value of this paper stems both from the insight it provides on the underlying molecular model for cell shape and from what it reveals about some key features of the evolutionary process. The paper, as it currently stands, provides more on which to chew for the molecular side than the evolutionary side. It provides valuable insights into the molecular architecture of how cells grow and what governs their shape. The evolutionary phenomena emphasized by the authors - the importance of loss-of-function mutations in driving rapid compensatory fitness gains and that multiple genetic and molecular routes to high fitness are o_en available, even in the relatively short time frame of a few hundred generations - are wellunderstood phenomena and so arguably of less broad interest. The more compelling evolutionary questions concern the nature and cause of stabilizing selection (in this case cell volume) and the evolution of complexity. The paper misses an opportunity to highlight the former and, while claiming to shed light on the latter, provides rather little useful insight. 

Thank you for these thoughts and comments. However, we disagree that the experimental results are an overlooked opportunity to discuss stabilising selection. Stabilising selection occurs when selection favours a particular phenotype causing a reduction in underpinning population-level genetic diversity. This is not happening when selection acts on SBW25 ∆mreB leading to a restoration of fitness. Driving the response are biophysical factors, primarily the critical need to balance elongation rate with rate of septation. This occurs without any change in underlying genetic diversity.  

Recommendations for the authors:  

Reviewer 1 (Recommendations for the Authors): 

Hereby my suggestion for improvement of the quantification of the data, the figures, and the text. 

-  p 14, what is the unit of elongation rate?  

At first mention we have made clear that the unit is given in minutes^-1

-  p 14, please give an error bar for both p=0.85 and f=0.77, to be able to conclude they are different 

Error on the probability p is estimated at the 95% confidence interval by the formula:1.96 , where N is the total number of cells. This has been added in the paragraph p »probability » of the Image Analysis section in the Material and Methods. 

We also added errors on p measurement in the main text.

-  p 14, all the % differences need an errorbar 

The error bars and means are given in Fig 3C and 3D.

-  Figure 1B adds units to compactness, and what does it represent? Is the cell size the estimated volume (that is mentioned in the caption)? Shouldn't the datapoints have error bars? 

Compactness is defined in the “Image Analysis” section of the Material and Methods. It is a dimensionless parameter. The distribution of individual cell shapes / sizes are depicted in Fig 1B. Error does arise from segmentation, but the degree of variance (few pixels) is much smaller than the representations of individual cells shown.

-  Figure 1C caption, are the 50.000 cells? 

Correct. Figure caption has been altered.

-  Figure 1D, first the elongation rate is described as a volume per minute, but now, looking at the units it is a rate, how is it normalized? 

Elongation rate is explained in the Materials and Methods (see the image analysis section) and is not volume per minute. It is dV/dt = r*V (the unit of r is min^-1). Page 9 includes specific mention of the unit of r.

-  Figure 1E, how many cells (n) per replicate? 

Our apologies. We have corrected the figure caption that now reads:

“Proportion of live cells in ancestral SBW25 (black bar) and ΔmreB (grey bar) based on LIVE/DEAD BacLight Bacterial Viability Kit protocol. Cells were pelleted at 2,000 x g for 2 minutes to preserve ΔmreB cell integrity. Error bars are means and standard deviation of three biological replicates (n>100).”

-  Figure 1G, how does this compare to the wildtype 

The volume for wild type SBW25 is 3.27µm^3 (within the “white zone”). This is mentioned in the text.

-  Figure 2B, is this really volume, not size? And can you add microscopy images? 

The x-axis is volume (see Materials and Methods, subsection image analysis). Images are available in Supp. Fig. 9.

-  Figure 3A what does L1, L4 and L7 refer too? Is it correct that these same lines are picked for WT and delta_mreB 

Thank you for pointing this out. This was an earlier nomenclature. It was shorthand for the mutants that are specified everywhere else by genotype and has now been corrected. 

-  Figure 3c: either way write out p, so which probability, or you need a simple cartoon that is plotted. 

The value p is the probability to proceed to the next generation and is explained in Materials and Methods  subsection image analysis.  We feel this is intuitive and does not require a cartoon. We nonetheless added a sentence to the Materials and Methods to aid clarity.

-  Figure 4B can you add a ladder to the gel? 

No ladder was included, but the controls provide all the necessary information. The band corresponding to PBP1A is defined by presence in SBW25, but absence in SBW25 ∆pbp1A.

-  Figure 4c, can you improve the quantification of these images? How were these selected and how well do they represent the community? 

We apologise for the lack of quantitative description for data presented in Fig 4C. This has now been corrected. In brief, we measured the intensity of fluorescent signal from between 10 and 14 cells and computed the mean and standard deviation of pixel intensity for each cell. To rule out possible artifacts associated with variation of the mean intensity, we calculated the ratio of the standard deviation divided by the square root of the mean. These data reveal heterogeneity in cell wall synthesis and provide strong statistical support for the claim that cell wall synthesis in ∆mreB is significantly more heterogeneous than the control. The data are provided in new Supp. Fig. 21. 

Minor comments: 

-  It would be interesting if the findings of this experimental evolution study could be related to comparative studies (if these have ever been executed).  

Little is possible, but Hendrickson and Yulo published a portion of the originally posted preprint separately. We include a citation to that paper. 

-  p 13, halfway through the page, the second paragraph lacks a conclusion, why do we care about DNA content? 

It is a minor observation that was included by way of providing a complete description of cell phenotype.  

-  p 17, "suggesting that ... loss-of-function", I do no not understand what this is based upon. 

We show that the fitness of a pbp1A deletion is indistinguishable from the fitness of one of the pbp1A point mutants. This fact establishes that the point mutation had the same effects as a gene deletion thus supporting the claim that the point mutations identified during the course of the selection experiment decrease (or destroy) PBP1A function.

-  p 25, at the top of the page: do you have a reference for the statement that a disorganized cell wall architecture is suited to the topology of spherical cells? 

The statement is a conclusion that comes from our reasoning. It stems from the fact that it is impossible to entirely map the surface of a sphere with parallel strands.

Warum der AV und nicht der Mittelwertunterschied der beiden Gruppen?

Können Sie dies etwas ausführen? Ich verstehe nicht, wie die Mittelwerte in einer AV entstehen sollen?

eLife Assessment

Gil Ávila et al. evaluated the aperiodic component in the medial prefrontal cortex using resting-state EEG recordings from 149 individuals with chronic pain and 115 healthy participants. The authors present compelling evidence that the aperiodic component of the EEG does not differentiate between those with chronic pain and healthy individuals. The study was well-designed and rigorously conducted, and the clear and conclusive results provide important insights that can guide future research in the field of pain neuroscience.

Reviewer #1 (Public review):

Summary:

In this study, Avila et al. tested the hypothesis that chronic pain states are associated with changes in excitability of the medial prefrontal cortex (mPFC). The authors used the slope of the aperiodic component of the EEG power spectrum (= the aperiodic exponent) as a novel, non-invasive proxy for the cortical excitation-inhibition ratio. They performed source localization to estimate the EEG signals generated specifically by the mPFC. By pooling resting-state EEG recordings from three existing datasets, the authors were able to compare the aperiodic exponent in the mPFC and across the whole brain (at all modeled cortical sources) between 149 chronic pain patients and 115 healthy controls. Additionally, they assessed the relationship between the aperiodic exponent and pain intensity reported by the patients. To account for heterogeneity in pain etiology, the analysis was also performed separately for two patient subgroups with different chronic pain conditions (chronic back pain and chronic widespread pain). The study found robust evidence against differences in the aperiodic exponent in the mPFC between people with chronic pain and healthy participants, and no correlation was observed between the aperiodic exponent and pain intensity. These findings were consistent across different patient subgroups and were corroborated by the whole-brain analysis.

Strengths:

The study is based on sound scientific reasoning and rigorously employs suitable methods to test the hypothesis. It follows a pre-registered protocol, which greatly increases the transparency and, consequently, the credibility of the reported results. In addition to the planned steps, the authors used a multiverse analysis to ensure the robustness of the results across different methodological choices. I find this particularly interesting, as the EEG aperiodic exponent has only recently been linked to network excitability, and the most appropriate methods for its extraction and analysis are still being determined. The methods are clearly and comprehensively described, making this paper very useful for researchers planning similar studies. The results are convincing, supported by informative figures, and the lack of the expected difference in mPFC excitability between the tested groups is thoroughly and constructively discussed.

Weaknesses:

Firstly, to augment the sample size, the authors pooled data recorded by different researchers using different experimental protocols. This inevitably increases sample variability and may limit the availability of certain measures, as was the case here with the reports of pain intensity in the patient group. Secondly, the analysis heavily relies on the estimation of cortical sources, an approach that may yield imprecise results, especially when default conduction models, source models, and electrode coordinates are used (as was the case here).

Comments on revisions:

The authors satisfactorily revised the manuscript and responded to previous questions and suggestions. I have no further comments.

Reviewer #2 (Public review):

Summary:

This study evaluated the aperiodic component in the medial prefrontal cortex (mPFC) using resting-state EEG recordings from 149 individuals with chronic pain and 115 healthy participants. The findings showed no significant differences in the aperiodic component of the mPFC between the two groups, nor was there any correlation between the aperiodic component and pain intensity. These results were consistent across various chronic pain subtypes and were corroborated by whole-brain analyses. The study's robustness was further reinforced by preregistration and multiverse analyses, which accounted for a wide range of methodological choices.

Strengths:

This study was rigorously conducted, yielding clear and conclusive results. Furthermore, it adhered to stringent open and reproducible science practices, including preregistration, blinded data analysis, and Bayesian hypothesis testing. All data and code have been made openly available, underscoring the study's commitment to transparency and reproducibility.

Weaknesses:

The aperiodic exponent of the EEG power spectrum is often regarded as an indicator of the excitatory/inhibitory (E/I) balance. However, this measure may not be the most accurate or optimal for quantifying E/I balance, a limitation that the authors might consider addressing in the future.

Comments on revisions:

All my comments have been well addressed.

Author response:

The following is the authors’ response to the original reviews.

Public Reviews

Reviewer #1: 

Summary:

In this study, Avila et al. tested the hypothesis that chronic pain states are associated with changes in the excitability of the medial prefrontal cortex (mPFC). The authors used the slope of the aperiodic component of the EEG power spectrum (= the aperiodic exponent) as a novel, non-invasive proxy for the cortical excitation-inhibition ratio. They performed source localization to estimate the EEG signals generated specifically by the mPFC. By pooling resting-state EEG recordings from three existing datasets, the authors were able to compare the aperiodic exponent in the mPFC and across the whole brain (at all modeled cortical sources) between 149 chronic pain patients and 115 healthy controls. Additionally, they assessed the relationship between the aperiodic exponent and pain intensity reported by the patients. To account for heterogeneity in pain etiology, the analysis was also performed separately for two patient subgroups with different chronic pain conditions (chronic back pain and chronic widespread pain). The study found robust evidence against differences in the aperiodic exponent in the mPFC between people with chronic pain and healthy participants, and no correlation was observed between the aperiodic exponent and pain intensity. These findings were consistent across different patient subgroups and were corroborated by the whole-brain analysis.

Strengths:

The study is based on sound scientific reasoning and rigorously employs suitable methods to test the hypothesis. It follows a pre-registered protocol, which greatly increases the transparency and, consequently, the credibility of the reported results. In addition to the planned steps, the authors used a multiverse analysis to ensure the robustness of the results across different methodological choices. I find this particularly interesting, as the EEG aperiodic exponent has only recently been linked to network excitability, and the most appropriate methods for its extraction and analysis are still being determined. The methods are clearly and comprehensively described, making this paper very useful for researchers planning similar studies. The results are convincing, and supported by informative figures, and the lack of the expected difference in mPFC excitability between the tested groups is thoroughly and constructively discussed.

We are grateful for the appreciation of the strengths of our study.  

Weaknesses:

Firstly, although I appreciate the relatively large sample size, pooling data recorded by different researchers using different experimental protocols inevitably increases sample variability and may limit the availability of certain measures, as was the case here with the reports of pain intensity in the patient group. Secondly, the analysis heavily relies on the estimation of cortical sources, an approach that offers many advantages but may yield imprecise results, especially when default conduction models, source models, and electrode coordinates are used. In my opinion, this point should be discussed as well.

We agree that the heterogeneous sample of people with chronic pain increases variability and limits the availability of clinical measures. We further agree on the limitations of source space analysis. Therefore, we have added these limitations to the discussion section.

Reviewer #2: 

Summary:

This study evaluated the aperiodic component in the medial prefrontal cortex (mPFC) using restingstate EEG recordings from 149 individuals with chronic pain and 115 healthy participants. The findings showed no significant differences in the aperiodic component of the mPFC between the two groups, nor was there any correlation between the aperiodic component and pain intensity. These results were consistent across various chronic pain subtypes and were corroborated by whole-brain analyses. The study's robustness was further reinforced by preregistration and multiverse analyses, which accounted for a wide range of methodological choices.

Strengths:

This study was rigorously conducted, yielding clear and conclusive results. Furthermore, it adhered to stringent open and reproducible science practices, including preregistration, blinded data analysis, and Bayesian hypothesis testing. All data and code have been made openly available, underscoring the study's commitment to transparency and reproducibility.

We appreciate the appraisal of the strengths of our study, highlighting our efforts in open and reproducible science practices.

Weaknesses:

The aperiodic exponent of the EEG power spectrum is often regarded as an indicator of the excitatory/inhibitory (E/I) balance. However, this measure may not be the most accurate or optimal for quantifying E/I balance, a limitation that the authors might consider addressing in the future.

We are grateful for this suggestion and fully agree that the aperiodic component of the power spectrum is not necessarily the most optimal and accurate measure for quantifying E/I balance. We have now included this limitation in the discussion section.

Recommendations for the authors

Reviewer #1: 

(1) In the Results section, it might be helpful to provide the mean values of the aperiodic exponent (before age correction) for all tested groups and subgroups. As this measure is still not widely used, providing these values would allow readers to better understand the normal range of the aperiodic exponent.

We have added the mean values of the aperiodic exponent and their standard deviation (before age correction) to the manuscript's results section (page 6 and 11).

(2) When reporting the aperiodic exponent across all cortical sources (Q3), I think it would be useful to include the raw values in Figure 6 in the main text rather than in the Supplementary Materials. At a glance, these plots seem to suggest that the aperiodic exponent differs between groups in the occipital and parietal regions, even though no tests were significant after correcting for multiple comparisons. Maybe this observation also deserves a mention in the text and possibly in the Discussion..?

We have moved the report on the aperiodic exponent across all cortical sources from the Supplementary Material to the main text. It is now Fig. 7 of the main manuscript. Moreover, we agree that the plots suggest group differences in certain brain regions. However, according to our rigorous open and reproducible science practices and pre-registration, we prefer not to speculate on these non-significant findings. 

(3) In the Methods section, when describing the participants, the authors state that "Gender was balanced across both groups...". It might be better to avoid referring to the datasets as "balanced," considering that the sample includes almost twice as many females as males.

We have replaced the misleading statement with the more precise statement that ”the gender ratio of both groups was similar.”

(4) In the Methods section, when describing the source localization, I find it slightly confusing that the authors first mention the anterior cingulate cortex as a possible label included in the mPFC cortical parcels but then state that the version of the cortical atlas used did not contain such a label. It might be simpler not to mention the cingulate cortex at all.

We have deleted the misleading sentence from the manuscript.  

Reviewer #2: 

(1) The aperiodic exponent of the EEG power spectrum is often considered an indicator of the excitatory/inhibitory (E/I) balance, but this measure can be susceptible to artifacts. It is important to acknowledge this limitation and consider exploring alternative measures to quantify the E/I ratio in future studies.

We are grateful for this suggestion and fully agree that the aperiodic component of the power spectrum is not necessarily the most optimal and accurate measure for quantifying E/I balance. We have now included this limitation in the discussion section.

(2) The study assumed a linear relationship between the E/I ratio (represented by the aperiodic exponent of the EEG power spectrum) and chronic pain. However, this assumption may not hold true in all cases, and this point could be discussed in the study.

We fully agree that the relationship between the E/I ratio and chronic pain might not be a linear one and have added this point to the discussion section.

(3) The aperiodic component was characterized in eyes-closed resting-state EEG recordings, although EEG data were collected in both eyes-closed and eyes-open conditions. The authors could also consider assessing the aperiodic component from EEG data with eyes open.

We thank the reviewer for this suggestion. We have focused our analysis on eyes-closed recordings since these recordings are usually less contaminated by artifacts than eyes-open recordings. Moreover, in our current datasets, some participants were missing eyes-open recordings. We agree that performing similar analyses for the eyes-open recordings would also be interesting. However, adding these analyses would double the amount of data included in the manuscript, which would likely overload it. We have, therefore, now included a statement to the discussion that future studies should also analyze eyes-open EEG recordings.  

(4) The EEG power spectrum was calculated from signals after source reconstruction, a crucial step for targeting specific brain regions. However, this process can introduce potential signal distortions, such as variations in source waveforms depending on different regularization parameters. To ensure the robustness of the results, the authors could perform the same analysis at the sensor level, for example, using signals recorded at Fz.

We agree on the potential shortcomings and limitations of source space analysis and have added this limitation to the discussion section.

(5) It would be beneficial to present the raw EEG power spectrum averaged across subjects for each condition, along with the scalp distribution of the aperiodic exponent. This would enhance readers' understanding of the study and help demonstrate the quality of the data.

We are grateful for this suggestion and added the power spectrum for each condition and the scalp distribution of the aperiodic exponent to the Supplementary Material.

(6) Linear regression models were used to control for the influence of age on aperiodic exponents and pain intensity ratings. However, it is unclear why other relevant variables, such as gender and medication use, were not considered.

We agree that the aperiodic exponent might be influenced by gender and medication. As these analyses had not been included in our pre-registered analysis plan, we have not performed them. Moreover, although we agree that gender might have an impact, we have not found any evidence for this so far. Regarding medication, we fully agree that medication can influence the measure. However, medication was very heterogeneous, including drugs with fundamentally different mechanisms of action. Thus, we do not see a robust way to appropriately analyze these effects with sufficient statistical power. We have now added this important point to the discussion section.

(7) The authors may consider addressing or discussing the impact of inter-individual variability on the negative results, particularly given that the data were derived from multiple experiments.

We agree that the heterogeneous sample of people with chronic pain increases variability and limits the availability of clinical measures. We have added this limitation to the discussion.

