Reviewer #3:
The authors combine minimal and detailed models of hippocampal theta rhythm generation to understand the underlying mechanisms at the cellular-network level. In their 3 steps approach, they extend previous minimal models, they compare these minimal models with more detailed models and they use a piece (segment) of the detailed model to compare it to the minimal models.
I have a number of methodological issues with the paper. First, both models should be validated against experimental evidence given that the experimental results exist. The validation of a "minimal" model with data from another model is circumstantial and useful to link two models, but in no way is a scientific validation, in my opinion. Second, the model reduction arguments are simply taken as a piece of a large model. This is in now way a systematic reduction, which the authors should provide. In the absence of that, the two models are simply two different models. Third, it is not clear what aspects of the mechanisms cannot be investigated using the larger models that require the reduced models, given that the models do not necessarily match. Fourth, the concept of a minimal model should be clearly explained. They used caricature (toy) models of (2D quadratic models, aka Izhikevich models) combined with biophysically plausible descriptions of synapses. The model parameters in 2D quadratic models are not biophysical as the authors acknowledge, but they can be related to biophysical parameters through the specific equations provided in Rotstein (JCNS, 2015) and Turquist & Rotstein (Encyclopedia of Computational Neuroscience, 2018). In fact, they can represent either h-currents or M-currents. I suggest the authors determine this from these references. In this framework, the dynamics would result from a combination of these currents and persistent sodium or fast (transient) sodium activation. Fifth, from the original paper (Ferguson et al., 2017) their minimal model has 500 PV and 10000 PYR cells (I couldn't find the number of PV cells in this paper, but I assumed they were as in the original paper). This is not what I would call a minimal model. It is minimal only in comparison with the more detailed model. While this is a matter of semantics, it should be clarified since there are other minimal model approaches in the literature (e.g., Kopell group, Erdi group). Related to these models, it is typically assumed that the relationship between PYR to PV is 5/1. This is certainly not holy, but seems to have been validated. Here it is 20/1. Is there any reason for that? Sixth, the networks are so big that it is very difficult to gain some profound insight. What is it about the large networks and their contribution to the generation of theta activity that cannot be learned from "more minimal" networks?
Because of these concerns and the development of the paper, I believe the paper is about the comparison between two existing models that the authors have constructed in the past and the parameter exploration of these models.
I find the paper extremely difficult to read. It is not about the narrative, but about the organization of the results and the lack (or scarcity) of clear statements. I can't seem to be able to easily extract the principles that emerge from the analysis. There are a big number of cases and data, but what do we get out of that? Perhaps creating "telling titles" for each section/subsection would help, where the main result is the title of the section/subsection. I also find an issue with the acronyms. One has to keep track of numbers, cases, acronyms (N, B), etc. All that gets in the way of the understanding. I believe figures would help.
Another confusing issue in the paper is the use of the concept of "building blocks". I am not opposed to the use of these words, on the contrary. But building blocks are typically associated with the model structure (e.g., currents in a neuron, neurons in a network). PIR, SFA and Rheo are a different type of building blocks, which I would call "functional building blocks". They are building blocks in a functional world of model behavior, but not in the world of modeling components. For example, PIR can be instantiated by different combinations of ionic currents receiving inhibitory inputs. Also, the definitions of the building blocks and how they are quantified should be clearly stated in a separate section or subsection.
I disagree with the authors' statement in lines 214-216, related to Fig. 4. They claim that "From them, we can say that the PYR cell firing does not speci1cally occur because of their IPSCs, as spiking can occur before or just after its IPSCs." Figure 4 (top, left panel) suggests the opposite, but instead of being a PIR mechanism, it is a "building-up" of the "adaptation" current in the PYR cell. (By "adaptation" current I mean the current corresponding to the second variable in the model. If this variable were the gating variable of the h-current, it would be the same type of mechanism suggested in Rotstein et al. (2005) and in the models presented in Stark et al. (2013).) The mechanism operates as follow: the first PV-spike (not shown in the figure) causes a rebound, which is not strong enough to produce a PYR spike before a new PV spike occurs (the first in the figure), this second PV-spike causes a stronger rebound (it is super clear in the figure), which is still not strong enough to produce a PYR-spike before the new PV-spike arrives, this third PV spike produces a still stronger rebound, which now causes a PYR spike. The fact that this PYR spike occurs before the PV spike is not indicative of the authors' conclusions, but quite the opposite.
The authors should check whether the mechanistic hypothesis I just described, which is consistent with Fig. 4 (top, left panel), is also consist with the rest of the panels and, more generally, with their modeling results and the experimental data and whether it is general and, if not, what are the conditions under which it is. If my hypothesis ends up not being proven, then they should come up with an alternative hypothesis. The condition the authors' state about the parameter "b" and PIR is not necessarily general. PIR and other phenomena are typically controlled by the combined effect of more than one parameter. As it stands, their basic assumption behind the PRC is not necessarily valid.
The subsequent hypothesis (about PYR bursting) is called to question in view of the previous comments. The experimental data should be able to provide an answer.
The authors' should provide a more detailed explanation and justification for the presence of an inhibitory "bolus". What would the timescale be? Again, the data should provide evidence of that. In their discussion about the PRC, the authors essentially conclude what they hypothesis, but this conclusion is based on the "bolus" idea. The validity of this should be revised.
The discussion about degeneracy of the theta rhythm generation is interesting. However, because of the size and complexity of the models, this degeneracy is expected. Their minimal modeling approach does not help in shedding any additional light. In addition, the authors' do not discuss the intrinsic sources of degeneracy and how they interact with the intrinsic ones.
The last two sections were difficult to follow and I found them anecdotal. I was expecting a deeper mechanistic analysis. However, I have to acknowledge that because of my difficulty in following the paper, I might have missed important issues.
The discussion is extensive, exhaustive and interesting. But it is not clear how the paper results are integrated in this big picture, except for a number of generic statements.
The proposal that the hippocampus has the circuitry to produce theta oscillations without the need of medial septum input has been proposed before by Gillies et. (2003) and the models in Rotstein et al. (2005) and Orban et al. (2005). But the idea from this work is not that the hippocampus (CA1) is a pacemaker, but rather what we now call a "resonator". To claim that the MS is simply an amplificatory of an existing oscillator is against the existing evidence.