Reviewer #1 (Public Review):
This paper aims to address the question of whether the rotational dynamics in motor cortex may be due to sensory feedback signals rather than to recurrent connections and autonomous dynamics as is typically assumed. This is indeed a question of importance in neural control of movement.
The authors employ both analyses of motor cortical data and simulation analyses where a neural network is trained to perform a motor task. For the simulations, the authors use a neural network model of a brain performing arm control tasks. Importantly, in addition to the task goals, the brain also receives delayed sensory feedback from the muscle activity and kinematics of the simulated arm. The brain is modeled either using a stack of two recurrent neural networks (RNN) or using two non-recurrent neural network layers to investigate the importance of autonomous recurrent dynamics. The authors use this framework to simulate the brain performing two tasks: 1) posture perturbation task, where the arm is perturbed by external loads and has to return to original posture, and 2) delayed center-out reach task. In both tasks, the authors apply jPCA to units of the trained network, simulated muscle activity, and simulated kinematics and investigate their rotational dynamics. They find that when using an RNN in the brain model, both the RNN layers and kinematics show rotational dynamics but the muscle activity does not. Interestingly, these conclusions for both tasks also hold when networks without recurrent connections are used instead of the RNNs. Also importantly, the rotational dynamics also exist in the sensory feedback signals about the limb state (e.g. joint position, velocity). These results suggest that recurrent dynamics are not necessary for the emergence of rotational dynamics in population activity, rather sensory feedback can also achieve the same.
The authors perform similar jPCA analyses on monkey motor cortical (MC) or somatosensory cortical activity during the same two tasks and find largely consistent results. As with simulations, neural population activity and kinematics show rotational dynamics but muscle activity, which is explored only in the posture task, does not. Importantly, population activity in both motor and somatosensory cortices shows rotational dynamics. This observation is more consistent with the view that rotational dynamics emerge due to inter-region communications and processing of sensory feedback and planning, rather than autonomous dynamics within the motor cortex.
The approach of the paper is interesting and valuable and the questions being addressed are very important to the field. To further improve the paper and the analyses, there are several major comments that should be addressed to fully support the conclusions and clarify the results:
Major:
1) In the Methods, the authors explain how they model a non-recurrent network as follows: "We also examined networks where we removed the recurrent connections from each layer by effectively setting Whh, Woo to zero for the entire simulation and optimization (NO-REC networks)". However, if this is the only modification, it still leaves recurrent elements in the network. For example, if we set W_{hh} to zero, equation 2 will be:
h_{t+1} = (1-a) * h_t + a * tanh(W_{sh} * s_t + b_h)
where a is a constant scalar (seems to be equal to 0.5). This is indeed still a recurrent neural network since h_{t+1} depends on h_t. If their explanation in the Methods is accurate, then the current approach restricts the recurrent dynamics to be a specific linear dynamic (i.e. "h_{t+1} = (1-a) * h_t + ...") but does not fully remove them. The second layer is also similar (equation 3) and will still have recurrent linear dynamics even if W_{oo} is set to 0. To be able to describe networks as non-recurrent, the first terms in equations 2 and 3 (that is (1-a)*h_t and (1-a)*o_t) should also be set to 0. This is critical as an important argument in the paper is that non-recurrent networks can also produce rotational dynamics, so the networks supporting that argument must be fully non-recurrent. Perhaps the authors have already done this but just didn't explain it in the Methods, in which case they should clarify the Methods. However, if the current Method description is accurate, they should rerun their NO-REC simulations by also setting the fixed linear recurrent components (that is (1-a)*h_t and (1-a)*o_t) to zero as explained above to have a truly non-recurrent model.