Ok, ery good. Well researched and documented and well witten.

eLife Assessment

This important study enhances our understanding of the foraging behaviour of aerial insectivorous birds. Using solid methodology, the authors have collected extensive data on bird movements and prey availability, which in turn provide support for the main claim of the study. The work will be of broad interest to behavioural ecologists.

Reviewer #1 (Public review):

This study tests whether Little Swifts exhibit optimal foraging, which the data seem to indicate is the case. This is unsurprising as most animals would be expected to optimize the energy income : expenditure ratio, however it hasn't been explicitly quantified before the way it was in this manuscript.

The major strength of this work is the sheer volume of tracking data and the accuracy of those data. The ATLAS tracking system really enhanced this study and allowed for pinpoint monitoring of the tracked birds. These data could be used to ask and answer many questions beyond just the one tested here.

The major weakness of this work lies in the sampling of insect prey abundance at a single point on the landscape, 6.5 km from the colony. This sampling then requires the authors to work under the assumption that prey abundance is simultaneously even across the study region. It may be fair to say that prey populations might be correlated over space but are not equal. It is uncertain whether other aspects of the prey data are problematic. For example, the radar only samples insects at 50m or higher from the ground - how often do Little Swifts forage under 50m high?

The finding that Little Swifts forage optimally is indeed supported by the data, notwithstanding some of the shortcomings in the prey abundance data. The authors achieved their aims and the results support their conclusions.

At its centre, this work adds to our understanding of Little Swift foraging and extends to a greater understanding of aerial insectivores in general. While unsurprising that Little Swifts act as optimal foragers, it is good to have quantified this and show that the population declines observed in so many aerial insectivores are not necessarily a function of inflexible foraging habits. Further, the methods used in this research have great potential for other work. For example, the ATLAS system poses some real advantages and an exciting challenge to existing systems, like MOTUS. The radar that was used to quantify prey abundance also presents exciting possibilities if multiple units could be deployed to get a more spatially-explicit view.

To improve the context of this work, it is worth noting that this research goes into much further depth than any previous studies on a similar topic in several flycatcher and swallow species. A further justification is posited that this research is needed due to dramatic insect population declines, however, the magnitude and extent of such declines are fiercely debated in the literature.

Reviewer #2 (Public review):

Summary:

Bloch et al. studied the relationships between aerial foragers (lesser swifts) tracked using an automated radio telemetry system (Atlas) and their prey (flying insects) monitored using a small vertical-looking radar (BirdScan MR1). The aim of the study was to check whether swifts optimise their foraging according to the abundance of their prey. The results provide evidence that small swifts can increase their foraging rate when aerial insect abundance is high, but found no correlation between insect abundance and flight energy expenditure.

Key points:

This study fills gaps in fundamental knowledge of prey-predator dynamics in the air. It describes the coincidence between the abundance of flying insects and the characteristics derived from monitoring individual swifts.

Weaknesses:

The paper uses assumptions largely derived from optimal foraging theory, but mixes up the form of natural selection: parental energy, parental survival (predation risk), nestling foraging and reproductive success. The results are partly inconsistent, and confounding factors (e.g., the brooding phase versus the nestling phase) remained ignored. In conclusion, the analyses performed are insufficient to rigorously assess whether lesser swifts are optimising their foraging beyond making shorter foraging trips.<br /> The filters applied to the monitoring data are necessary but may strongly influence the characteristics derived based on maximum or mean values. Sensitivity tests or the use of characteristics that are less dependent on extreme values could provide more robust results.

Author response:

The following is the authors’ response to the original reviews.

eLife Assessment

This valuable work advances our understanding of the foraging behaviour of aerial insectivorous birds. Its major strength is the large volume of tracking data and the accuracy of those data. However, the evidence supporting the main claim of optimal foraging is incomplete.

We deeply appreciate the thoughtful review provided by the reviewers, including their valuable insights and meticulous attention to detail. Each comment has been thoroughly evaluated, leading to substantial improvements in the manuscript. Your constructive critique has been instrumental in refining our research and rectifying any oversights. We are confident that the revised article will make a substantial contribution to ecological research, particularly in advancing our understanding of foraging theories and the behaviors of aerial insectivores.

Public Reviews:

Reviewer #1 (Public Review):

This study tests whether Little Swifts exhibit optimal foraging, which the data seem to indicate is the case. This is unsurprising as most animals would be expected to optimize the energy income: expenditure ratio; however, it hasn't been explicitly quantified before the way it was in this manuscript.

The major strength of this work is the sheer volume of tracking data and the accuracy of those data. The ATLAS tracking system really enhanced this study and allowed for pinpoint monitoring of the tracked birds. These data could be used to ask and answer many questions beyond just the one tested here.

The major weakness of this work lies in the sampling of insect prey abundance at a single point on the landscape, 6.5 km from the colony. This sampling then requires the authors to work under the assumption that prey abundance is simultaneously even across the study region - an assumption that is certainly untrue. The authors recognize this problem and say that sampling in a spatially explicit way was beyond their scope, which I understand, but then at other times try to present this assumption as not being a problem, which it very much is.

Further, it is uncertain whether other aspects of the prey data are problematic. For example, the radar only samples insects at 50 m or higher from the ground - how often do Little Swifts forage under 50 m high?

Another example might be that the phrases "high abundance" and "low abundance" are often used in the manuscript, but never defined.

It may be fair to say that prey populations might be correlated over space but are not equal. It is this unknown degree of spatial correlation that lends confidence to the findings in the Results. As such, the finding that Little Swifts forage optimally is indeed supported by the data, notwithstanding some of the shortcomings in the prey abundance data. The authors achieved their aims and the results support their conclusions.

Thanks for this comment.

The basic assumption of this paper is that the abundance of insects bioflow in the airspace is correlated in space and varies over time. This has been demonstrated by different studies, see for example Bell et al. (Bell, J. R., Aralimarad, P., Lim, K. S., & Chapman, J. W. (2013). Predicting insect migration density and speed in the daytime convective boundary layer. PloS one, 8(1), e54202) in which positive correlation in insect bioflow is demonstrated between different sites that are more than 100 km away in Southern England. Given the much closer proximity of the colony and the radar site, as well as the large foraging distance of the swifts that often forage in the vicinity of the radar and beyond it, it is reasonable to assume that the radar was able to successfully capture between-day variation in the abundance of flying insects in the airspace, which is highly relevant for the foraging swifts. This is likely because meteorological variables such as temperature and wind, which tend to vary over a synoptic-system scale of several hundred kilometers, significantly influence the abundance of aerial insects. Furthermore, the direction of insect flight that has been recorded by the radar points to an overall south-north directionality of the insects during the period of the study (Werber et al. Under Review: Werber, Y., Chapman, J. W., Reynolds, D. R. and Sapir, N. Active navigation and meteorological selectivity drive patterns of mass intercontinental insect migration through the Levant). Hence, it is reasonable to assume that since the colony is positioned approximately 6.5 km south of the radar site, the radar is able to reliable estimate the between-day variation in aerial insect abundance experienced by the foraging swifts. Importantly, this between-day variation is very high, and detailed information regarding this variation is provided in the paper.  We thank the reviewer for the comments on the wording and have corrected it accordingly so that it is explicitly stated that the spatial distribution of the flying insects is indeed not uniform, but is expected to be simultaneously affected by environmental variables creating spatially correlated bioflow of aerial insects.

The term "high abundance" or "low abundance" is relative to the variable being examined but throughout the manuscript we did not use these terms to describe an absolute amount or a certain threshold but rather to describe the ecological circumstances experienced by the birds on different days that substantially varied in abundance of insect recorded by the radar. However, we have improved the wording of the text so that it is now clear that we refer to relative  and not to absolute values.

At its centre, this work adds to our understanding of Little Swift foraging and extends to a greater understanding of aerial insectivores in general. While unsurprising that Little Swifts act as optimal foragers, it is good to have quantified this and show that the population declines observed in so many aerial insectivores are not necessarily a function of inflexible foraging habits. Further, the methods used in this research have great potential for other work. For example, the ATLAS system poses some real advantages and an exciting challenge to existing systems, like MOTUS. The radar that was used to quantify prey abundance also presents exciting possibilities if multiple units could be deployed to get a more spatially-explicit view.

To improve the context of this work, it is worth noting that the authors suggest that this work is important because it has never been done before for an aerial insectivore; however, that justification is untrue as it has been assessed in several flycatcher and swallow species. A further justification is that this research is needed due to dramatic insect population declines, but the magnitude and extent of such declines are fiercely debated in the literature. Perhaps these justifications are unnecessary, and the work can more simply be couched as just a test of optimality theory.

We appreciate the reviewer's helpful comment. A flycatcher is indeed an aerial insect eater, but its foraging strategy is very different from that of swifts. A comparison with the foraging strategy of the swallow is much more relevant. However, the methods used to quantify bird movement in the airspace in previous articles limited the ability to examine the optimal foraging theory in detail. Following the comment, we revised the text to better describe the uniqueness of our research. Further, since we studied insectivores, it is important to provide a broad context to potentially significant threats to the birds, albeit being debatable

Reviewer #2 (Public Review):

Summary:

Bloch et al. investigate the relationships between aerial foragers (little swifts) tracked with an automated radio-telemetry system (Atlas) and their prey (flying insects) monitored with a small-scale vertical-looking radar device (BirdScan MR1). The aim of the study was to test whether little swifts optimise their foraging with the abundance of their prey. However, the results provided little evidence of optimal foraging behaviour.

Strengths:

This study addresses fundamental knowledge gaps on the prey-predator dynamics in the airspace. It describes the coincidence between the abundance of flying insects and features derived from tracking individual swifts.

Weaknesses:

The article uses hypotheses broadly derived from optimal foraging theory, but mixes the form of natural selection: parental energetics, parental survival (predation risks), nestling foraging, and breeding success.

While this study explores additional behavioral theories alongside optimal foraging theory, its findings unequivocally support the latter. The highly statistically significant observed reduction in flight distance from the breeding colony in elation to increasing insect abundance (supporting predictions 1 and 2) coupled with an increased rate of colony visits (supporting prediction 5) demonstrate the Little Swifts' adeptness at optimizing their aerial foraging behavior. This behavior manifests in an enhanced frequency of visits to the breeding colony, underscoring their food provisioning maximization.

Results are partly incoherent (e.g., "Thus, even when the birds foraged close to the colony under optimal conditions, the shorter traveling distance is not thought to not confer lower flight-related energetic expenditure because more return trips were made.", L285-287),

Thanks for the comment. We have corrected this sentence.

and confounding factors (e.g., brooding vs. nestling phase) are ignored.

The breeding stage may indeed affect food provisioning properties but this factor is not confounded since insect abundance, and the consequent changes in bird foraging properties, fluctuated between sequential days while brooding and nestling phases take place over a period of several weeks, each. Further, despite the possible influence of breeding stages on bird behavior, variability in reproductive stages is expected among pairs in a breeding colony occupying dozens of pairs, despite some coordination in nesting initiation. Practically, the narrow and concealed nest openings hindered direct observation of the nests, posing challenges in determining the precise reproductive stage of each pair. Anyway, we added a short description of the dense colony structure to the Methods section.

Some limits are clearly recognised by the authors (L329 and ff).

See above the response about the distribution of insects in space.

To illustrate potential confounding effects, the daily flight duration (Prediction 4) should decrease with prey abundance, but how far does the daily flight duration coincide with departure and arrival at sunrise and sunset (note that day length increases between March and May), respectively, and how much do parents vary in the duration of nest attendance during the day across chick ages?

We added the following explanation to the Methods section:

To standardize the effect of day length on daily foraging duration, we calculated and subtracted the day length from the total daily foraging time (Day duration - Daily foraging duration = Net foraging duration). The resulting data represent the daily foraging duration in relation to sunrise and sunset, independent of day length.

To conclude, insufficient analyses are performed to rigorously assess whether little swifts optimize their foraging.

We disagree. See our responses above.

Filters applied on tracking data are necessary but may strongly influence derived features based on maximum or mean values. Providing sensitivity tests or using features less dependent on extreme values may provide more robust results.

Thank you for highlighting the importance of considering the impact of data filtering on derived features. In our analysis, we employed rigorous filtering methods to emphasize central data tendencies while mitigating the influence of extreme values. These methods, validated through consultation with experts in tracking data analysis, follow established practices in the literature. Detailed descriptions of our filtering procedures can be found in the Methods section, with citations to relevant published studies.

Radar insect monitoring is incomplete and strongly size-dependent. What is the favourite prey size of swifts? How does it match with BirdScan MR1 monitoring capability?

We added an explanation to the Methods section to address this comment:

The Radar Cross Section (RCS) quantifies the reflectivity of a target, serving as a proxy for size by representing the cross-sectional area of a sphere with identical reflectivity to water, whose diameter equals the target's body length. Recent findings indicate that the BirdScan MR1 radar can detect insects with an RCS as low as 3 mm², enabling the detection of insects with body lengths as small as 2 mm. These capabilities make the radar suitable for locating the primary prey of swifts, which typically range in size from 1 to 16 mm.

Recommendations for the authors:

Reviewer #1 (Recommendations For The Authors):

Lines 53-59 - major run-on sentence

Thanks for the comment. Done.

Line 133 - describe better. Attached where? Were feathers clipped or removed?

Thanks for the comment. Done.

Line 153 - shouldn't be a new paragraph

Done.

Line 157 - justify choosing four 

To ensure a robust analysis of swifts' behavior relative to food abundance across multiple individuals simultaneously, we opted to exclude data from instances where only 3 tags were active. This decision was motivated by the fact that these instances accounted for only 2.9% of the data, and their exclusion minimally impacted overall data volume while enhancing data quality. In contrast, instances with 4 tags, comprising 16.2% of the data, provided substantial insights. Omitting these instances would have resulted in significant data loss. Thus, setting a threshold of 4 simultaneous tags represents a balance between maintaining adequate data quantity and ensuring high data quality for meaningful analysis.

It took me a long time to determine whether the average and maximum flight distance was actual or Euclidean. It was only in the Results that I grasped it was actual. Define up front in the Methods.

Thanks for the comment. Done.

In my public review, I mention that optimal foraging has been assessed in other aerial insectivores. Here are some of the papers I was referring to:

• Davies (1977) Prey selection and the search strategy of the spotted flycatcher (Muscicapa striata): A field study on optimal foraging. Animal Behaviour 25: 1016-1022.

• Lifjeld & Slagsvold (1988) Effects of energy costs on the optimal diet: an experiment with pied flycatchers Ficedula hypoleuca feeding nestlings. Ornis Scandinavica 19: 111-118.

• Quinney & Ankney (1985) Prey size selection by tree swallows. Auk 102: 245-250.

• Turner (1982) Optimal foraging by the swallow (Hirundo rustica, L): Prey size selection. Animal Behaviour 30:862-872.

Lastly, in terms of the work not being spatially-explicit, I do note that in lines 323-324 you acknowledge that prey populations can be patchy, then ten lines later, you provide citations to say that patchiness is not a problem because of spatial correlations. This is a bit overly dismissive, in my view, and to suggest (lines 336-337) that "patches of high insect concentration...might not exist at all" is certainly incorrect (and misleading). I do note the valiant attempt to address the spatial shortcoming in the remainder of the paragraph - although addressing it does not make the problem go away.

Thanks for the comment.

We revised the text to make it more coherent.

Reviewer #2 (Recommendations For The Authors):

L161: typo > missing space in 'meanof'

Corrected.

L192-193: Did the authors use the timing of sunrise and sunset to determine daytime?

Yes. The daytime was calculated in relation to sunrise and sunset.

Did the authors calculate the MTR from sunrise to sunset, or averaging the hourly MTR?

If using hourly MTR, specify the criteria to assign an hourly MTR to daytime when sunset/sunrise is happening during that hour.

A simplified terminology for "Average daily insect MTR" might be useful, in particular for the result section (insect MTR).

Average daily insect MTR is calculated for a fixed period from 5 am to 8 pm local time. An explanation has been added to the Methods section, and the terminology in the text has been simplified as suggested

Note that the 'M' of MTR stands for migration, which may not be appropriate in this context, and simply using "insect traffic rate" may be a better terminology.

Thanks for the comment. The 'M' of MTR can also stand for movement, as the insects detected by the radar move in the airspace. This is how this term has been defined in the paper (e.g. in line 23 of the Summary section). Therefore, we did not change the terminology to “insect traffic rate”, which is a term not used in other studies.

Considering the large number of predictions (10!), it would be appropriate to list them in the results (e.g., "on the daily average flight distance from the breeding colony (Prediction 3)").

We added prediction numbers to the Results and the Discussion.

Note that the terminology varies; e.g., in the introduction "overall daily flight distance" (L75), in the results "average length of the daily flight route" (L236), and further confusion with "daily average flight distance from the breeding colony" (L232).

Thanks for the comment. fixed.

The terminology - average daily 'air/flight' distance (L74-76) - needs clarification.

Done.

Results: Use only a relevant and consistent number of decimals to report on the effect size and p-values.

Done.

The authors are citing non-peer-reviewed publications:

21. Bloch I, Troupin D, Sapir N. Movement and parental care characteristics during the nesting season of 468 the Little Swift (Apus affinis) [Poster presentation]. 12th European Ornithologists' Union Congress. Cluj Napoca, Romania. 2019.

62. Zaugg S, Schmid B, Liechti F. Ensemble approach for automated classification of radar echoes into functional bird sub-types. In: Radar Aeroecology. 2017. p. 1. doi:10.13140/RG.2.2.23354.80326

It is acceptable to cite non-peer-reviewed sources if they have a significant contribution to the background of the article without a critical impact on the core of the research.

eLife Assessment

This important study describes two findings: first, that TEAD is subject to turnover by the ubiquitin-proteasome system involving RNF146 and Parylation, and second, the development of a pan-TEAD heterobifunctional degrader that is used to inhibit growth of a YAP-dependent cancer cell line and to characterize TEAD binding sites in the genome. Convincing evidence supports the development and specificity of the degrader. This article will be of relevance to cancer biologists and scientists interested in proteostasis, cellular signaling, and post-translation modification of proteins.

Reviewer #1 (Public review):

Summary:

In the first half of this study, Pham et al. investigate the regulation of TEAD via ubiquitination and PARylation, identifying an E3 ubiquitin ligase, RNF146, as a negative regulator of TEAD activity through an siRNA screen of ubiquitin-related genes in MCF7 cells. The study also finds that depletion of PARP1 reduced TEAD4 ubiquitination levels, suggesting a certain relationship between TEAD4 PARylation and ubiquitination which was also explored through an interesting D70A mutation. Pham et al. subsequently tested this regulation in D. melanogaster by introducing Hpo loss-of-function mutations and rescuing the overgrowth phenotype through RNF146 overexpression.

