Two motor neuron synergies, invariant across ankle joint angles, activate the triceps surae during plantarflexion

Abstract Recent studies have suggested that the nervous system generates movements by controlling groups of motor neurons (synergies) that do not always align with muscle anatomy. In this study, we determined whether these synergies are robust across tasks with different mechanical constraints. We identified motor neuron synergies using principal component analysis (PCA) and cross‐correlations between smoothed discharge rates of motor neurons. In part 1, we used simulations to validate these methods. The results suggested that PCA can accurately identify the number of common inputs and their distribution across active motor neurons. Moreover, the results confirmed that cross‐correlation can separate pairs of motor neurons that receive common inputs from those that do not receive common inputs. In part 2, 16 individuals performed plantarflexion at three ankle angles while we recorded EMG signals from the gastrocnemius lateralis (GL) and medialis (GM) and the soleus (SOL) with grids of surface electrodes. The PCA revealed two motor neuron synergies. These motor neuron synergies were relatively stable, with no significant differences in the distribution of motor neuron weights across ankle angles (P = 0.62). When the cross‐correlation was calculated for pairs of motor units tracked across ankle angles, we observed that only 13.0% of pairs of motor units from GL and GM exhibited significant correlations of their smoothed discharge rates across angles, confirming the low level of common inputs between these muscles. Overall, these results highlight the modularity of movement control at the motor neuron level, suggesting a sensible reduction of computational resources for movement control. Key points The CNS might generate movements by activating groups of motor neurons (synergies) with common inputs. We show here that two main sources of common inputs drive the motor neurons innervating the triceps surae muscles during isometric ankle plantarflexions. We report that the distribution of these common inputs is globally invariant despite changing the mechanical constraints of the tasks, i.e. the ankle angle. These results suggest the functional relevance of the modular organization of the CNS to control movements.

We look forward to receiving your revised submission.
If you have any queries, please reply to this email and we will be pleased to advise.

Richard Carson Senior Editor
The Journal of Physiology ----------------REQUIRED ITEMS -Author photo and profile.First (or joint first) authors are asked to provide a short biography (no more than 100 words for one author or 150 words in total for joint first authors) and a portrait photograph.These should be uploaded and clearly labelled with the revised version of the manuscript.See Information for Authors for further details.
-You must start the Methods section with a paragraph headed Ethical Approval.If experiments were conducted on humans confirmation that informed consent was obtained, preferably in writing, that the studies conformed to the standards set by the latest revision of the Declaration of Helsinki, and that the procedures were approved by a properly constituted ethics committee, which should be named, must be included in the article file.If the research study was registered (clause 35 of the Declaration of Helsinki) the registration database should be indicated, otherwise the lack of registration should be noted as an exception (e.g.The study conformed to the standards set by the Declaration of Helsinki, except for registration in a database).For further information see: https://physoc.onlinelibrary.wiley.com/hub/human-experiments-The Journal of Physiology funds authors of provisionally accepted papers to use the premium BioRender site to create high resolution schematic figures.Follow this link and enter your details and the manuscript number to create and download figures.Upload these as the figure files for your revised submission.If you choose not to take up this offer we require figures to be of similar quality and resolution.If you are opting out of this service to authors, state this in the Comments section on the Detailed Information page of the submission form.The link provided should only be used for the purposes of this submission.Authors will be charged for figures created on this premium BioRender account if they are not related to this manuscript submission.
-Please upload separate high-quality figure files via the submission form.
-Please ensure that any tables are in Word format and are, wherever possible, embedded in the article file itself.
-Please ensure that the Article File you upload is a Word file.
-A Statistical Summary Document, summarising the statistics presented in the manuscript, is required upon revision.It must be on the Journal's template, which can be downloaded from the link in the Statistical Summary Document section here: https://jp.msubmit.net/cgi-bin/main.plex?form_type=display_requirements#statistics.
In summary: -If n {less than or equal to} 30, all data points must be plotted in the figure in a way that reveals their range and distribution.A bar graph with data points overlaid, a box and whisker plot or a violin plot (preferably with data points included) are acceptable formats.
-If n > 30, then the entire raw dataset must be made available either as supporting information, or hosted on a not-for-profit repository e.g.FigShare, with access details provided in the manuscript.
-'n' clearly defined (e.g.x cells from y slices in z animals) in the Methods.Authors should be mindful of pseudoreplication.
-All relevant 'n' values must be clearly stated in the main text, figures and tables, and the Statistical Summary Document (required upon revision).
-The most appropriate summary statistic (e.g.mean or median and standard deviation) must be used.Standard Error of the Mean (SEM) alone is not permitted.
-Exact p values must be stated.Authors must not use 'greater than' or 'less than'.Exact p values must be stated to three significant figures even when 'no statistical significance' is claimed.

EDITOR COMMENTS
Reviewing Editor: Both reviewers recognize the contribution of the manuscript and have raised a number of issues which should be addressed before it is ready for publication.