2) Assuming my comment in 1 is addressed and the results stay similar, the authors show in simulations that even without recurrent dynamics (referred to as the NO-REC case), rotational dynamics are observed in the simulated brain during both tasks (Figure 8). This result is used to suggest that the sensory feedback is what causes the rotational dynamics in the brain model in this case. However, I think to fully demonstrate the role of feedback, additional simulations are also needed where the sensory feedback is removed from the brain model. In other words, what would happen if recurrent and non-recurrent brain models are trained to perform the tasks but are not provided with the sensory feedback (only receive task goals)? One would expect the recurrent model to still be able to perform the task and autonomously produce similar rotational dynamics (as has been shown in prior work), but the non-recurrent model to fail in doing the task well and in showing rotational dynamics. I think adding such simulations without the feedback signals would really strengthen the paper and help its message.
3) A measure of how well each trained network is able to perform the task should be provided. For example, is the non-recurrent network able to perform the tasks as accurately as the recurrent models? The authors could use an appropriate measure, for example average displacement in the posture task and time-to-target in the center-out task, to objectively quantify task performance for each network. Another performance measure could be the first term of the loss in equation 5. Also, plots of example trials that show the task performance should be provided for the non-recurrent networks (for example by adding to Figure 8), similar to how they are shown for the recurrent models in Figures 2 and 6.
4) An important observation is that rotational dynamics also exist in the sensory signals about the limb state. This may imply that the task structure that dictates the limb state and thus the associated sensory feedback may play an important role in the rotations without the recurrent connections. While the present study will be a valuable addition regardless of what the answer is, this is an important point to address: What is the role of the task structure in producing rotational dynamics? In both the posture task and the center-out task, the task instruction instructs subjects to return to the initial movement 'state' by the end of the trial: in the posture task the simulated arm needs to return to the original posture upon disturbance, and in the center out task the arm needs to start from zero velocity and settle at the target with zero velocity. Is this structure what's causing the rotational dynamics? This is an important question both for this paper and for the field and the authors have a great simulation setup to explore it. For example, what happens if the task instructions u* instruct the arm to follow a random trajectory continuously, instead of stopping at some targets? With a simulated tracking task like this, one could eliminate obvious cases of return-to-original-state from the task. Would the network still produce rotational dynamics? Of course, I don't expect the authors to collect experimental monkey data for such new tasks, rather to just change the task instructions in their numerical simulations to explore the dependence of observed rotational dynamics on the task structure. I think this will help the message of the paper and can be very useful for the field.
5) It would be beneficial if the authors could elaborate in the discussion on intuitive explanations of why sensory feedback can produce rotational dynamics even with no internal recurrent dynamics in the brain model. To me, it seems like sensory feedback is providing a path for recurrence to exist in the overall brain-arm system, so the non-recurrent neural networks can learn to exploit that path to effectively implement some recurrent dynamics. Some intuitive explanations like this will be helpful for readers.
6) One main result in data from non-human primates is that there exist rotations also in the somatosensory cortex not just in motor cortex. A more thorough discussion of prior work on rotational dynamics or lack thereof across brain regions and behavioral tasks is important to add here. For example, besides the works cited by the authors, there are other works such as (Kao et al., 2015; Gao et al., 2016; Remington et al., 2018; Stavisky et al., 2019; Aoi et al., 2020; Sani et al., 2021) that discuss or show rotational dynamics in various brain regions and behavioral tasks and should be cited and discussed.
7) The authors state that "In contrast, rotational dynamics appear to be absent in... MC activity during grasping driven by sensory inputs (Suresh et al., 2020)." There are other papers that study dynamics during reach-grasps and still finds rotational dynamics and modes (Abbaspourazad et al., 2021; Vaidya et al., 2015) and should be cited and discussed. The recent paper on naturalistic reach-grasps (Abbaspourazad et al., 2021) also argues for the involvement of a large-scale network in these movements, which further supports the authors' interpretation that "This interpretation of motor control emphasizes that the objective of the motor system is to attain the behavioural goal and this requires feedback processed by a distributed network." A discussion of this point made in this recent paper in the intro/discussion is important. Finally, there is a recent paper that argues for the input-driven nature of motor cortex (Sauerbrei et al., 2020) and is cited/discussed by the authors but briefly and mainly in the discussion. I think given the relevance of this recent paper to the core message here, it should also be briefly discussed in the introduction to better set up the work.