In the second half of this study, Pham et al. designed and assayed several potential TEAD degraders with a heterobifunctional design, which they term TEAD-CIDE. Compounds D and E were found to effectively degrade pan-TEAD, an effect which could be disrupted by treatment with TEAD lipid pocket binders, proteasome inhibitors, or E1 inhibitors, demonstrating that the TEAD-CIDEs operate in a proteasome-dependent manner. These TEAD-CIDEs could reduce cell proliferation in OVCAR-8, a YAP deficient cell line, but not SK-N-FI, a Hippo pathway independent cell line. Finally, this study also utilizes ATAC-seq on Compound D to identify reductions in chromatin accessibility at the regions enriched for TEAD DNA binding motifs.

Strengths:

The study provides compelling evidence that the E3 ubiquitin ligase RNF146 is a novel negative regulator of TEAD activity. The authors convincingly delineate the mechanism through multiple techniques and approaches. The authors also describe the development of heterobifunctional pan-degraders of TEAD, that could serve as valuable reagents to more deeply study TEAD biology.

Weaknesses:

The scope of this study is extremely broad. The first half of the paper highlights the mechanisms underlying TEAD degradation; however, the connection to the second half of the paper on small molecule degraders of TEAD is jarring, and it seems as though two separate stories were combined into this single massive study. In my opinion, the study would be stronger if it chose to focus on only one of these topics and instead went deeper.

Additionally, the figure clarity needs to be substantially improved, as readability and interpretation was difficult in many panels. Lastly, there are numerous typos and poor grammar throughout the text that need to be addressed.

Comments on revisions:

The authors have addressed most of our critiques. The manuscript has improved significantly, particularly in the clarity of the figures and the flow of the text. The findings of this study contribute valuable insights into TEAD biology in cancer and provide useful resources for further research into TEAD.

However, as noted by other reviewers, the manuscript still feels somewhat disjointed, despite the attempt to connect the two parts on RNF146-mediated TEAD degradation and the development of TEAD degraders. Certain data inconsistencies and technical limitations may have made some aspects of the data hard to interpret accurately and could benefit from further clarification.

Author response:

The following is the authors’ response to the original reviews.

Public Reviews:

Reviewer #1 (Public Review):

Summary:

In the first half of this study, Pham et al. investigate the regulation of TEAD via ubiquitination and PARylation, identifying an E3 ubiquitin ligase, RNF146, as a negative regulator of TEAD activity through an siRNA screen of ubiquitin-related genes in MCF7 cells. The study also finds that depletion of PARP1 reduced TEAD4 ubiquitination levels, suggesting a certain relationship between TEAD4 PARylation and ubiquitination which was also explored through an interesting D70A mutation. Pham et al. subsequently tested this regulation in D. melanogaster by introducing Hpo loss-of-function mutations and rescuing the overgrowth phenotype through RNF146 overexpression.

In the second half of this study, Pham et al. designed and assayed several potential TEAD degraders with a heterobifunctional design, which they term TEAD-CIDE. Compounds D and E were found to effectively degrade pan-TEAD, an effect which could be disrupted by treatment with TEAD lipid pocket binders, proteasome inhibitors, or E1 inhibitors, demonstrating that the TEAD-CIDEs operate in a proteasome-dependent manner. These TEAD-CIDEs could reduce cell proliferation in OVCAR-8, a YAP-deficient cell line, but not SK-N-FI, a Hippo pathway independent cell line. Finally, this study also utilizes ATAC-seq on Compound D to identify reductions in chromatin accessibility at the regions enriched for TEAD DNA binding motifs.

Strengths:

The study provides compelling evidence that the E3 ubiquitin ligase RNF146 is a novel negative regulator of TEAD activity. The authors convincingly delineate the mechanism through multiple techniques and approaches. The authors also describe the development of heterobifunctional pan-degraders of TEAD, which could serve as valuable reagents to more deeply study TEAD biology.

Weaknesses:

The scope of this study is extremely broad. The first half of the paper highlights the mechanisms underlying TEAD degradation; however, the connection to the second half of the paper on small molecule degraders of TEAD is jarring, and it seems as though two separate stories were combined into this single massive study. In my opinion, the study would be stronger if it chose to focus on only one of these topics and instead went deeper.

We thank the reviewer for the thoughtful feedback. In our mind, the two parts of the paper are inherently related as they both focus on proteasome-mediated degradation of TEADs. We first demonstrated that TEAD can be turned over by the ubiquitin proteasome system under endogenous conditions and identified a PARylation-dependent E3 ligase RNF146 as a major regulator of TEAD stability. Intriguingly, we observed that the four TEAD paralogs show different levels of polyubiquitination with some of them being highly stable in cells. These observations raised the question of whether the activity of the ubiquitin-proteasome system could be further enhanced pharmacologically to effectively target TEADs. We then tackled this question by providing a proof-of-concept demonstration of engineered heterobifunctional protein degraders can effectively degrade TEADs in cells and can be exploited as a therapeutic strategy for treating Hippo-dependent cancers.

Additionally, the figure clarity needs to be substantially improved, as readability and interpretation were difficult in many panels. Lastly, there are numerous typos and poor grammar throughout the text that need to be addressed.

We appreciate the suggestions from the reviewer and have updated the figures with high resolution images. We also corrected typos and grammatical errors in the text.

Reviewer #2 (Public Review):

The paper is made of two parts. One deals with RNF146, the other with the development of compounds that may cause TEAD degradation. The two parts are rather unrelated to each other.

The main limit of this work is the lack of evidence that TEAD factors are in fact regulated by the proteasome and ubiquitylation under endogenous conditions. Also lacking is the demonstration that TEADs are labile proteins to the extent that such quantitative regulation at the level of stability can impact on YAP-TAZ biology. Without these two elements, the relevance and physiological significance of all these data is lacking.

As for the development of new inhibitors of TEAD, this is potentially very interesting but underdeveloped in this manuscript. Irrespectively, if TEAD is stable, these molecules are likely lead compounds of interest. If TEAD is unstable, as entertained in the first part of the paper, then these molecules are likely marginal.

We thank the reviewer for evaluating our manuscript. As the reviewer pointed out, the paper aimed to address 1) whether TEAD is being regulated by the proteasome and ubiquitination under endogenous conditions, and 2) whether TEAD can be inhibited through pharmacologically-induced degradation. First, we demonstrated that TEAD is ubiquitinated in cells and mapped the lysine residues that are poly-ubiquitinated (Fig. 1). Next, we identified RNF146 as a major E3 ligase that ubiquitinates TEADs and reduces their stability. Third, we show that RNF146-mediated TEAD ubiquitination is functionally important: RNF146 suppresses TEAD activity, and RNF146 genetically interacts with Hippo pathway components in fruit flies. Furthermore, as we showed in Fig. S2H, RNF-146 does not affect TEAD1 and TEAD4 to the same extent. Across all four cell lines evaluated, TEAD1 is more stable than TEAD4, raising the question of whether more consistent degradation of different TEAD paralogues could be achieved. To this end, we demonstrated that while the TEAD family of proteins is labile under endogenous conditions, more complete degradation of the TEAD proteins could be achieved using a heterobifunctional CRBN degrader. We further characterized these TEAD degraders in a series of cellular and genomic assays to demonstrate their cellular activity, selectivity, and inhibitory effects against YAP/TAZ target genes. We believe these degrader compounds would be of great interest to the Hippo community. We have revised the main text to clarify these points.

Here are a few other specific observations:

(1) The effect of MG is shown in a convoluted way, by MS. What about endogenous TEAD protein stability?

We thank the reviewer for the question. The MS experiment shown in Figure 1 is a standard KGG experiment, where we used MS to map ubiquitination sites on TEADs. The graphical representation of the process is included in Fig. 1C, and the details of the procedure are included in the Methods section. Fig. 1D shows the different KGG peptides detected with or without MG-132 treatment. Fig. 1E shows the quantified abundance of each of the peptides across the four conditions indicated at the bottom of the plot. Regarding endogenous TEAD stability, ​​we conducted cycloheximide chase experiments to assess the stability of endogenously expressed TEAD isoforms upon RNF146 knockdown (Fig. S2G and S2H). Using isoform-specific antibodies, we demonstrated that siRNF146 significantly stabilized TEAD4 in multiple cell lines, including H226, PATU-8902, Detroit-562, and OVCAR-8 (Fig. S2G, S2H, and S2I), supporting the notion that RNF146 is a negative regulator of TEAD stability. Notably, the effect of siRNF146 on TEAD1 stability was less pronounced, and TEAD1 is more stable than TEAD4 across all four cell lines. These results are consistent with the lower level of ubiquitination of TEAD1 (Fig. 1A) and are corroborated by various biochemical, molecular, and genetic characterizations (Fig. 3A-C and S3E).

(2) The relevance of siRNF on YAP target genes of Fig.2D is not statistically significant.

We thank the reviewer for this comment. We have now removed the statistically significant claim.

(3) All assays are with protein overexpression and Ub-laddering

We thank the reviewer for the comment. To examine the ubiquitination level of TEAD proteins, we adopted an in vivo ubiquitination assay as described in our Materials and Methods section. To our knowledge, this assay is very standard in the ubiquitination field. Furthermore, as mentioned above, we have included in our revised manuscript cycloheximide chase experiments to assess the stability of endogenously expressed TEAD isoforms upon RNF146 knockdown (Fig. S2G and S2H). In addition to the overexpression system, we also assessed endogenously expressed TEAD using isoform-specific antibodies. We demonstrated that siRNF146 firmly stabilized TEAD4 in multiple cell lines, including H226, PATU-8902, Detroit-562, and OVCAR-8 (Fig. S2G with quantification and t-test), supporting the notion that RNF146 is a negative regulator of TEAD stability.

(4) An inconsistency exists on the only biological validation (only by overexpression) on the fly eye size. RNF gain in Fig4C is doing the opposite of what is expected from what is portrayed here as a YAP/TEAD inhibitor: RNF gain is shown to INCREASE eye size, phenocopying a Hippo loss of function phenotype. According to the model proposed, RNF addition should reduce eye size. The authors stated that " This is in contrast to the anti-growth effect of RNF-146 in the Hpo loss-of-function background and indicates RNF146 may regulate other genes/pathways controlling eye sizes besides its role as a negative regulator of Sd/yki activity". This raises questions on what the authors are really studying: why, according to the authors, these caveats should occur on the controls, and not when they study Hpo mutants?

We thank the reviewer for the comment. We acknowledge the complexity of the fly phenotype compared to tumor growth. TEAD (Sd) isn’t the only substrate of RNF146 in the fly. For instance, RNF146 is known to positively regulate Wnt signaling by degrading Axin. Previous studies have shown that activation of the Wnt signaling pathway by removal of the negative regulator Axin from clones of cells results in an overgrowth phenotype (Legent and Treisman, 2008). The overgrowth phenotype that we observed with overexpressing RNF146 only, therefore, likely is due to the role of RNF146 in regulating other signaling pathways. Importantly, we showed that upon Hippo loss of function, overexpression of RNF146 can rescue the Hippo overgrowth phenotype (Fig 4B). This differential outcome of RNF146 expression in wildtype versus Hippo-deficient flies indicates that the genetic interactions between RNF146 and Hippo pathway components altered the phenotypic outcome, and the phenotype we get with RNF146 overexpression in a Hippo loss of function background is not simply due to additive effects of functional loss of either component alone.

Complementary to these overexpression data, we showed that knockdown of RNF146 increased the eye size further (Fig. S4A, B) in Hippo loss of function background, further supporting the role of RNF146 as a negative regulator of the overall pro-growth signals induced by yki upon Hippo loss of function.

(5) The role of TEAD inactivation on YAP function is already well known. Disappointingly, no prior literature is cited. In any case, this is a mere control.

We thank the reviewer for the suggestion. We have cited several published reviews that touch upon this aspect of the TEAD-YAP function, including Calses et al., 2019; Dey et al., 2020; Halder and Johnson, 2011; Wang et al., 2018. We are open to your suggestions on additional citations.

(6) The second part of the paper on the Development and Screening of pan-TEAD lipid pocket degraders is interesting but unconnected to the above. The degradation pathway it involves has nothing to do with the enzyme described in the first figures.

We thank the reviewer for the comment. We acknowledge that our paper broadly covers two aspects. We believe that they are inherently connected as they both address ubiquitin/proteasome-mediated TEAD degradation and the functional consequences of TEAD degradation. Given the increasing interest in targeting TEAD/YAP/TAZ in cancers, we think the pharmacological approaches to enhance TEAD degradation using orthogonal E3 ligases provide an important toolbox to understand how this pathway can be regulated under both physiological and pathological conditions. While RNF146 appears to be a major E3 ligase responsible for TEAD turnover under physiological conditions, we showed that the four TEAD paralogs have different poly-ubiquitination levels (Fig. 1A), and are differentially labile in cells (Fig. S2G-I). These observations raised the question of whether the activity of the ubiquitination-proteasome system could be further enhanced to allow more complete removal of TEADs. To this end, we demonstrated that E3 ligases that do not regulate TEAD under endogenous conditions can be leveraged pharmacologically to achieve deep TEAD degradation, thus providing a proof of concept that TEADs can be targeted simultaneously using such approaches. Finally, in addition to establishing the basic biological concept linking RNF146 to TEAD degradation, the compounds we engineered will serve as valuable chemical tools for future studies of TEAD biology and the Hippo pathway in cancers and beyond.

(7) The role of CIDE on YAP accessibility to Chromatin is superficially executed. Key controls are missing along with the connection with mechanisms and prior knowledge of TEAD, YAP, chromatin, and other TEAD inhibitors, just to mention a few.

We used ATAC-seq to assess chromatin accessibility comparing cells treated with DMSO and two different concentrations of compound D. We acknowledge there are small molecule inhibitors of TEADs that can modulate accessibility of YAP binding sites. Potential mechanistic differences between TEAD degraders versus TEAD small molecule inhibitions will be a future area of investigation.

(8) The physiological relevance and the mechanistic interpretation of what should be in the ATAC seq in ovcar cells is missing.

We showed in Fig. 7A-D the dose response of OVCAR cells to the TEAD degraders. As evident from those experiments, TEAD degraders inhibit the proliferation of OVCAR cells as expected from their dependencies on the TEAD/YAP/TAZ transcription complex. In the ATAC-seq experiment, we showed that the canonical TEAD/YAP/TAZ target genes ANKRD1 and CCN1 have reduced chromatin accessibility at their promoter/enhancer regions (Fig. 8C). By unbiased motif and pathway analyses, we show that TEAD binding sites and YAP signatures are most significantly downregulated in OVCAR-8 cells (Fig. 8D-E). These results are incorporated into the results section of the manuscript.

Reviewer #3 (Public Review):

Summary

Pham, Pahuja, Hagenbeek, et al. have conducted a comprehensive range of assays to biochemically and genetically determine TEAD degradation through RNF146 ubiquitination. Additionally, they designed a PROTAC protein degrader system to regulate the Hippo pathway through TEAD degradation. Overall, the data appears robust. However, the manuscript lacks detailed methodological descriptions, which should be addressed and improved before publication. For instance, the methods used to analyze the K48 ubiquitination site on TEAD and the gene expression analysis of Hippo Signaling are unclear. Furthermore, the multiple proteomics, RNA-seq, and ATAC-seq data must be made publicly available upon publication to ensure reproducibility. Most of the main figures are of low resolution, which needs addressing.

We thank the reviewer for evaluating our manuscript. All of the data will be uploaded to public databases. We apologize for the low figure resolution and have updated the figures in the revised manuscript. We also expanded the methods section with more details.

Strengths:

- A broad range of assays was used to robustly determine the role of RNF146 in TEAD degradation.

- Development of novel PROTAC for degrading TEAD.

Weaknesses:

- An orthogonal approach is needed (e.g., PARP1 inhibitor) to demonstrate PARP1's dependency in TEAD ubiquitination.

We thank the reviewer for the suggestion. We had attempted to assess the effect of PARP inhibitors (including veliparib and olaparib) on TEAD ubiquitination, but the data is relatively complex to interpret. Besides inhibiting PARP1/2 catalytic activities, these PARP inhibitors also trap PARP on chromatin. Hence, these inhibitors could induce other cellular changes in addition to inhibiting the catalytic activities of PARP1/2. Given these potential pitfalls, we decided not to include these inconclusive data. Even though the experiments with PARP inhibitors were inconclusive, our study supports that TEAD2 and TEAD4 are PARylated in cells using an anti-PAR antibody (Fig. 3B). Furthermore, we show that mutation of the D70 PARsylation site to alanine greatly abolished TEAD4 ubiquitination in cells, suggesting PARylation is important for TEAD4 ubiquitination. In addition, PARP1 depletion by siRNA and CRISPR guide RNA reduced TEAD2 and TEAD4 ubiquitination levels, indicating PARP1 is one of the PARPs responsible for TEAD PARylation in cells.

- The data from Table 2 is unclear in illustrating the association of identified K48 ubiquitination with TEAD4, especially since the experiments were presumably to be conducted on whole cell lysates with KGG enrichment. This raises the possibility that the K48 ubiquitination could originate from other proteins. Alternatively, if the authors performed immunoprecipitation on TEAD followed by mass spectrometry, this should be explicitly described in the text and materials and methods section.

We thank the reviewer for this question. The experiment was an IP-mass spectrometry study in a TEAD4 amplified cell line model (PATU-8902) after IP with a pan-TEAD antibody. Here, we observed K48 ubiquitin and other ubiquitin linkages as shown in the Supplementary Table S2 of the original submission. Although it is possible that the IP wash steps could be more stringent, we did enrich for TEAD protein prior to mass spectrometry. While the ubiquitin linkage signals may come mainly from TEAD protein (mainly TEAD4), we recognized that some signals may come from other proteins. Given the caveat, we have now removed the table from our paper and updated the text accordingly.

- Figure 2D: The methodology for measuring the Hippo signature is unclear, as is the case for Figures 7E and F regarding the analysis of Hippo target genes.

We apologize for the lack of clarification. In short, we previously developed the Hippo signature using machine learning and chemogenomics as described previously (Pham et al. Cancer Discovery 2021). In the revised version of the manuscript, we added the methodology for measuring the Hippo signature and cited our previous publication where we developed the Hippo signature.

- Figure S3F requires quantification with additional replicates for validation.

We thank the reviewer for the suggestion. We added the quantification for the blot and indicated the replication in the figure legend. Note that Figure S3F is now S3G.

- There is a misleading claim in the discussion stating "TEAD PARylation by PAR-family members (Figure 3)"; however, the demonstration is only for PARP1, which should be corrected.

We apologize for the statement. We observed both PARP1 and PARP9 in our TEAD IP-mass spec (now Figure S3E), which suggest both PARP-family members could be invovled. Nonetheless, we primarily focus on PARP1, which is widely expressed aross cell line models and present in higher abundance. Thus, our study only experimentally validated PARP1's role in regulating TEAD.

Recommendations for the authors:

Reviewer #1 (Recommendations For The Authors):

General comments:

(1) Please provide a smoother transition and well-defined connection between the first and second parts of the manuscript. The manuscript reads as two papers that were combined into one, without much attempt to disguise the fact.

We thank the reviewer for the suggestion. We have added a transition paragraph to smoothen the transition. We acknowledge that our paper broadly covers two aspects. However, they both touch upon TEAD ubiquitination and degradation. In the first part of the manuscript, we described TEAD biology and showed that TEADs are post-translationally modified and subsequently regulated through PARylation-dependent RNF146-mediated ubiquitination. In the second part, we highlighted our abilities to leverage the PROTAC system for degrading such labile oncogenic proteins like TEADs. In addition to the biological concept, the compounds we engineered will serve as valuable chemical tools for future studies of TEAD biology and the Hippo pathway in cancers and beyond.

(2) To confirm the proteasome mechanism of action, viability assays should be conducted with a CRBN KO.

We thank the reviewer for the comment. In Figure 6E, we measured TEAD protein levels under CRBN knockdown and observed an expected change in TEAD stability. This observation and the other data presented in Figure 6 suggest that TEAD proteins are targeted for proteasomal degradation under compound D treatment.

(3) As a control, sgPARP1 or PARP1 inhibitors should be used to confirm TEAD PARylation reduction.

We thank the reviewer for the suggestion. We had attempted to assess the effect of PARP inhibitors (including veliparib and olaparib) on TEAD ubiquitination, but the data is relatively complex to interpret. Besides inhibiting PARP1/2 catalytic activities, PARP inhibitors also trap PARP on chromatin. Hence, these inhibitors could induce other cellular changes in addition to inhibit the catalytic activities of PARP1/2. Given these pitfalls, we decided not to include these inconclusive data. Even though the experiments with PARP inhibitors were inconclusive, our study supports that TEAD2 and TEAD4 are PARylated in cells using an anti-PAR antibody (Fig. 3B). Furthermore, we show that mutation of the D70 PARsylation site to alanine greatly abolished TEAD4 ubiquitination in cells, suggesting PARylation is important for TEAD4 ubiquitination. In addition, PARP1 depletion by siRNA and CRISPR guide RNA reduced TEAD2 and TEAD4 ubiquitination levels, indicating PARP1 is one of the PARPs responsible for TEAD PARylation in cells.

(4) MS data looks convincing but an FDR of 1% should be applied - this is the accepted standard in the proteomics field. Please research the data with the more stringent filter.

We thank the reviewer for the suggestion. Our IP-MS experiment comparing siNTC versus siYAP1/WWTR1 in Patu-8902 cells did not have replicates and FDR could not be derived. Therefore, we listed the raw data in Supplemental Table 3 without showing statistics. To validate the putative interactions identified by IP-MS, we performed IP-Western experiments to confirm that TEAD4 interacts with PARP1 (Figure 3A). It is important to note that in addition to our report, the interaction between PARP1 and TEADs has been observed in other publications (Calses et al., 2023; Yang et al., 2017). We have included more details of the IP-MS experiment reported in Supplemental Table 3 in the revised manuscript and cited previous work reporting TEAD-PARP1 interaction.

(5) Proofread the manuscript more thoroughly for typos and grammatical errors.

We thank the reviewer for raising this issue and have addressed it in the revision.

(6) Improve figure clarity (e.g., clearly labeling graph axes).

We apologize for the oversight. The revised manuscript contains high resolution figures.

Specific points:

Generally, the manuscript could use additional proofreading for grammar and clarity. It would not be practical to list all, but some representative examples are listed below:

Run-on: "They act through an event-driven mechanism instead of conventional occupancy-driven pharmacology, in addition, target protein degradation removes all functions of the target protein and may also lead to destabilization of entire multidomain protein complexes."

Typo: "Compound D exhibits significant inhibition of cell proliferation and downstream signaling compared to compound A, a reversible TEAD lipid pocket binder that lack the ubiquitin ligase binding moiety."

Typo: "Thus, we sought to deplete TEAD proteins by directly target them for ubiquitination and proteasomal degradation via pharmacologically inducing interactions between TEAD and other abundantly expressed and PARylation-independent E3 ligases."

Typo: "Compound A is a close in analog of Compound B as described previously (Holden et al., 2020)."

We have revised the manuscript and corrected the typos and grammatical errors listed above and beyond.

Specific comments on the figures are listed below:

Figure 2:

• Figures 2B and 2C should be separated into separate panels for clarity.

We have updated the Figures 2B and 2C as suggested.

• Figure 2C - "To further assess the function of RNF146, we depleted RNF146 by either sgRNA or siRNA." This should say either CRISPR-Cas9 KO or siRNA-mediated knockdown.

We thank the reviewer for the suggestion. We revised the text to address this issue.

• Figure 2D - y-axis is not labeled well/clearly. Additionally, there are different resolutions for the p-values on the graph (the top p-value is slightly clearer than the other two, suggesting either a different font was used or the value was pasted on top of a picture of the graph at a different resolution).

We updated the figures according to the suggestions.

• Figure S2A - "We identified three ubiquitin ligases - RNF146, TRAF3, and PH5A - as potential negative regulators for the Hippos pathway from the primary screen using the luciferase reporter." However, the siPHF5A data appears to decrease luciferase levels whereas siRNF146 and siTRAF3 increase it.

We thank the reviewer for catching this error. We removed PH5A from this list.

Figure 3:

• Figure 3A - label more clearly. Is this an endogenous TEAD4 co-IP?

We thank the reviewer for the suggestion. The experiment was an IP-mass spectrometry study in a TEAD4 amplified cell line model (PATU-8902) with pan-TEAD antibody. We have included the details to in the figure legends. Figure 3A is now Figure S3E in the revised manuscript.

• Figure 3C - why are the dark and light exposures not matching/corresponding? In the dark exposure, there are two particularly dark bands, the darkest of which is at the top of the gel. However, this darkest band disappears in the light exposure gel. Additionally, the last lane is marked as +TEAD2 and +TEAD4. Not sure if this is a typo, and meant to be only +TEAD4? Seems a bit strange to have a double TEAD lane.

We thank the reviewer for this comment and apologize for the oversight. There was a typo in the label. The light exposure image was from a replicate run instead of the same run, therefore the lanes didn’t all match up. We have removed the light exposure panel to resolve the confusion. (Figure 3B).

Figure 5:

• Figure 5B - why is shTEAD1-4/Sucrose a much higher tumor volume than shNTC/Sucrose negative control? Additionally, should the legend say "sNTC/Sucrose" as it does or "shNTC/Sucrose"?

The labels for shTEAD1-4/Sucrose and shNTC/Sucrose are correct. We do not understand why there is a slight increase in tumor volume for shTEAD1-4/Sucrose and suspect that is due to the considerable variation in the experiment. This slight change, however, doesn’t influence our observation of tumor regression in shTEAD1-4 under the Doxycycline treatment.

"sNTC/Sucrose" is a typo. We apologize for the oversight and have revised the figure.

• Figure 5E - cited in text after Figures 6 and 7.

We have updated the text accordingly.

Figure 6:

• Figure 6B - it is very interesting how this clearly shows the Hook effect for Compound D, but it's a bit harder to see for compound E that the compound degrades pan-TEAD. Would it be possible to quantify the blots to reinforce claims about protein degradation here?

We thank the reviewer for the question. There may seem to be some hook effect across the three concentrations of compound D treatment in Fig. 6B.  However, in Fig. 6C-E, we observed pretty consistent TEAD degradation levels across a variety of concentrations. In addition, these experiments have been repeated in multiple cell lines with consistent results. We respectfully argue that more detailed investigation of the hook effect is beyond the scope of our study.

Figure 7:

• Figure 7F - this heat map is extremely difficult to interpret. Are there any interesting clusters? What are the darker/lighter bands for Compound D compared to DMSO control?

We thank the reviewer for the comment and apologize for the lack of information on the figure. These are genes from a Hippo signature derived from our earlier work (Pham et al. Cancer Discovery). As a result of degrading TEAD when treating the cells with Compound D, we observed an expected downregulation of most of these genes compared to compound A.

Figure 8:

• Figure 8B - these two pie charts are also difficult to interpret. Perhaps try to present the data in a form other than encircling pie charts?

We thank the reviewer for the suggestion. However, this is a very descriptive pie chart, we used this format to save space.

• Figure 8C - what is GNE-6915? Is this Compound D?

Yes, this is compound D. The text is updated accordingly.

Reviewer #3 (Recommendations For The Authors):

Figure 3A would benefit from explicitly stating the conditions within the figure, rather than referring to the legend. This clarity is also needed for Figure 8C, indicating whether the treatment was with compound D or GNE-6915.

We thank the reviewer for the suggestion. We have added the details to the figures and made the suggested edits.

Standardize the terms "ubiquitination" and "ubiquitylation" throughout the paper for consistency.

We now use the term “ubiquitination” throughout the manuscript.

The statement "In this study, we show that the activity of TEAD transcription factors can be post-transcriptionally regulated via the ubiquitin/proteasome system" should be corrected to "post-translationally regulated."

We have update the manuscript accordingly.

There is an additional exclamation mark above Figure 5E that should be removed.

We have revised Figure 5E.

eLife Assessment

This study presents a useful model of genetic drift by incorporating variance in reproductive success, claiming to address several paradoxes in molecular evolution. However, some of the claimed "paradoxes" seem to be overstatements, as previous literature has pointed out the limitations of the standard model and proposed more advanced models to address those limitations. While the proposed new model presented in this paper yields some intriguing theoretical predictions, the analysis and simulations presented are incomplete to support the authors' strong claims, and it is unclear how much the model helps explain empirical observations.

Reviewer #1 (Public review):

The revision by Ruan et al clarifies several aspects of the original manuscript that were difficult to understand, and I think it presents some useful and interesting ideas. I understand that the authors are distinguishing their model from the standard Wright-Fisher model in that the population size is not imposed externally, but is instead a consequence of the stochastic reproduction scheme. Here, the authors chose a branching process but in principle any Markov chain can probably be used. Within this framework, the authors are particularly interested in cases where the variance in reproductive success changes through time, as explored by the DDH model, for example. They argue with some experimental results that there is a reason to believe that the variance in reproductive success does change over time.

One of the key aspects of the original manuscript that I want to engage with is the DDH model. As the authors point out, their equations 5 and 6 are assumptions, and not derived from any principles. In essence, the authors are positing that that the variance in reproductive success, given by 6, changes as a function of the current population size. There is nothing "inherent" to a negative binomial branching mechanism that results in this: in fact, the the variance in offspring number could in principle be the same for all time. As relates to models that exist in the literature, I believe that this is the key difference: unlike Cannings models, the authors allow for a changing variance in reproduction through time.

This is, of course, an interesting thing to consider, and I think that the situation the authors point out, in which drift is lower at small population sizes and larger at large population sizes, is not appreciated in the literature. However, I am not so sure that there is anything that needs to be resolved in Paradox 1. A very strong prediction of that model is that Ne and N could be inversely related, as shown by the blue line in Fig 3b. This suggests that you could see something very strange if you, for example, infer a population size history using a Wright-Fisher framework, because you would infer a population *decline* when there is in fact a population *expansion*. However, as far as I know there are very few "surprising population declines" found in empirical data. An obvious case where we know there is very rapid population growth is human populations; I don't think I've ever seen an inference of recent human demographic history from genetic data that suggests anything other than a massive population expansion. While I appreciate the authors empirical data supporting their claim of Paradox 1 (more on the empirical data later), it's not clear to me that there's a "paradox" in the literature that needs explaining so much as this is a "words of caution about interpreting inferred effective population sizes". To be clear, I think those words of caution are important, and I had never considered that you might be so fundamentally misled as to infer decline when there is growth, but calling it a "paradox" seems to suggest that this is an outstanding problem in the literature, when in fact I think the authors are raising a *new* and important problem. Perhaps an interesting thing for the authors to do to raise the salience of this point would be to perform simulations under this model and then infer effective population sizes using e.g. dadi or psmc and show that you could identify a situation in which the true history is one of growth, but the best fit would be one of decline

The authors also highlight that their approach reflects a case where the population size is determined by the population dynamics themselves, as opposed to being imposed externally as is typical in Cannings models. I agree with the authors that this aspect of population regulation is understudied. Nonetheless, several manuscripts have dealt with the case of population genetic dynamics in populations of stochastically fluctuating size. For example, Kaj and Krone (2003) show that under pretty general conditions you get something very much like a standard coalescent; for example, combining their theorem 1 with their arguments on page 36 and 37, they find that exchangeable populations with stochastic population dynamics where the variance does not change with time still converge to exactly the coalescent you would expect from Cannings models. This is strongly suggestive that the authors key result isn't about stochastic population dynamics per se, but instead related to arguing that variance in reproductive success could change through time. In fact, I believe that the result of Kaj and Krone (2003) is substantially more general than the models considered in this manuscript. That being said, I believe that the authors of this manuscript do a much better job of making the implications for evolutionary processes clear than Kaj and Krone, which is important---it's very difficult to understand from Kaj and Krone the conditions under which effective population sizes will be substantially impacted by stochastic population dynamics.

I also find the authors exposition on Paradox 3 to be somewhat strange. First of all, I'm not sure there's a paradox there at all? The authors claim that the lack of dependence of the fixation probability on Ne is a paradox, but this is ultimately not surprising---fixation of a positively selected allele depends mostly on escaping the boundary layer, which doesn't really depend on the population size (see Gillespie's book "The Causes of Molecular Evolution" for great exposition on boundary layer effects). Moreover, the authors *use a Cannings-style argument* to get gain a good approximation of how the fixation probability changes when there is non-Poisson reproduction. So it's not clear that the WFH model is really doing a lot of work here. I suppose they raise the interesting point that the particularly simple form of p(fix) = 2s is due to the assumption that variance in offspring is equal to 1.

In addition, I raised some concerns about the analysis of empirical results on reproductive variance in my original review, and I don't believe that the authors responded to it at all. I'm not super worried about that analysis, but I think that the authors should probably respond to me.

Overall, I feel like I now have a better understanding of this manuscript. However, I think it still presents its results too strongly: Paradox 1 contains important words of caution that reflect what I am confident is an under appreciated possibility, and Paradox 3 is, as far as I'm concerned, not a paradox at all. I have not addressed Paradox 2 very much because I think that another reviewer had solid and interesting comments on that front and I am leaving it to them. That being said, I do think Paradox 2 actually presents a deep problem in the literature and that the authors' argument may actually represent a path toward a solution.

This manuscript can be a useful contribution to the literature, but as it's presented at the moment, I think most of it is worded too strongly and it continues to not engage appropriately with the literature. Theoretical advances are undoubtedly important, and I think the manuscript presents some interesting things to think about but ultimately needs to be better situated and several of the claims strongly toned down.

References:<br /> Kaj, I., & Krone, S. M. (2003). The coalescent process in a population with stochastically varying size. Journal of Applied Probability, 40(1), 33-48.

Reviewer #2 (Public review):

Summary:

This theoretical paper examines genetic drift in scenarios deviating from the standard Wright-Fisher model. The authors discuss Haldane's branching process model, highlighting that the variance in reproductive success equates to genetic drift. By integrating the Wright-Fisher model with the Haldane model, the authors derive theoretical results that resolve paradoxes related to effective population size.

Strengths:

The most significant and compelling result from this paper is perhaps that the probability of fixing a new beneficial mutation is 2s/V(K). This is an intriguing and potentially generalizable discovery that could be applied to many different study systems.

The authors also made a lot of effort to connect theory with various real-world examples, such as genetic diversity in sex chromosomes and reproductive variance across different species.

Comments on revisions:

The author has addressed some of the concerns in my review, and I think the revised manuscript is more clear. I like the discussion about the caveats of the WFH model.

I hope the authors could also discuss the conditions needed for V(K)/Ne to be a reasonable approximation. It is currently unclear how the framework should be adopted in general.

The idea about estimating male-female V(K) ratios from population genetic data is interesting. Unfortunately, the results fell short. The accuracy of their estimators (derived using approximation Ne/V(K) approximation, and certain choice of theta, and then theta estimated with Watterson's estimator) should be tested with simulated results before applying to real data. The reliability of their estimator and their results from real data are unclear.

Arguments made in this paper sometimes lack precision (perhaps the authors want to emphasize intuition, but it seems more confusing than otherwise). For example: The authors stated that "This independence from N seems intuitively obvious: when an advantageous mutation increases to say, 100 copies in determining a population (depending mainly on s), its fixation would be almost certain, regardless of N.". Assuming large Ne, and with approximation, one could assume the probability of loss is e^(-2sn), but the writing about "100 copies" and "almost certain" is very imprecise, in fact, a mutation with s=0.001 segregating at 100 copies in a large Ne population is most probably lost. Whereas in a small population, it will be fixed. Yet the following sentence states "regardless of N. This may be a most direct argument against equating genetic drift, certainly no less important than 1/ N . with N, or Ne (which is supposed to be a function of N's)." I find this new paragraph misleading.

Some of the statements/wordings in this paper still seem too strong to me.

Reviewer #3 (Public review):

Summary:

Ruan and colleagues consider a branching process model (in their terminology the "Haldane model") and the most basic Wright-Fisher model. They convincingly show that offspring distributions are usually non-Poissonian (as opposed to what's assumed in the Wright-Fisher model), and can depend on short-term ecological dynamics (e.g., variance in offspring number may be smaller during exponential growth). The authors discuss branching processes and the Wright-Fisher model in the context of 3 "paradoxes" --- 1) how Ne depends on N might depend on population dynamics; 2) how Ne is different on the X chromosome, the Y chromosome, and the autosomes, and these differences do match the expectations base on simple counts of the number of chromosomes in the populations; 3) how genetic drift interacts with selection. The authors provide some theoretical explanations for the role of variance in the offspring distribution in each of these three paradoxes. They also perform some experiments to directly measure the variance in offspring number, as well as perform some analyses of published data.