Minor:
1) The Methods are clear and comprehensive, but just to make understanding of the simulation setup easier, it would help to have a diagram of the computation graph for the recurrent and non-recurrent networks that shows their number of units, activations/nonlinearities, RNN cell type, etc., added as supplementary figure.
2) Again, to help more clearly convey the simulations, it would help to show the task goals (x*) that are inputs to the simulated brain for example trials in each task (for example added to Figures 2 and 6).
3) Similar to how VAF is shown on top of all plots of jPC planes, it would be helpful to have the rotation frequency for each jPC plane noted next to it. Currently it is difficult to find the jPC frequency associated with each plot from the text.
4) I am a bit surprised by how different the null distributions are for modeling muscle activity (Figure 3F) and kinematics (Figure 3H). The null distribution is simply the R2 for a constrained or unconstrained dynamic model fit to a subsampled version of the neural activity. The only difference between the null distributions in Figure 3F and Figure 3H seems to be the downsampled dimension, which for muscle activity is 6 and for kinematics is 4 (per equation 1). Any insight will be welcome as to why down sampling the population activity to 4 (Figure 3H) results in so much worse R2 compared with down sampling it to 6 (Figure 3F)?
References:
Abbaspourazad, H., Choudhury, M., Wong, Y.T., Pesaran, B., Shanechi, M.M., 2021. Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp behavior. Nature Communications 12, 607. https://doi.org/10.1038/s41467-020-20197-x
Aoi, M.C., Mante, V., Pillow, J.W., 2020. Prefrontal cortex exhibits multidimensional dynamic encoding during decision-making. Nature Neuroscience 1-11. https://doi.org/10.1038/s41593-020-0696-5
Gao, Y., Archer, E.W., Paninski, L., Cunningham, J.P., 2016. Linear dynamical neural population models through nonlinear embeddings, in: Lee, D.D., Sugiyama, M., Luxburg, U.V., Guyon, I., Garnett, R. (Eds.), Advances in Neural Information Processing Systems 29. Curran Associates, Inc., pp. 163-171.
Kao, J.C., Nuyujukian, P., Ryu, S.I., Churchland, M.M., Cunningham, J.P., Shenoy, K.V., 2015. Single-trial dynamics of motor cortex and their applications to brain-machine interfaces. Nature Communications 6, 7759. https://doi.org/10.1038/ncomms8759
Remington, E.D., Narain, D., Hosseini, E.A., Jazayeri, M., 2018. Flexible Sensorimotor Computations through Rapid Reconfiguration of Cortical Dynamics. Neuron 98, 1005-1019.e5. https://doi.org/10.1016/j.neuron.2018.05.020
Sani, O.G., Abbaspourazad, H., Wong, Y.T., Pesaran, B., Shanechi, M.M., 2021. Modeling behaviorally relevant neural dynamics enabled by preferential subspace identification. Nature Neuroscience 24, 140-149. https://doi.org/10.1038/s41593-020-00733-0
Stavisky, S.D., Willett, F.R., Wilson, G.H., Murphy, B.A., Rezaii, P., Avansino, D.T., Memberg, W.D., Miller, J.P., Kirsch, R.F., Hochberg, L.R., Ajiboye, A.B., Druckmann, S., Shenoy, K.V., Henderson, J.M., 2019. Neural ensemble dynamics in dorsal motor cortex during speech in people with paralysis. eLife 8, e46015. https://doi.org/10.7554/eLife.46015
Vaidya, M., Kording, K., Saleh, M., Takahashi, K., Hatsopoulos, N.G., 2015. Neural coordination during reach-to-grasp. Journal of Neurophysiology 114, 1827-1836. https://doi.org/10.1152/jn.00349.2015