Strengths:

- The theoretical results are well-described and easy to follow.<br /> - The analyses of different variances in offspring number (both experimentally and analyzing public data) are convincing that non-Poissonian offspring distributions are the norm.<br /> - The point that this variance can change as the population size (or population dynamics) change is also very interesting and important to keep in mind.<br /> - I enjoyed the Density-Dependent Haldane model. It was a nice example of the decoupling of census size and effective size.<br /> - Equation (10) is a nice result (but see below)

Weaknesses:

- I am not convinced that these types of effects cannot just be absorbed into some time-varying Ne and still be well-modeled by the Wright-Fisher process. As a concrete example, Mohle and Sagitov 2001 show that a "coalescent Ne" for the WF model should be (N-1)/Var(K). This resolves the exponentially growing bacteria "paradox" raised in the present paper --- when the bacteria are growing Var(K) ~ 0, and hence there should be very little drift. This exactly resolves the "paradox" raised by the authors. Instead, it merely underscores that Ne does not need to be equal to (or even positively correlated!) with N. I absolutely do not see this as a failure of the WF model. Whether one finds branching processes or the WF model more biologically intuitive is a matter of taste, but to say that WF models cannot explain this "paradox" is false, when a well-known paper from more than 20 years ago does just that.<br /> - Along these lines, the result that Ne in the Wright-Fisher process might not be related to N in any straightforward (or even positively correlated) way are well-known (e.g., Neher and Hallatschek 2012; Spence, Kamm, and Song 2016; Matuszewski, Hildebrandt, Achaz, and Jensen 2018; Rice, Novembre, and Desai 2018; the work of Lounès Chikhi on how Ne can be affected by population structure; etc...)<br /> - I was also missing some discussion of the relationship between the branching process and the Wright-Fisher model (or more generally Cannings' Exchangeable Models) when conditioning on the total population size. In particular, if the offspring distribution is Poisson, then conditioned on the total population size, the branching process is identical to the Wright-Fisher model.<br /> - Given that Cannings' exchangeable models decouple N and Ne, it would not surprise me if something like equation (10) could be derived under such a model. I have not seen such a derivation, and the authors' result is nice, but I do not see it as proof that WF-type models (i.e., Cannings' models) are irreparably broken.

Author response:

The following is the authors’ response to the original reviews.

eLife Assessment

This study presents a useful modification of a standard model of genetic drift by incorporating variance in offspring numbers, claiming to address several paradoxes in molecular evolution. It is unfortunate that the study fails to engage prior literature that has extensively examined the impact of variance in offspring number, implying that some of the paradoxes presented might be resolved within existing frameworks.

The prior literature the reviewers referred to are all "modified WF models". In the original submission, we lumped the standard and modified WF models together as the "generalized WF models". As the lumping causes confusions, their distinctions are now made clear.  That said, the Haldane model in our proposal is not a modification of the standard WF model because, conceptually, the two models are very different. WF is based on sampling whereas the Haldane model is based on gene transmission.

While the "modified WF models" often incorporate V(K) [variance in progeny number], the modification is still based on the WF model of population sampling. The modification is mathematically feasible but biologically untenable, as explained explicitly in the revised text. Most important, all four paradoxes are as incompatible with the modified WF models as with the standard model. Note that the Haldane model does not have the sampling step, which is absorbed into the V(K) term. In the integrated WF-Haldane model, these paradoxes are resolved (see the new sections of Discussion, quoted below).

If readers do not have time to ponder on all four paradoxes, they may simply read the first one, as follows. When the population size (N) is growing exponentially, such as in a bacteria culture, drift is nearly absent when N is small and becomes stronger as N increases, especially when approaching the carrying capacity.  Such common observations are exactly opposite of the WF model's central prediction. Any model based on sampling cannot escape the constraint of "greater drift, smaller N".

Revision - The following text is a reproduction of the last 7 paragraphs of Discussion.

“The standard WF model has been extended in several directions (overlapping generations, multiple alleles, ploidy, etc.). The modification most relevant to our studies here is the introduction of V(K) into the model, thus permitting V(K) ≠ E(K). While the modifications are mathematically valid, they are often biologically untenable. Kimura and Crow (1963) may be the first to offer a biological mechanism for V(K) ≠ E(K), effectively imposing the Haldane model on the WF model. Other models (Kimura and Crow 1963; Lynch, et al. 1995; Sjodin, et al. 2005; Der, et al. 2011; Cannings 2016) indeed model mathematically the imposition of the branching process on the population, followed by the WF sampling. The constructions of such models are biologically dubious but, more importantly, still unable to resolve the paradoxes. It would seem more logical to use the Haldane model in the first place by having two parameters, E(K) and V(K). 

Even if we permit V(K) ≠ E(K) under the WF sampling, the models would face other difficulties. For example, a field biologist needs to delineate a Mendelian population and determine its size, N or Ne. In all WF models, one cannot know what the actual population being studied is. Is it the fly population in an orchard being sampled, in the geographical region, or in the entire species range? It is unsatisfactory when a population biologist cannot identify the population being studied. The Haldane model is an individual-output model (Chen, et al. 2017), which does not require the delineation of a Mendelian population.

We shall now review the paradoxes specifically in relation to the modified WF models, starting with the multi-copy gene systems such as viruses and rRNA genes covered in the companion study (Wang, et al. 2024). These systems evolve both within and between hosts. Given the small number of virions transmitted between hosts, drift is strong in both stages as shown by the Haldane model (Ruan, Luo, et al. 2021; Ruan, Wen, et al. 2021; Hou, et al. 2023). Therefore, it does not seem possible to have a single effective population size in the WF models to account for the genetic drift in two stages. The inability to deal with multi-copy gene systems may explain the difficulties in accounting for the SARS-CoV-2 evolution (Deng, et al. 2022; Pan, Liu, et al. 2022; Ruan, Wen, et al. 2022; Hou, et al. 2023; Ruan, et al. 2023).

We now discuss the first paradox of this study, which is about the regulation of N. In the general WF models, N is imposed from outside of the model, rather than self-generating within the model. When N is increasing exponentially as in bacterial or yeast cultures, there is almost no drift when N is very low and drift becomes intense as N grows to near the carrying capacity. As far as we know, no modifications of the WF model can account for this phenomenon that is opposite of its central tenet. In the general WF models, N is really the carrying capacity, not population size. 

The second paradox of sex chromosomes is rooted in V(K) ≠ E(K). As E(K) is the same between sexes but V(K) is different, clearly V(K) = E(K) would not be feasible. The mathematical solution of defining separate Ne's for males and females (Kimura and Crow 1963; Lynch, et al. 1995; Sjodin, et al. 2005; Der, et al. 2011; Cannings 2016) unfortunately obscures the interesting biology. As shown in Wang et al. (2024; MBE), the kurtosis of the distribution of K indicates the presence of super-breeder males. While the Haldane model can incorporate the kurtosis, the modified WF models are able to absorb only up to the variance term, i.e., the second moment of the distribution. The third paradox of genetic drift is manifested in the fixation probability of an advantageous mutation, 2_s_/V(K). As explained above, the fixation probability is determined by the probability of reaching a low threshold that is independent of N itself. Hence, the key parameter of drift in the WF model, N (or Ne), is missing. This paradox supports the assertion that genetic drift is fundamentally about V(K) with N being a scaling factor. 

As the domain of evolutionary biology expands, many new systems do not fit into the WF models, resulting in the lack of a genetic drift component in their evolutionary trajectories. Multi-copy gene systems are obvious examples. Others include domestications of animals and plants that are processes of rapid evolution  (Diamond 2002; Larson and Fuller 2014; Purugganan 2019; Chen, Yang, et al. 2022; Pan, Zhang, et al. 2022; Wang, et al. 2022). Due to the very large V(K) in domestication, drift must have played a large role. Somatic cell evolution is another example with “undefinable” genetic drift (Wu, et al. 2016; Chen, et al. 2017; Chen, et al. 2019; Ruan, et al. 2020; Chen, Wu, et al. 2022). The Haldane (or WFH) model, as an "individual output" model, can handle these general cases of genetic drift.

The Haldane model and the WF model are fundamentally different approaches to random forces of evolution. While the WF models encounter many biological contradictions, they have provided approximate mathematical solutions to more realistic scenarios. In systems such as in viral evolution (Ruan, Hou, et al. 2022; Hou, et al. 2023) or somatic cell evolution (Chen, Wu, et al. 2022; Zhai, et al. 2022) whereby the WF solution is absent, further development of the WFH model will be necessary.”

In addition, while the modified model yields intriguing theoretical predictions, the simulations and empirical analyses are incomplete to support the authors' claims.

This point is addressed in the responses to reviewers' comments. Since they are quite technical, they do not fit in the overview here.

Public Reviews:

Reviewer #1 (Public Review):

Summary:

The authors present a theoretical treatment of what they term the "Wright-Fisher-Haldane" model, a claimed modification of the standard model of genetic drift that accounts for variability in offspring number, and argue that it resolves a number of paradoxes in molecular evolution. Ultimately, I found this manuscript quite strange.

The notion of effective population size as inversely related to the variance in offspring number is well known in the literature, and not exclusive to Haldane's branching process treatment. However, I found the authors' point about variance in offspring changing over the course of, e.g. exponential growth fairly interesting, and I'm not sure I'd seen that pointed out before.

Weaknesses:

I have several outstanding issues. First of all, the authors really do not engage with the literature regarding different notions of an effective population. Most strikingly, the authors don't talk about Cannings models at all, which are a broad class of models with non-Poisson offspring distributions that nonetheless converge to the standard Wright-Fisher diffusion under many circumstances, and to "jumpy" diffusions/coalescents otherwise (see e.g. Mohle 1998, Sagitov (2003), Der et al (2011), etc.). Moreover, there is extensive literature on effective population sizes in populations whose sizes vary with time, such as Sano et al (2004) and Sjodin et al (2005).

Of course in many cases here the discussion is under neutrality, but it seems like the authors really need to engage with this literature more.

The reviewer's summary and weakness statement reflects the general criticism summarized by the editors. The reply and revision to these criticisms have been presented in the long reply to elife assessment above.

We hence re-emphasize only the key points here.

(1) The literature that the reviewers fault us for not citing is about the modifications of the standard WF model. We now cite them as well as a few others in that vein. However, the WF-Haldane model we propose is conceptually very different from the modified WF models. This WFH model is in essence the Haldane model which may use the results of the WF models as the starting point to find the exact solutions.

(2) The check of the power of the modified WF models is whether they can resolve the paradoxes. None of them can. The arguments apply to neutral cases as well as selection effects. Hence, our central point is that the modifications of the standard WF model [e.g., by incorporating V(K)] do not help the WF model in resolving the paradoxes.  Besides, the incorporation of V(K) is mathematically feasible but biologically untenable as presented in the new sections of Discussion.

Nonetheless, I don't think the authors' modeling, simulations, or empirical data analysis are sufficient to justify their claims.

The most interesting part of the manuscript, I think, is the discussion of the Density Dependent Haldane model (DDH). However, I feel like I did not fully understand some of the derivation presented in this section, …… - this is the whole notion of exchangeability, also neglected in this manuscript). As such, I don't believe that their analysis of the empirical data supports their claim. [Since the comments above are highly technical and fairly long, they are not copied verbatim.]

We thank this reviewer for the detailed comments with respect to the potential confusion in the discussion of the Density Dependent Haldane (DDH) model.

First, the reviewer appears to ask how Eqs (5-6) are derived. We should clarify that both Eq (5) and (6) are assumptions rather than derived results. Both equations are assumptions based on population ecology. Eq (7) is then derived by substituting the assumptions in Eq (5) and (6) into Eq (3).

The definition in Equation (5) allows the growth rate of the population size to be dependent on N itself, such that growth rate E(K) (average offspring number per generation) is greater than 1 when N < Ck and less than 1 when N > Ck. The parameter z is introduced to adjust the sensitivity of E(K) to changes in population size (as shown in Fig. 3a).

Second, we appreciate the comments regarding the use of individual-based simulations and the apparent lack of interaction between individuals. In our simulations, there is indeed an interaction among individuals, which is represented by Eq (5). This equation reflects how the competition between two alleles affects the expected growth rate 𝐸(𝐾), which decreases as the population size increases. Furthermore, once 𝐸(𝐾) for the entire population is determined, the offspring numbers of the alleles are independent.

We believe that the primary purpose of our simulations was not clearly stated. This lack of clarity may be the root of the criticisms. We now note that the simulations are aimed at testing the accuracy of Equation (10).

Note that Eq. (10) is a textbook result and quite important in our study. This equation shows that the strength of genetic drift, as given by Pf (the fixation probability of an advantageous mutation), is not a function of N at all. This approximate solution has been obtained using the WF model by Kimura.  The Haldane model solution that can explain Paradox 1 is based on Equation (7) as shown below

Since the fixation probability of Equation (10) cannot be easily obtained using Eq. (7), we conducted simulations to confirm the accuracy of Eq. (10) when applied to the Haldane model.

We have revised the relevant sections of the manuscript to clarify these points and to better distinguish between assumptions and results. 

Revision - Details of the DDH model are given in the Supplementary Information. A synopsis is given here: We consider a non-overlapping haploid population with two neutral alleles. The population size at time t is Nt. We assume that expected growth rate E(K) is greater than 1 when N < Ck and less than 1 when N > Ck, as defined by Eq. (5) below:

The slope of E(K) vs. N (i.e., the sensitive of growth rate to changes in population size), as shown in Fig 3a, depends on z. To determine the variance V(K), we assume that K follows the negative binomial distribution whereby parents would suffer reproduction-arresting injury with a probability of pt at each birthing (Supplementary Information). Accordingly, V(K) can then be expressed as

By Eq. (6), the ratio of V(K)/E(K) could be constant, decrease or increase with the increase of population size. With E(K) and V(K) defined, we could obtain the effective population size by substituting Eq. (5) and Eq. (6) into Eq. (3).

Eq. (7) presents the relationship between effective population size (Ne) and the population size (N) as shown in Fig. 3. The density-dependent E(K) could regulate N with different strength (Fig. 3a). The steeper the slope in Fig. 3a, the stronger the regulation.

Simulation of genetic drift in the Haldane model and the Wright-Fisher (WF) model. In both models, interactions between individuals are implicitly included through the dependency of the average number of offspring on population size, as defined by Eq. (5). This dependency leads to the logistic population growth, reflecting the density-dependent interactions.

Thus, while I think there are some interesting ideas in this manuscript, I believe it has some fundamental issues:

first, it fails to engage thoroughly with the literature on a very important topic that has been studied extensively. Second, I do not believe their simulations are appropriate to show what they want to show. And finally, I don't think their empirical analysis shows what they want to show.

References omitted

The comments are the summary of previous ones, which have been addressed in detail in the preceding sections.

Reviewer #2 (Public Review):

Summary:

This theoretical paper examines genetic drift in scenarios deviating from the standard Wright-Fisher model. The authors discuss Haldane's branching process model, highlighting that the variance in reproductive success equates to genetic drift. By integrating the Wright-Fisher model with the Haldane model, the authors derive theoretical results that resolve paradoxes related to effective population size [Ne]

Thanks.  The issue of Ne will be addressed below where the reviewer returns to this issue. The strength of the integrated WFH model is that N (or Ne) is generated by the model itself, rather than externally imposed as in WF models.

Strengths:

The most significant and compelling result from this paper is perhaps that the probability of fixing a new beneficial mutation is 2s/V(K). This is an intriguing and potentially generalizable discovery that could be applied to many different study systems.

The authors also made a lot of effort to connect theory with various real-world examples, such as genetic diversity in sex chromosomes and reproductive variance across different species.

Thanks. 

Weaknesses:

One way to define effective population size is by the inverse of the coalescent rate. This is where the geometric mean of Ne comes from. If Ne is defined this way, many of the paradoxes mentioned seem to resolve naturally. If we take this approach, one could easily show that a large N population can still have a low coalescent rate depending on the reproduction model. However, the authors did not discuss Ne in light of the coalescent theory. This is surprising given that Eldon and Wakeley's 2006 paper is cited in the introduction, and the multiple mergers coalescent was introduced to explain the discrepancy between census size and effective population size, superspreaders, and reproduction variance - that said, there is no explicit discussion or introduction of the multiple mergers coalescent.

The Haldane model treats N’s very differently from the WF models.  In the WF models, N’s are imposed externally (say, constant N, exponentially growing N, temporally fluctuating N’s and so on; all provided from outside of the model). Ne and coalescence are all derived from these given N’s.  In order to account for the first paradox (see the next paragraph), N needs to be regulated but the WF models cannot regulate N’s. The density-dependent Haldane model that Reviewer 1 inquired above is a model that regulates N internally. It can thus account for the paradox.

Paradox 1 -  When the population size (N) is growing exponentially, such as in a bacteria culture, drift is nearly absent when N is small and is much stronger as N increases, especially when approaching the carrying capacity.  Such a pattern is a common observation and is exactly opposite of the WF model's central prediction. In short, a model that does not regulate N cannot explain the paradox

Ne is a fix of the WF model in order to account for the missing components of genetic drift. The paradoxes presented in this one and the companion study show that the fix is rather inadequate.  In contrast, by the WFH model, N is regulated within the model itself as E(K) and V(K) are both functions of N.

The Wright-Fisher model is often treated as a special case of the Cannings 1974 model, which incorporates the variance in reproductive success. This model should be discussed. It is unclear to me whether the results here have to be explained by the newly introduced WFH model, or could have been explained by the existing Cannings model. The abstract makes it difficult to discern the main focus of the paper. It spends most of the space introducing "paradoxes".

We appreciate greatly the illuminating advice.  Nevertheless, we should explain, or should have explained, more clearly that these four paradoxes presented are central to this pair of eLife papers. The WF and Haldane models are very different conceptual ideas altogether. The choice should not be based on mathematical grounds but on how they help us understand biological evolution. We are using four paradoxes to highlight the differences.  We have said in the papers that the origin and evolution of COVID-19 caused a lot of confusions partly because the WF models cannot handle multi-copy gene systems, including viruses that evolve both within- and between- hosts.

The standard Wright-Fisher model makes several assumptions, including hermaphroditism, non-overlapping generations, random mating, and no selection. It will be more helpful to clarify which assumptions are being violated in each tested scenario, as V(K) is often not the only assumption being violated. For example, the logistic growth model assumes no cell death at the exponential growth phase, so it also violates the assumption about non-overlapping generations.

We appreciate the question which has two aspects.  First, why do we think the WF models are insufficient? After all, for each assumption of the WF model (as given in the reviewer’s examples), there is often a solution by modifying Ne which relaxes the assumption. In this sense, there is only one grand assumption made by the WF models. That is, however complex the biology is, it is possible to find Ne that can make the WF model work. Our argument is that Ne is a cumbersome fix of the WF model and it does not work in many situations. That is how we replied about the importance of the paradoxes above.  We shall again use the first paradox as an example whereby drift is stronger as N becomes larger, the fix has to make Ne negatively correlated with N. In reality, it does not appear possible to resolve this paradox. Another paradox is the evolution of multi-copy gene systems. In short, it seems clear that Ne is not a useful or usable fix.

The second aspect is that “why, among the many modifications the WF models make, do we only emphasize the inclusion of V(K)?” This is the essence of the two papers of ours.  Although V(K) is a modification of the WF models, it does not enable the WF models to resolve the paradoxes. In contrast, the Haldane model has incorporate E(K) and V(K) in the model. In presenting paradox 3, it was stated that

This equation shows that the strength of genetic drift, as given by Pf (the fixation probability of an advantageous mutation), is not a function of N at all. It supports the view that the essence of genetic drift is V(K) with N as a scaling factor. Note that, if V(K) = 0, there is no genetic drift regardless of N. As V(K) is not an add-on to the Haldane model (unlike in WF models), the Haldane model can resolve the paradoxes.

The theory and data regarding sex chromosomes do not align. The fact that \hat{alpha'} can be negative does not make sense. The authors claim that a negative \hat{alpha'} is equivalent to infinity, but why is that? It is also unclear how theta is defined. It seems to me that one should take the first principle approach e.g., define theta as pairwise genetic diversity, and start with deriving the expected pair-wise coalescence time under the MMC model, rather than starting with assuming theta = 4Neu. Overall, the theory in this section is not well supported by the data, and the explanation is insufficient.

a' can be negative for the same reason that a (the male/female ratio in mutation rate) can be negative (Miyata, et al. 1987; Li, et al. 2002; Makova and Li 2002). Clearly, this has not been a problem in the large literature on a becoming negative.  In fact, in many reports, a is negative, which is read as a approaching infinity.  Imagine that our equation is a'^2 = 0.25, then a' can be 0.5 or -0.5, although the latter solution is not biologically meaningful.

As for theta, the reviewer asked why we do not use the pairwise genetic diversity (or theta[pi]) as the first-principle approach to estimating theta. While theta(pi) is the first estimator of theta used, the general principle is that every bin of the frequency spectrum can be used for estimating theta since the expected value is theta/i where i is the occurrence of the mutation in the sample.  (If the sample size is 100, then i is between 1 and 99.)  Hence, the issue is which part of the spectrum has the best statistical properties for the questions at hand.  The pairwise measure is theta(pi) [which the reviewer recommends]. While theta(pi) and theta(w) are most commonly used, there are in fact numerous ways to estimate theta.  ((Fu 2022) presents an excellent review.) For our purpose, we need a theta estimate least affected by selection and we choose the lowest frequency bin of the spectrum, which is theta(1) based on the singletons. Theta(1), least affected by selection, is the basis of the Fu and Li test. 

Reviewer #3 (Public Review):

Summary:

Ruan and colleagues consider a branching process model (in their terminology the "Haldane model") and the most basic Wright-Fisher model. They convincingly show that offspring distributions are usually non-Poissonian (as opposed to what's assumed in the Wright-Fisher model), and can depend on short-term ecological dynamics (e.g., variance in offspring number may be smaller during exponential growth). The authors discuss branching processes and the Wright-Fisher model in the context of 3 "paradoxes": (1) how Ne depends on N might depend on population dynamics; (2) how Ne is different on the X chromosome, the Y chromosome, and the autosomes, and these differences do match the expectations base on simple counts of the number of chromosomes in the populations; (3) how genetic drift interacts with selection. The authors provide some theoretical explanations for the role of variance in the offspring distribution in each of these three paradoxes. They also perform some experiments to directly measure the variance in offspring number, as well as perform some analyses of published data.

Strengths:

(1) The theoretical results are well-described and easy to follow.

(2) The analyses of different variances in offspring number (both experimentally and analyzing public data) are convincing that non-Poissonian offspring distributions are the norm.

(3) The point that this variance can change as the population size (or population dynamics) change is also very interesting and important to keep in mind.

(4) I enjoyed the Density-Dependent Haldane model. It was a nice example of the decoupling of census size and effective size.

Thanks.

Weaknesses:

(1) I am not convinced that these types of effects cannot just be absorbed into some time-varying Ne and still be well-modeled by the Wright-Fisher process.

Please allow us to refer to, again, two of the four paradoxes.  We believe that that no modification of the WF model can resolve the paradoxes.

(1) When the population size (N) is growing exponentially, such as in a bacteria culture, drift is nearly absent when N is small and is much stronger as N increases, especially when approaching the carrying capacity.  Such common observations are exactly opposite of the WF model's key prediction. It is not possible for a model that does not regulate N to explain the paradox.

(2) There is no way the WF models can formulate Ne for, say viruses or ribosomal RNA genes that have two levels of populations – the within-host populations as well as the host population itself.

The fact that there are numerous Ne's suggests that Ne is a collection of cumbersome fixes of the WF model. By the WF-Haldane model, all factors are absorbed into V(K) resulting in a simpler model in the end. V(K) is often a measurable quantity. Note that, even if V(K) is incorporated into the WF model, the paradoxes remain unresolvable.

(2) Along these lines, there is well-established literature showing that a broad class of processes (a large subset of Cannings' Exchangeable Models) converge to the Wright-Fisher diffusion, even those with non-Poissonian offspring distributions (e.g., Mohle and Sagitov 2001). E.g., equation (4) in Mohle and Sagitov 2001 shows that in such cases the "coalescent Ne" should be (N-1) / Var(K), essentially matching equation (3) in the present paper.

The criticism of lack of engagement with well-established literature has been responded extensively above.  Briefly, the literature is about modifications of the WF model which share the same feature of population sampling. With that feature, the paradoxes are unresolvable.  For example, however Ne is defined, the fixation probability of an advantageous mutation does not depend on N or Ne. This is the third paradox of the WF models.

(3) Beyond this, I would imagine that branching processes with heavy-tailed offspring distributions could result in deviations that are not well captured by the authors' WFH model. In this case, the processes are known to converge (backward-in-time) to Lambda or Xi coalescents (e.g., Eldon and Wakely 2006 or again in Mohle and Sagitov 2001 and subsequent papers), which have well-defined forward-in-time processes.

We admire the learned understanding of the literature expressed by the review, which raise two points.  First, our model may not be able to handle the heavy-tailed progeny distribution (i.e., the kurtosis of the distribution of k). Second, the Xi coalescence models (cited above) can do that.  Below are our clarifications.

First, the WFH model is based on the general distribution of K, which includes flexible and realistic representations of offspring number distributions. In fact, we have used various forms of K distribution in our publications on the evolution of SARS-CoV-2 (see the Ruan et al publications in the bibliography). Power-law distribution is particularly useful as the K-distribution in viral transmission is highly kurtotic. This is reflected in the super-spreader hypothesis. In short, the branching process on which the WFH model is based in is mainly about the distribution of K. Nevertheless, the variance V(K) can often yield good approximations when the kurtosis is modest.

Second, we would like to comment on the models of Eldon and Wakely 2006. or Mohle and Sagitov 2001 and subsequent papers. These papers are based on the Moran model by considering a highly skewed distribution of offspring numbers. Fundamentally, the Moran models generally behave like WF models (standard or modified) and hence have the same problems with the paradoxes that are central to our studies. In fact, the reservations about introducing V(K) into the WF models apply as well to the Moran models.  The introduction of V(K) is mathematically valid but biologically untenable. Essentially, the WF models incorporate the Haldane model as a first step in the generation transition. The introduction of V(K) into the Moran model is even less biologically sensible. Furthermore, the model allows K to take only three discrete values: 0, 2, and Nψ (see Eq. (7) in Eldon and Wakely). Their model also assumes a constant population size, which contrasts with our model's flexibility in handling varying population sizes and more complex distributions for K.

In short, the modifications of the WF (and Moran) models are unnecessarily complicated, biologically untenable but still fail to account for the paradoxes. The WFH model can rectify these problems. 

(4) These results that Ne in the Wright-Fisher process might not be related to N in any straightforward (or even one-to-one) way are well-known (e.g., Neher and Hallatschek 2012; Spence, Kamm, and Song 2016; Matuszewski, Hildebrandt, Achaz, and Jensen 2018; Rice, Novembre, and Desai 2018; the work of Lounès Chikhi on how Ne can be affected by population structure; etc...)

The reviewer is correct in pointing out the inexact correlation between N and Ne. Nevertheless, it should still be true that the WF models predict qualitatively weaker drift as N increases. The first paradox is as stated:

When the population size (N) is growing exponentially, such as in a bacteria culture, drift is nearly absent when N is small and is much stronger as N increases, especially when approaching the carrying capacity.  Such common observations are exactly opposite of the WF model's key prediction.

(5) I was also missing some discussion of the relationship between the branching process and the Wright-Fisher model (or more generally Cannings' Exchangeable Models) when conditioning on the total population size. In particular, if the offspring distribution is Poisson, then conditioned on the total population size, the branching process is identical to the Wright-Fisher model.

We thank the reviewer for this important comment. The main difference is that N is imposed from outside the WF models but can be generated from within the Haldane model (see the density-dependent Haldane model). In nature, N of the next generation is the sum of K’s among members of the population. It is how the Haldane model determines N(t+1) from N(t). In the WF models, N is imposed from outside the model and, hence the given N determines the distribution of K.  For this reason, N regulation is not possible in the WF models, thus resulting in the paradoxes.

(6) In the discussion, it is claimed that the last glacial maximum could have caused the bottleneck observed in human populations currently residing outside of Africa. Compelling evidence has been amassed that this bottleneck is due to serial founder events associated with the out-of-Africa migration (see e.g., Henn, Cavalli-Sforza, and Feldman 2012 for an older review - subsequent work has only strengthened this view). For me, a more compelling example of changes in carrying capacity would be the advent of agriculture ~11kya and other more recent technological advances.

We thank the reviewer and have used this more convincing case as suggested by the reviewer.

Recommendations for the authors:

General replies - We thank the editors and reviewers again.  The points below are re-iterations of the comments received above and have since been replied in detail. Specific instructions about wording and notations have also been rectified. Again, we are grateful for the inputs from which we learned a great deal.

Reviewing Editor Comments:

The reviewers recognize the value of this model and some of the findings, particularly results from the density-dependent Haldane model. However, they expressed considerable concerns with the model and overall framing of this manuscript.

First, all reviewers pointed out that the manuscript does not sufficiently engage with the extensive literature on various models of effective population size and genetic drift, notably lacking discussion on Cannings models and related works.

We have addressed this issue in the beginning of Introduction and Discussion, pointing to the long section in the new second half of Discussion. The essence is that the literature is all about the modified WF models.  The WF-Haldane model is conceptually and operationally distinct from the WF models, either standard or modified ones,

Second, there is a disproportionate discussion on the paradoxes, yet some of the paradoxes might already be resolved within current theoretical frameworks. All three reviewers found the modeling and simulation of the yeast growth experiment hard to follow or lacking justification for certain choices. The analysis approach of sex chromosomes is also questioned.

This criticism is addressed together with the next one as they make the same point.

The reviewers recommend a more thorough review of relevant prior literature to better contextualize their findings. The authors need to clarify and/or modify their derivations and simulations of the yeast growth experiment to address the identified caveats and ensure robustness. Additionally, the empirical analysis of the sex chromosome should be revisited, considering alternative scenarios rather than relying solely on the MSE, which only provides a superficial solution. Furthermore, the manuscript's overall framing should be adjusted to emphasize the conclusions drawn from the WFH model, rather than focusing on the "unresolved paradoxes", as some of these may be more readily explained by existing frameworks. Please see the reviewers' overall assessment and specific comments.

Many thanks.  We have carefully reframed and presented the WF-Haldane model to make it clear and logically consistent. Whether a new model (i.e., the WF-Haldane model) deserves to be introduced depends on whether it makes any contribution for understanding nature. That is why we emphasize the four paradoxes. 

A most important disagreement between the reviewers and the authors is about the nature of the paradoxes. While the reviewers suggest that they "may" be resolvable by the conventional WF model (standard or modified), they did not offer the possible resolutions.  To use the analogy in our provisional response: the WF vs. Haldane models are compared to gas cars vs electric vehicles.  We can say confidently that the internal combustion engine cannot resolve the conflicting demands of transportation and zero emission. Its design has limited its capability. 

Reviewer #2 (Recommendations For The Authors):

Many thanks.  We have incorporated all these suggestions.  When the incorporation is not straightforward, we have carefully revised the text to minimize mis-communications.

In the introduction -- "Genetic drift is simply V(K)" -- this is a very strong statement. You can say it is inversely proportional to V(K), but drift is often defined based on changes in allele frequency.

We change the word “simply” to “essentially”. This wording is supported by the fixation probability of advantageous mutations, 2s/(V(k). We have shown in the text that N does not matter here because the fixation is nearly deterministic when the copy number reaches, say, 100, regardless of whether N is 10^4 or 10^8,

Page 3 line 86. "sexes is a sufficient explanation."--> "sex could be a sufficient explanation"

The strongest line of new results is about 2s/V(K). Perhaps, the paper could put more emphasis on this part and demonstrate the generality of this result with a different example.

The math notations in the supplement are not intuitive. e.g., using i_k and j_k as probabilities. I also recommend using E[X] and V[X]for expectation and variance rather than \italic{E(X)} to improve the readability of many equations.

Thank you for your careful reading. Regarding the use of i_k and j_k  as probabilities, we initially considered using 𝑝 or 𝑞 to represent probabilities. However, since 𝑝 and 𝑞 are already used in the main text, we opted for 𝑖 and 𝑗 to avoid potential confusion potential confusion. As for your recommendation to use

E[X] and V[X] for expectation and variance, we would like to clarify that we follow the standard practice of italicizing these symbols to represent variables.

Eq A6, A7, While I manage to follow, P_{10}(t) and P_{10} are not defined anywhere in the text.<br /> Supplement page 7, the term "probability of fixation" is confusing in a branching model.

Thank you for your observation. We have carefully revised the supplement to provide clarity on these points.<br /> Revision - In population genetics, the fixation of M allele means that the population consist entirely of the M allele, with no W alleles remaining. We define the fixation probability of M allele by generation t as follows:

Given that M and W allele reproduce independently, this can be factored as:

As t approaches infinity, the ultimate fixation probability of M allele can be derived as follows:

E.q. A 28. It is unclear eq. A.1 could be used here directly. Some justification would be nice.

We appreciate your careful review, and we will ensure this connection between the two equations is made clearer in the supplement. 

Revision - Note we would like to clarify that Eq. (A1) and Eq. (A28) are essentially the same, with the only difference being the subscript 𝑡, which indicates the time dependence in the dynamic process.

Supplement page 17. "the biological meaning of negative..". There is no clear justification for this claim. As a reader, I don't have any intuition as to why that is the case.

Thank you for raising this concern. We have addressed this issue earlier.

Not a bad point re class implications of different strategies

https://typespec.com/the-2025-calendars-are-here-15-each/

The original text of the poem, written in Middle English, is as follows:

Fyrst he watz funden fautlez in his fyue wyttez,

And efte fayled neuer þe freke in his fyue fyngres,

And alle his afyaunce vpon folde watz in þe fyue woundez Þat Cryst kaȝt on þe croys, as þe crede tellez;

And quere-so-euer þys mon in melly watz stad,

His þro þoȝt watz in þat, þurȝ alle oþer þyngez,

Þat alle his forsnes he feng at þe fyue joyez

Þat þe hende heuen-quene had of hir chylde;

At þis cause þe knyȝt comlyche hade

In þe inore half of his schelde hir ymage depaynted,

Þat quen he blusched þerto his belde neuer payred.

Þe fyft fyue þat I finde þat þe frek vsed

Watz fraunchyse and felaȝschyp forbe al þyng,

His clannes and his cortaysye croked were neuer,

And pité, þat passez alle poyntez, þyse pure fyue

Were harder happed on þat haþel þen on any oþer.

Now alle þese fyue syþez, for soþe, were fetled on þis knyȝt,

And vchone halched in oþer, þat non ende hade,

And fyched vpon fyue poyntez, þat fayld neuer,

Ne samned neuer in no syde, ne sundred nouþer,

Withouten ende at any noke I oquere fynde,

Whereeuer þe gomen bygan, or glod to an ende.

Þerfore on his schene schelde schapen watz þe knot

Ryally wyth red golde vpon rede gowlez, [folio 100r]

Þat is þe pure pentaungel wyth þe peple called with lore.

Now grayþed is Gawan gay,

And laȝt his launce ryȝt þore,

And gef hem alle goud day,

He wende for euermore.

"Sir Gawain and the Green Knight." Corpus of Middle English Prose and Verse, University of Michigan Library Digital Collections, https://name.umdl.umich.edu/Gawain. . Accessed December 20, 2024.

Because Middle English is difficult to rhyme, English poems from the Middle Ages often used alliteration for visual and audial effect. This modern English translation keeps the alliteration from the original version of the poem.

This poem, the 28th out of the 101 poems that make up the epic Gawain and the Green Knight, describes Gawain's virtues in five groups of five. Put together, these fives are symbolized by the "pentangle" or five-pointed star painted on Gawain's shield, which, like Gawain's virtues, is interconnected and never-ending. Several of these virtues, such as his faith in the "five wounds", "five joys" and his "piety" are specifically Christian values. Religious imagery appears frequently throughout Gawain, sometimes literally, as with the portrait of "holy Heaven's Queen" or the Virgin Mary on the inside of the shield. The close associations between Gawain's virtues and his armor show that both will protect him, a theme that is developed further throughout the poem, as when the Green Knight spares his life because of his chivalrous behavior. In addition, this imagery links morality to appearance, another theme which is explored through the poem's portrayals of the Green Knight himself and his lady.

Taken from A.S. Kline's modernized version of Sir Gawain and the Green Knight (2007).

Sir Gawain and the Green Knight. Poetry in Translation, translated by A.S. Kline, 2007, https://www.poetryintranslation.com/PITBR/English/GawainAndTheGreenKnight.php. Accessed Dec 20, 2024.

lol

Die Forderung nach einem Energiegipfel ist in diesem Kontext als ein Versuch zu werten, fossile Kapitalnteressen noch besser in Stelllung zu bringen. Die Klimawissenschaft wird in diesem Zusammenhang nie genannt.

Dazu passt, dass man an den Wassertoff-Hype anschließt und damit ein weiteres Argument der Klimaverzögerer übernimmt. Es ist ausdrücklich nicht von „grünem Wasserstoff“ die Rede.

Über den Verbrennungsmotor heisst es, dass er „für den Wohlstand Europas von eminenter Bedeutung ist“. Dass er eine der Hauptursachen für die globale Erhitzung ist, bleibt unerwähnt, auch nicht, dass er ineffizient ist und dass das Festhalten am Verbrennungsmotor die Wettbewerbsfähigkeit der europäischen Industrie schwächt.

Erneuerbare Energien sollen nur da vorgeschrieben werden können, wo sie die "Wettbewerbsfähigkeit heimischer Unternehmen" nicht einschränken. Damit wird ein Scheingegensatz behauptet, und es wird die Wettbewerbsfähigkeit – ohne Angabe, um welche Betriebe, um welche Bedingungen und um welche Zeit es geht – dem KLimaschutz untergeordnet.

Es passt zur Heimattümelei der Vereinbarung, dass Agrophotovoltaik nur als Ausnahme zugelassen wird. Damit wird nicht nur die Energiewende erschwert, es wird auch Landwirten und Landwirtinnen einen Einnahmnequelle genommen. Dezentrale Energiepruduktion ist offenbar unerwünscht.

Die Forderung nach „Technologieoffenheit“, ein Standard-Topos der Klima-Verzögerer, wird mehrfach erhoben.

نصف القطر

الاحداثيات

متعدد الاضلاع

الشكل

الاحداثيات

ال usemap بتساوي # مع ال name تبع ال map

المناطق القابلة للنقر

Adam Gitner (20 December 2024). LATIN WORD OF THE YEAR 2024 – VOX ANNI MMXXIV. Parerga . Retrieved 20 December 2024 from https://doi.org/10.58079/12yyj<br /> https://parerga.hypotheses.org/3568

retotatototato

eLife Assessment

In this important study, the authors employed three types of theoretical/computational models (coarse-grained molecular dynamics, analytical theory and field-theoretical simulations) to analyze the impact of salt on protein liquid-liquid phase separation. These different models reinforce each other and together provide convincing evidence to explain distinct salt effects on ATP mediated phase separation of different variants of caprin1. The insights and general approach are broadly applicable to the analysis of protein phase separation. Still, modeling at the coarse-grained level misses key effects that have been revealed by all-atom simulations, including salt-backbone coordination and strengthening of pi-type interactions by salt.

Reviewer #1 (Public review):

Summary:

The authors used multiple approaches to study salt effects in liquid-liquid phase separation (LLPS). Results on both wild-type Caprin1 and mutants and on different types of salts contribute to a comprehensive understanding.

Strengths:

The main strength of this work is the thoroughness of investigation. This aspect is highlighted by the multiple approaches used in the study, and reinforced by the multiple protein variants and different salts studied.

Weaknesses:

(1) The multiple computational approaches are a strength, but they're cruder than explicit-solvent all-atom molecular dynamics (MD) simulations and may miss subtle effects of salts. In particular, all-atom MD simulations demonstrate that high salt strengthens pi-types of interactions (ref. 42 and MacAinsh et al, https://www.biorxiv.org/content/10.1101/2024.05.26.596000v3).<br /> (2) The paper can be improved by distilling the various results into a simple set of conclusions. By example, based on salt effects revealed by all-atom MD simulations, MacAinsh et al. presented a sequence-based predictor for classes of salt dependence. Wild-type Caprin1 fits right into the "high net charge" class, with a high net charge and a high aromatic content, showing no LLPS at 0 NaCl and an increasing tendency of LLPS with increasing NaCl. In contrast, pY-Caprin1 belongs to the "screening" class, with a high level of charged residues and showing a decreasing tendency of LLLPS.<br /> (3) Mechanistic interpretations can be further simplified or clarified. (i) Reentrant salt effects (e.g., Fig. 4a) are reported but no simple explanation seems to have been provided. Fig. 4a,b look very similar to what has been reported as strong-attraction promotor and weak-attraction suppressor, respectively (ref. 50; see also PMC5928213 Fig. 2d,b). According to the latter two studies, the "reentrant" behavior of a strong-attraction promotor, CL- in the present case, is due to Cl-mediated attraction at low to medium [NaCl] and repulsion between Cl- ions at high salt. Do the authors agree with this explanation? If not, could they provide another simple physical explanation? (ii) The authors attributed the promotional effect of Cl- to counterion-bridged interchain contacts, based on a single instance. There is another simple explanation, i.e., neutralization of the net charge on Caprin1. The authors should analyze their simulation results to distinguish net charge neutralization and interchain bridging; see MacAinsh et al.<br /> (4) The authors presented ATP-Mg both as a single ion and as two separate ions; there is no explanation of which of the two versions reflects reality. When presenting ATP-Mg as a single ion, it's as though it forms a salt with Na+. I assume NaCl, ATP, and MgCl2 were used in the experiment. Why is Cl- not considered? Related to this point, it looks ATP is just another salt ion studied and much of the Results section is on NaCl, so the emphasis of ATP ("Diverse Roles of ATP" in the title is somewhat misleading.

Comments on revisions:

This revision addressed all my previous comments.

Reviewer #2 (Public review):

Summary:

In this paper, Lin and colleagues aim to understand the role of different salts on the phase behavior of a model protein of significant biological interest, Caprin1, and its phosphorylated variant, pY-Caprin1. To achieve this, the authors employed a variety of methods to complement experimental studies and obtain a molecular-level understanding of ion partitioning inside biomolecular condensates. A simple theory based on rG-RPA is shown to capture the different salt dependencies of Caprin1 and pY-Caprin1 phase separation, demonstrating excellent agreement with experimental results. The application of this theory to multivalent ions reveals many interesting features with the help of multicomponent phase diagrams. Additionally, the use of CG model-based MD simulations and FTS provides further clarity on how counterions can stabilize condensed phases.

Strengths:

The greatest strength of this study lies in the integration of various methods to obtain complementary information on thermodynamic phase diagrams and the molecular details of the phase separation process. The authors have also extended their previously proposed theoretical approaches, which should be of significant interest to other researchers. Some of the findings reported in this paper, such as bridging interactions, are likely to inspire new studies using higher-resolution atomistic MD simulations.

Reviewer #3 (Public review):

Authors first use rG-RPA to reproduce two observed trends. Caprin1 does not phase separate at very low salt but then undergoes LLPS with added salt while further addition of salt reduces its propensity to LLPS. On the other hand pY-Caprin1 exhibits a monotonic trend where the propensity to phase separate decreases with the addition of salt. This distinction is captured by a two component model and also when salt ions are explicitly modeled as a separate species with a ternary phase diagram. The predicted ternary diagrams (when co and counter ions are explicitly accounted for) also predict the tendency of ions to co-condense or exclude proteins in the dense phase. Predicted trends are generally in line with the measurement for Cparin1. Next, the authors seek to explain the observed difference in phase separation when Arginines are replaced by Lysines creating different variants. In the current rG-RPA type models both Arginine (R) and Lysine (K) are treated equally since non-electrostatic effects are only modeled in a mean-field manner that can be fitted but not predicted. For this reason, coarse grain MD simulation is suitable. Moreover, MD simulation affords structural features of the condensates. They used a force field that is capable of discriminating R and K. The MD predicted degrees of LLPS of these variants again is consistent with the measurement. One additional insight emerges from MD simulations that a negative ion can form a bridge between two positively charged residues on the chain. These insights are not possible to derive from rG-RPA. Both rG-RPA and MD simulation become cumbersome when considering multiple types of ions such as Na, Cl, [ATP] and [ATP-Mg] all present at the same time. FTS is well suited to handle this complexity. FTS also provides insights into the co-localization of ions and proteins that is consistent with NMR. By using different combinations of ions they confirm the robustness of the prediction that Caprin1 shows salt-dependent reentrant behavior, adding further support that the differential behavior of Caprin1, and pY-Caprin1 is likely to be mediated by charge-charge interactions.

Comments on revisions:

The authors addressed my comments and it is ready for publication.

Author response:

The following is the authors’ response to the current reviews.

Reviewer #1 (Public Review):

Comments on revisions:

This revision addressed all my previous comments.

Reviewer #3 (Public Review):

Comments on revisions:

The authors addressed my comments and it is ready for publication.

We are grateful for the reviewers’ effort and are encouraged by their generally positive assessment of our manuscript.

Reviewer #1 (Recommendations For The Authors):

This revision addressed all my previous comments. The only new issue concerns the authors’ response to the following comment of reviewer 3:

(2) Authors note ”monovalent positive salt ions such as Na+ can be attracted, somewhat counterintuitively, into biomolecular condensates scaffolded by positively-charged polyelectrolytic IDRs in the presence of divalent counterions”. This may be due to the fact that the divalent negative counterions present in the dense phase (as seen in the ternary phase diagrams) also recruit a small amount of Na+.

Author reply: The reviewer’s comment is valid, as a physical explanation for this prediction is called for. Accordingly, the following sentence is added to p. 10, lines 27-29: ...

Here are my comments on this issue. Most IDPs with a net positive charge still have negatively charged residues, which in theory can bind cations. In fact, Caprin1 has 3 negatively charged residues (same as A1-LCD). All-atom simulations of MacAinsh et al (ref 72) have shown that these negatively charged residues bind Na+; I assume this effect can be captured by the coarsegrained models in the present study. Moreover, all-atom simulations showed that Na+ has a strong tendency to be coordinated by backbone carbonyls, which of course are present on all residues. Suggestions:

(a) The authors may want to analyze the binding partners of Na+. Are they predominantly the3 negatively charged residues, or divalent counterions, or both?

(b) The authors may want to discuss the potential underestimation of Na+ inside Caprin1 condensates due to the lack of explicit backbone carbonyls that can coordinate Na+ in their models. A similar problem applies to backbone amides that can coordinate anions, but to a lesser extent (see Fig. 3A of ref 72).

The reviewer’s comments are well taken. Regarding the statement in the revised manuscript “This phenomenon arises because the positively charge monovalent salt ions are attracted to the negatively charged divalent counterions in the protein-condensed phase.”, it should be first noted that the statement was inferred from the model observation that Na+ is depleted in condensed Caprin1 (Fig. 2a) when the counterion is monovalent (an observation that was stated almost immediately preceding the quoted statement). To make this logical connection clearer as well as to address the reviewer’s point about the presence of negatively charged residues in Caprin1, we have modified this statement in the Version of Record (VOR) as follows:

“This phenomenon most likely arises from the attraction of the positively charge monovalent salt ions to the negatively charged divalent counterions in the proteincondensed phase because although the three negatively charged D residues in Caprin1 can attract Na+, it is notable that Na+ is depleted in condensed Caprin1 when the counterion is monovalent (Fig. 2a).”

The reviewer’s suggestion (a) of collecting statistics of Na+ interactions in the Caprin1 condensate is valuable and should be attempted in future studies since it is beyond the scope of the present work. Thus far, our coarse-grained molecular dynamics has considered only monovalent Cl− counterions. We do not have simulation data for divalent counterions.

Following the reviewer’s suggestion (b), we have now added the following sentence in Discussion under the subheading “Effects of salt on biomolecular LLPS”:

“In this regard, it should be noted that positively and negatively charged salt ions can also coordinate with backbone carbonyls and amides, respectively, in addition to coordinating with charged amino acid sidechains (MacAinsh et al., eLife 2024). The impact of such effects, which are not considered in the present coarse-grained models, should be ascertained by further investigations using atomic simulations (MacAinsh et al., eLife 2024; Rauscher & Pom`es, eLife 2017; Zheng et al., J Phys Chem B 2020).”

Here we have added a reference to Rauscher & Pom`es, eLife 2017 to more accurately reflect progress made in atomic simulations of biomolecular condensates.

More generally, regarding the reviewer’s comments on the merits of coarse-grained versus atomic approaches, we re-emphasize, as stated in our paper, that these approaches are complementary. Atomic approaches undoubtedly afford structurally and energetically high-resolution information. However, as it stands, simulations of the assembly-disassembly process of biomolecular condensate are nonideal because of difficulties in achieving equilibration even for a small model system with < 10 protein chains (MacAinsh et al., eLife 2024) although well-equilibrated simulations are possible for a reasonably-sized system with ∼ 30 chains when the main focus is on the condensed phase (Rauscher & Pom`es, eLife 2017). In this context, coarse-grained models are valuable for assessing the energetic role of salt ions in the thermodynamic stability of biomolecular condensates of physically reasonable sizes under equilibrium conditions.

In addition to the above minor additions, we have also added citations in the VOR to two highly relevant recent papers: Posey et al., J Am Chem Soc 2024 for salt-dependent biomolecular condensation (mentioned in Dicussion under subheadings “Tielines in protein-salt phase diagrams” and “Counterion valency” together with added references to Hribar et al., J Am Chem Soc 2002 and Nostro & Ninham, Chem Rev 2012 for the Hofmeister phenomena discussed by Posey et al.) and Zhu et al., J Mol Cell Biol 2024 for ATP-modulated reentrant behavior (mentioned in Introduction). We have also added back a reference to our previous work Lin et al., J Mol Liq 2017 to provide more background information for our formulation.

Reviewer #2 (Recommendations For The Authors):

The authors have done a great job addressing previous comments.

We thank this reviewer for his/her effort and are encouraged by the positive assessment of our revised manuscript.

---

The following is the authors’ response to the original reviews.

Reviewer #1 (Public Review):

Summary:

The authors used multiple approaches to study salt effects in liquid-liquid phase separation (LLPS). Results on both wild-type Caprin1 and mutants and on different types of salts contribute to a comprehensive understanding.

Strengths:

The main strength of this work is the thoroughness of investigation. This aspect is highlighted by the multiple approaches used in the study, and reinforced by the multiple protein variants and different salts studied.

We are encouraged by this positive overall assessment.

Weaknesses: (1) The multiple computational approaches are a strength, but they’re cruder than explicit-solvent all-atom molecular dynamics (MD) simulations and may miss subtle effects of salts. In particular, all-atom MD simulations demonstrate that high salt strengthens pi-types of interactions (ref. 42 and MacAinsh et al, https://www.biorxiv.org/content/10.1101/2024.05.26.596000v3).

The relative strengths and limitations of coarse-grained vs all-atom simulation are now more prominently discussed beginning at the bottom of p. 5 through the first 8 lines of p. 6 of the revised manuscript (page numbers throughout this letter refer to those in the submitted pdf file of the revised manuscript), with MacAinsh et al. included in this added discussion (cited as ref. 72 in the revised manuscript). The fact that coarse-grained simulation may not provide insights into more subtle structural and energetic effects afforded by all-atom simulations with regard to π-related interaction is now further emphasized on p. 11 (lines 23–30), with reference to MacAinsh et al. as well as original ref. 42 (Krainer et al., now ref. 50 in the revised manuscript).

(2) The paper can be improved by distilling the various results into a simple set of conclusions. By example, based on salt effects revealed by all-atom MD simulations, MacAinsh et al. presented a sequence-based predictor for classes of salt dependence. Wild-type Caprin1 fits right into the “high net charg”e class, with a high net charge and a high aromatic content, showing no LLPS at 0 NaCl and an increasing tendency of LLPS with increasing NaCl. In contrast, pY-Caprin1 belongs to the “screening” class, with a high level of charged residues and showing a decreasing tendency of LLPS.

This is a helpful suggestion. We have now added a subsection with heading “Overview of key observations from complementary approaches” at the beginning of the “Results” section on p. 6 (lines 18–37) and the first line of p. 7. In the same vein, a few concise sentences to summarize our key results are added to the first paragraph of “Discussion” (p. 18, lines 23– 26). In particular, the relationship of Caprin1 and pY-Caprin1 with the recent classification by MacAinsh et al. (ref. 72) in terms of “high net charge” and “screening” classes is now also stated, as suggested by this reviewer, on p. 18 under “Discussion” (lines 26–30).

(3) Mechanistic interpretations can be further simplified or clarified. (i) Reentrant salt effects (e.g., Fig. 4a) are reported but no simple explanation seems to have been provided. Fig. 4a,b look very similar to what has been reported as strong-attraction promotor and weak-attraction suppressor, respectively (ref. 50; see also PMC5928213 Fig. 2d,b). According to the latter two studies, the “reentrant” behavior of a strong-attraction promotor, CL- in the present case, is due to Cl-mediated attraction at low to medium [NaCl] and repulsion between Cl- ions at high salt. Do the authors agree with this explanation? If not, could they provide another simple physical explanation? (ii) The authors attributed the promotional effect of Cl- to counterionbridged interchain contacts, based on a single instance. There is another simple explanation, i.e., neutralization of the net charge on Caprin1. The authors should analyze their simulation results to distinguish net charge neutralization and interchain bridging; see MacAinsh et al.

The relationship of Cl− in bridging and neutralizing configurations, respectively, with the classification of “strong-attraction promoter” and “weak-attraction suppressor” by Zhou and coworkers is now stated on p. 13 (lines 29–31), with reference to original ref. 50 by Ghosh, Mazarakos & Zhou (now ref. 59 in the revised manuscript) as well as the earlier patchy particle model study PMC5928213 by Nguemaha & Zhou, now cited as ref. 58 in the revised manuscript. After receiving this referee report, we have conducted an extensive survey of our coarse-grained MD data to provide a quantitative description of the prevalence of counterion (Cl−) bridging interactions linking positively charged arginines (Arg+s) on different Caprin1 chains in the condensed phase (using the [Na+] = 0 case as an example). The newly compiled data is reported under a new subsection heading “Explicit-ion MD offers insights into counterion-mediated interchain bridging interactions among condensed Caprin1 molecules” on p. 12 (last five lines)–p. 14 (first 10 lines) [∼ 1_._5 additional page] as well as a new Fig. 6 to depict the statistics of various Arg+–Cl−–Arg+ configurations, with the conclusion that a vast majority (at least 87%) of Cl− counterions in the Caprin1-condensed phase engage in favorable condensation-driving interchain bridging interactions.

(4) The authors presented ATP-Mg both as a single ion and as two separate ions; there is no explanation of which of the two versions reflects reality. When presenting ATP-Mg as a single ion, it’s as though it forms a salt with Na+. I assume NaCl, ATP, and MgCl2 were used in the experiment. Why is Cl- not considered? Related to this point, it looks like ATP is just another salt ion studied and much of the Results section is on NaCl, so the emphasis of ATP (“Diverse Roles of ATP” in the title is somewhat misleading.

We model ATP and ATP-Mg both as single-bead ions (in rG-RPA) and also as structurally more realistic short multiple-bead polymers (in field-theoretic simulation, FTS). We have now added discussions to clarify our modeling rationale in using and comparing different models for ATP and ATP-Mg, as follows:

p. 8 (lines 19–36):

“The complementary nature of our multiple methodologies allows us to focus sharply on the electrostatic aspects of hydrolysis-independent role of ATP in biomolecular condensation by comparing ATP’s effects with those of simple salt. Here, Caprin1 and pY-Caprin1 are modeled minimally as heteropolymers of charged and neutral beads in rG-RPA and FTS. ATP and ATP-Mg are modeled as simple salts (singlebead ions) in rG-RPA whereas they are modeled with more structural complexity as short charged polymers (multiple-bead chains) in FTS, though the latter models are still highly coarse-grained. Despite this modeling difference, rG-RPA and FTS both rationalize experimentally observed ATP- and NaCl-modulated reentrant LLPS of Caprin1 and a lack of a similar reentrance for pY-Caprin1 as well as a prominent colocalization of ATP with the Caprin1 condensate. Consistently, the same contrasting trends in the effect of NaCl on Caprin1 and pY-Caprin1 are also seen in our coarse-grained MD simulations, though polymer field theories tend to overestimate LLPS propensity [99]. The robustness of the theoretical trends across different modeling platforms underscores electrostatics as a significant component in the diverse roles of ATP in the context of its well-documented ability to modulate biomolecular LLPS via hydrophobic and π-related effects [63, 65, 67].”

Here, the last sentence quoted above addresses this reviewer’s question about our intended meaning in referring to “diverse roles of ATP” in the title of our paper. To make this point even clearer, we have also added the following sentence to the Abstract (p. 2, lines 12–13):

“... The electrostatic nature of these features complements ATP’s involvement in π-related interactions and as an amphiphilic hydrotrope, ...”

Moreover, to enhance readability, we have now added pointers in the rG-RPA part of our paper to anticipate the structurally more complex ATP and ATP-Mg models to be introduced subsequently in the FTS part, as follows:

p. 9 (lines 13–15):

“As mentioned above, in the present rG-RPA formulation, (ATP-Mg)²⁻ and ATP⁴⁻ are modeled minimally as a single-bead ion. They are represented by charged polymer models with more structural complexity in the FTS models below.”

p. 11 (lines 8–11):

These observations from analytical theory will be corroborated by FTS below with the introduction of structurally more realistic models of (ATP-Mg) ²⁻, ATP⁴⁻ together with the possibility of simultaneous inclusion of Na⁺, Cl−, and Mg²⁺ in the FTS models of Caprin1/pY-Caprin1 LLPS systems.

Reviewer #2 (Public Review):

Summary:

In this paper, Lin and colleagues aim to understand the role of different salts on the phase behavior of a model protein of significant biological interest, Caprin1, and its phosphorylated variant, pY-Caprin1. To achieve this, the authors employed a variety of methods to complement experimental studies and obtain a molecular-level understanding of ion partitioning inside biomolecular condensates. A simple theory based on rG-RPA is shown to capture the different salt dependencies of Caprin1 and pY-Caprin1 phase separation, demonstrating excellent agreement with experimental results. The application of this theory to multivalent ions reveals many interesting features with the help of multicomponent phase diagrams. Additionally, the use of CG model-based MD simulations and FTS provides further clarity on how counterions can stabilize condensed phases.

Strengths:

The greatest strength of this study lies in the integration of various methods to obtain complementary information on thermodynamic phase diagrams and the molecular details of the phase separation process. The authors have also extended their previously proposed theoretical approaches, which should be of significant interest to other researchers. Some of the findings reported in this paper, such as bridging interactions, are likely to inspire new studies using higher-resolution atomistic MD simulations.

Weaknesses:

The paper does not have any major issues.

We are very encouraged by this reviewer’s positive assessment of our work.

Reviewer #3 (Public Review):

Authors first use rG-RPA to reproduce two observed trends. Caprin1 does not phase separate at very low salt but then undergoes LLPS with added salt while further addition of salt reduces its propensity to LLPS. On the other hand pY-Caprin1 exhibits a monotonic trend where the propensity to phase separate decreases with the addition of salt. This distinction is captured by a two component model and also when salt ions are explicitly modeled as a separate species with a ternary phase diagram. The predicted ternary diagrams (when co and counter ions are explicitly accounted for) also predict the tendency of ions to co-condense or exclude proteins in the dense phase. Predicted trends are generally in line with the measurement for Cparin1 [sic]. Next, the authors seek to explain the observed difference in phase separation when Arginines are replaced by Lysines creating different variants. In the current rG-RPA type models both Arginine (R) and Lysine (K) are treated equally since non-electrostatic effects are only modeled in a meanfield manner that can be fitted but not predicted. For this reason, coarse grain MD simulation is suitable. Moreover, MD simulation affords structural features of the condensates. They used a force field that is capable of discriminating R and K. The MD predicted degrees of LLPS of these variants again is consistent with the measurement. One additional insight emerges from MD simulations that a negative ion can form a bridge between two positively charged residues on the chain. These insights are not possible to derive from rG-RPA. Both rG-RPA and MD simulation become cumbersome when considering multiple types of ions such as Na, Cl, [ATP] and [ATP-Mg] all present at the same time. FTS is well suited to handle this complexity. FTS also provides insights into the co-localization of ions and proteins that is consistent with NMR. By using different combinations of ions they confirm the robustness of the prediction that Caprin1 shows salt-dependent reentrant behavior, adding further support that the differential behavior of Caprin1, and pY-Caprin1 is likely to be mediated by charge-charge interactions.

We are encouraged by this reviewer’s positive assessment of our manuscript.

Reviewer #1 (Recommendations For The Authors):

Analysis:

Analyze the simulation results to distinguish net charge neutralization and interchain bridging; see MacAinsh et al.

Please see response above to points (3) and (4) under “Weaknesses” in this reviewer’s public review. We have now added a 1.5-page subsection starting from the bottom of p. 12 to the top of p. 14 to discuss a new extensive analysis of Arg⁺–Cl⁻–Arg⁺ configurations to identify bridging interactions, with key results reported in a new Fig. 6 (p. 42). Recent results from MacAinsh, Dey & Zhou (cited now as ref. 72) are included in the added discussion. Relevant advances made in MacAinsh et al., including clarification and classification of salt-mediated interactions in the phase separation of A1-LCD are now mentioned multiple times in the revised manuscript (p. 5, lines 19–20; p. 6, lines 2–5; p. 11, line 30; p. 14, line 10; p. 18, lines 28–29; and p. 20, line 4).

Writing and presentation

(1) Cite subtle effects that may be missed by the coarser approaches in this study

Please see response above to point (1) under “Weaknesses” in this reviewer’s public review.

(2) Try to distill the findings into a simple set of conclusions

Please see response above to point (2) under “Weaknesses” in this reviewer’s public review.

(3) Clarify and simplify physical interpretations

Please see response above to point (2) under “Weaknesses” in this reviewer’s public review.

(4) Explain the treatment of ATP-Mg as either a single ion or two separate ions; reconsider modifying the reference to ATP in the title

Please see response above to point (4) under “Weaknesses” in this reviewer’s public review.

(5) Minor points:

p. 4, citation of ref 56: this work shows ATP is a driver of LLPS, not merely a regulator (promotor or suppressor)

This citation to original ref. 56 (now ref. 63) on p. 4 is now corrected (bottom line of p. 4).

p. 7 and throughout: “using bulk [Caprin1]” – I assume this is the initial overall Caprin1 concentration. It would avoid confusion to state such concentrations as “initial” or “initial overall”

We have now added “initial overall concentration” in parentheses on p. 8 (line 4) to clarify the meaning of “bulk concentration”.

p. 7 and throughout: both mM (also uM) and mg/ml have been used as units of protein concentration and that can cause confusion. Indeed, the authors seem to have confused themselves on p. 9, where 400 (750) mM is probably 400 (750) mg/ml. The same with the use of mM and M for salt concentrations (400 mM Mg2+ but 0.1 and 1.0 M Na+)

Concentrations are now given in both molarity and mass density in Fig. 1 (p. 37), Fig. 2 (p. 38), Fig. 4 (p. 40), and Fig. 7 (p. 43), as noted in the text on p. 8 (lines 4–5). Inconsistencies and errors in quoting concentrations are now corrected (p. 10, line 18, and p. 11, line 2).

p. 7, “LCST-like”: isn’t this more like a case of a closed coexistence curve that contains both UCST and LCST?

The discussion on p. 8 around this observation from Fig. 1d is now expanded, including alluding to the theoretical possibility of a closed co-existence curve mentioned by this reviewer, as follows:

“Interestingly, the decrease in some of the condensed-phase [pY-Caprin1]s with decreasing T (orange and green symbols for ≲ 20◦C in Fig. 1d trending toward slightly lower [pY-Caprin1]) may suggest a hydrophobicity-driven lower critical solution temperature (LCST)-like reduction of LLPS propensity as temperature approaches ∼ 0◦C as in cold denaturation of globular proteins [7,23] though the hypothetical LCST is below 0◦C and therefore not experimentally accessible. If that is the case, the LLPS region would resemble those with both an UCST and a LCST [4]. As far as simple modeling is concerned, such a feature may be captured by a FH model wherein interchain contacts are favored by entropy at intermediate to low temperatures and by enthalpy at high temperatures, thus entailing a heat capacity contribution in χ(T), with [7,109,110] beyond the temperature-independent ϵ_h and ϵ_s used in Fig. 1c,d and Fig. 2. Alternatively, a reduction in overall condensed-phase concentration can also be caused by formation of heterogeneous locally organized structures with large voids at low temperatures even when interchain interactions are purely enthalpic (Fig. 4 of ref. [111]).”

p. 8 “Caprin1 can undergo LLPS without the monovalent salt (Na+) ions (LLPS regions extend to [Na+] = 0 in Fig. 2e,f”: I don’t quite understand what’s going on here. Is the effect caused by a small amount of counterion (ATP-Mg) that’s calculated according to eq 1 (with z s set to 0)?

The discussion of this result in Fig. 2e,f is now clarified as follows (p. 10, lines 8–14 in the revised manuscript):

“The corresponding rG-RPA results (Fig. 2e–h) indicate that, in the present of divalent counterions (needed for overall electric neutrality of the Caprin1 solution), Caprin1 can undergo LLPS without the monvalent salt (Na+) ions (LLPS regions extend to [Na+] = 0 in Fig. 2e,f; i.e., ρs \= 0, ρc > 0 in Eq. (1)), because the configurational entropic cost of concentrating counterions in the Caprin1 condensed phase is lesser for divalent (zc \= 2) than for monovalent (zc \= 1) counterions as only half of the former are needed for approximate electric neutrality in the condensed phase.”

p. 9 “Despite the tendency for polymer field theories to overestimate LLPS propensity and condensed-phase concentrations”: these limitations should be mentioned earlier, along with the very high concentrations (e.g., 1200 mg/ml) in Fig. 2

This sentence (now on p. 11, lines 11–18) is now modified to clarify the intended meaning as suggested by this reviewer:

“Despite the tendency for polymer field theories to overestimate LLPS propensity and condensed-phase concentrations quantitatively because they do not account for ion condensation [99]—which can be severe for small ions with more than ±1 charge valencies as in the case of condensed [Caprin1] ≳ 120 mM in Fig. 2i–l, our present rG-RPA-predicted semi-quantitative trends are consistent with experiments indicating “

In addition, this limitation of polymer field theories is also mentioned earlier in the text on p. 6, lines 30–31.

Reviewer #2 (Recommendations For The Authors):

(1) he current version of the paper goes through many different methodologies, but how these methods complement or overlap in terms of their applicability to the problem at hand may not be so clear. This can be especially difficult for readers not well-versed in these methods. I suggest the authors summarize this somewhere in the paper.

As mentioned above in response to Reviewer #1, we have now added a subsection with heading “Overview of key observations from complementary approaches” at the beginning of the “Results” section on p. 6 (lines 18–37) and the first line of p. 7 to make our paper more accessible to readers who might not be well-versed in the various theoretical and computational techniques. A few sentences to summarize our key results are added as well to the first paragraph of “Discussion” (p. 18, lines 23–26).

(2) It wasn’t clear if the authors obtained LCST-type behavior in Figure 1d or if another phenomenon is responsible for the non-monotonic change in dense phase concentrations. At the very least, the authors should comment on the possibility of observing LCST behavior using the rG-RPA model and if modifications are needed to make the theory more appropriate for capturing LCST.

As mentioned above in response to Reviewer #1, the discussion regarding possible LCSTtype behanvior in Fig. 1d is now expanded to include two possible physical origins: (i) hydrophobicity-like temperature-dependent effective interactions, and (ii) formation of heterogeneous, more open structures in the condensed phase at low temperatures. Three additional references [109, 110, 111] (from the Dill, Chan, and Panagiotopoulos group respectively) are now included to support the expanded discussion. Again, the modified discussion is as follows:

“Interestingly, the decrease in some of the condensed-phase [pY-Caprin1]s with decreasing T (orange and green symbols for ≲ 20◦C in Fig. 1d trending toward slightly lower [pY-Caprin1]) may suggest a hydrophobicity-driven lower critical solution temperature (LCST)-like reduction of LLPS propensity as temperature approaches ∼ 0◦C as in cold denaturation of globular proteins [7,23] though the hypothetical LCST is below 0◦C and therefore not experimentally accessible. If that is the case, the LLPS region would resemble those with both an UCST and a LCST [4]. As far as simple modeling is concerned, such a feature may be captured by a FH model wherein interchain contacts are favored by entropy at intermediate to low temperatures and by enthalpy at high temperatures, thus entailing a heat capacity contribution in χ(T), with [7,109,110] beyond the temperature-independent ϵ_h and ϵ_s used in Fig. 1c,d and Fig. 2. Alternatively, a reduction in overall condensed-phase concentration can also be caused by formation of heterogeneous locally organized structures with large voids at low temperatures even when interchain interactions are purely enthalpic (Fig. 4 of ref. [111]).”

(3) In Figures 4c and 4d, ionic density profiles could be shown as a separate zoomed-in version to make it easier to see the results.

This is an excellent suggestion. Two such panels are now added to Fig. 4 (p. 40) as parts (g) and (h).

Reviewer #3 (Recommendations For The Authors):

I would suggest authors make some minor edits as noted here.

(1) Please note down the chi values that were used when fitting experimental phase diagrams with rG-RPA theory in Figure 2a,b. At present there aren’t too many such values available in the literature and reporting these would help to get an estimate of effective chi values when electrostatics is appropriately modeled using rG-RPA.

The χ(T) values and their enthalpic and entropic components ϵh and ϵs used to fit the experimental data in Fig. 1c,d are now stated in the caption for Fig. 1 (p. 37). Same fitted χ(T) values are used in Fig. 2 (p. 38) as it is now stated in the revised caption for Fig. 2. Please note that for clarity we have now changed the notation from ∆h and ∆s in our originally submitted manuscript to ϵh and ϵs in the revised text (p. 7, last line) as well as in the revised figure captions to conform to the notation in our previous works [18, 71].

(2) Authors note “monovalent positive salt ions such as Na+ can be attracted, somewhat counterintuitively, into biomolecular condensates scaffolded by positively-charged polyelectrolytic IDRs in the presence of divalent counterions”. This may be due to the fact that the divalent negative counterions present in the dense phase (as seen in the ternary phase diagrams) also recruit a small amount of Na+.

The reviewer’s comment is valid, as a physical explanation for this prediction is called for. Accordingly, the following sentence is added to p. 10, lines 27–29:

“This phenomenon arises because the positively charge monovalent salt ions are attracted to the negatively charged divalent counterions in the protein-condensed phase.”

(3) In the discussion where authors contrast the LLPS propensity of Caprin1 against FUS, TDP43, Brd4, etc, they correctly note majority of these other proteins have low net charge and possibly higher non-electrostatic interaction that can promote LLPS at room temperature even in the absence of salt. It is also worth noting if some of these proteins were forced to undergo LLPS with crowding which is sometimes typical. A quick literature search will make this clear.

A careful reading of the work in question (Krainer et al., ref. 50) does not suggest that crowders were used to promote LLPS for the proteins the authors studied. Nonetheless, the reviewer’s point regarding the potential importance of crowder effects is well taken. Accordingly, crowder effects are now mentioned briefly in the Introduction (p. 4, line 13), with three additional references on the impact of crowding on LLPS added [30–32] (from the Spruijt, Mukherjee, and Rakshit groups respectively). In this connection, to provide a broader historical context to the introductory discussion of electrostatics effects in biomolecular processes in general, two additional influential reviews (from the Honig and Zhou groups respectively) are now cited as well [15, 16].

يزعج

بشكل افتراضي، يتم تكرار الصورة بحيث تغطي العنصر بأكمله.

while it is true that loneliness can be combatted with the company of others, it can require some action on the lonely's half

the earlier screen thing is definitely a concern

a huge culprit that is only briefly touched on is the pandemic, mainly children that grew up during that period. growing up in an era that doesn't allow large amounts of human interaction has intense effects on children

so this kinda a pro human connection piece? cool. the loneliness example is strange simply because something like that is hard to measure.

the rest of the comments are for Rose Hinds

such a topic is very important to dive deep. Its scary to think that many of my female friends may receive worse care than I would.

what would be the best steps that could be taken to reform our current medical systems?

research that is focused solely on male physicality is dangerous in more way than one :(

I can see how a gender gap could be a huge problem in the medical world, Even my girlfriend suffered from this mistake.

Sometime's I forget just how big empires like Russia's and the Ottaman's truly were. So many roots that people may not need.

What were the boarder problem's that Mexico faced and why did it happen? I also wonder what weapons were tested.

Educational-Film Director Ted Peshak Dies by [[Adam Bernstein]]

whisper.cppだけturboにしているのはなぜですか?

速度比較をするのであれば同じモデルを使ってほしい。 large-v3-turboモデルはlarge-v3よりも速いです。

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