Senior Editor:
As you will note, the Referees were positively disposed towards the intent and the execution of the project.As also emphasised by the Reviewing Editor however, there are certain aspects of the presentation that detract from the potential impact of this work.Most conspicuous among these is the application of a clustering algorithm to the motor unit weights.It is emphasised by both referees that neither the logic nor the conceptual basis for this step appear convincing.In the event that you opt to revise your submission, I would ask that you pay particular attention to this issue. -----------------

REFEREE COMMENTS
Referee #1: This study investigated the robustness of motor neuron synergies, i.e., groups of motor neurons belonging to motor neuron pools of multiple muscles and sharing the same common input, across task conditions.First, the use of principal component analysis (PCA) on the smoothed discharge rates of multiple motor units to identify the number of independent common inputs and of cross-correlation to identify pairs of motor units receiving the same common input were validated using simulated data.Then, PCA and cross-correlation analyses were applied to the smoothed discharge rates of motor units identified in gastrocnemius lateralis (GL), gastrocnemius medialis (GM), and soleus (SOL) from high-density surface electromyographic recordings during generation of isometric plantarflexion torque at three different ankle angles.Even if the task involved a single degree of freedom, PCA allowed to identify two motor neuron synergies with most of the motor units assigned to each synergy maintaining a significant cross-correlation across angles.
The investigation of motor neuron synergies is critical to gain insights in the neural implementation of a modular control architecture.This study is novel and important because it demonstrates for the first time the robustness of motor neuron synergies across different task conditions, supporting the hypothesis that such synergies represent a set of invariant modules that may reduce the computational burden of movement control.There is, however, one key aspect of the conceptual framework used to interpret the results and to define one of the steps of the analysis of both simulated and experimental data that is unnecessary and potentially misleading.
Classifying each motor neuron as belonging to one motor neuron synergies, and consequently applying a clustering algorithm on the weights of each motor unit in the two first principal components, is justified under the assumption that each motor neuron belongs to only one synergy.While this is a reasonable possibility, there is no reason not to also consider the possibility that each motor neurons may belong to more than one synergy.Indeed, this possibility is implemented in the simulation, where 60% of the motor neurons received both common inputs.Then, if each motor neurons may have synaptic weights of different magnitudes for both common inputs, there is no need and no justification for a classification of each motor neuron.If the representation of the motor neurons in the two-dimensional space of synaptic weights (or equivalently of the weight of the two principal components) is not concentrated in specific portions of the space, clustering becomes arbitrary.Indeed, in many of the cases illustrated in Fig. 4 (e.g., for P#1, P#5, P#14), the distribution of the motor units appears rather uniform in a broad region of space.Clearly one can apply a clustering algorithm to a uniform distribution and classify its elements, but this operation likely does not provide any additional information on the property of that distribution.In fact, the key insight and important result of the study, the identification of two motor unit synergies, does not depend on the potentially unsupported observation of distinct clusters.
On the contrary, considering the fact that motor neurons may belong to more than one motor neuron synergies, makes motor neuron synergies a plausible model for the implementation of muscle synergies and avoids presenting motor neuron synergies and muscle synergies as two contrasting views.Synergies defined at the muscle levels do not prescribe any specific neural implementation, as muscle synergy models describe the generation of muscle patterns at a functional rather than at a neural implementation level.Thus, synergies at the muscle level do not require the "implicit assumption" that "all motor neurons innervating a muscle (i.e., a motor neuron pool) receive the same common inputs" (lines 88-89, 631-632), as they do not model the generation of muscle patterns at the motor unit level.*** Referee #2: In this study, the authors seek to uncover invariant patterns of motoneuronal co-activations across the three muscles belonging to the triceps surae (medial (GM) and lateral (GL) heads of gastrocnemius and soleus (SOL)).Prior studies of motor modularity usually involve analysis of multi-muscle EMGs with muscle synergies defined at the whole-muscle level.Here, by uncovering common inputs to motor units belonging to potentially different muscles, the authors extend the motor modularity concept to the motoneuronal level.High-density EMGs (64 channels) were recorded during an isometric task with the ankle fixed at three different angles.After the motor unit spikes were decomposed from the hd-EMG, a procedure based on the principal component analysis (PCA), validated by simulations, was used to reveal how multiple motor units were co-activated by common inputs.The authors found two motoneuronal synergies, involving GL-SOL and GM-SOL, that recruited the same motoneurons across the three ankle angles.These synergies are interpreted to be plausible modules of lower-limb motor control.
Overall, this is a very well written paper that addresses a timely, important question in motor neuroscience.It demonstrates how motor modularity may be productively studied at the motorneuronal level.The methods adopted here may also become a framework for later hd-EMG studies that investigate motorneuronal synergies.But to further enhance the paper's potential impact, the authors are suggested to further clarify the following points in their revision.

MAJOR COMMENTS
(1) To identify the motorneuronal synergies from the smoothed discharge rates of the motor unit spikes, the authors relied on PCA, which necessarily assumes that each motor unit can be under the influence of more than one common input, and that this influence may either be excitatory or inhibitory.But then, after PCA, the authors performed an additional step of plotting the weights of every motor unit of the first two principal components on x and y coordinates, and then applied kmeans on this plane to cluster each motor unit into a single motoneuronal synergy (lines 313-315).This step essentially forces each motor unit to receive a single common input, thus making the PCA strength of allowing each data channel to be contributed by multiple sources appearing superfluous.These analytic steps seem all the more curious when the authors explicitly noted that the assignment of motor units to clusters became inconsistent when the units receive balanced activations from multiple common inputs (e.g., lines 382-383).
Importantly, in light of the above methodological choices, the statement "74% of the motor units belonged to the same clusters across all the conditions" (lines 477-479) should be qualified with the caveat that synergy robustness was observed only after the additional step of assigning each motor unit into a single synergy.
I suggest reporting the actual principal components (PCs) (i.e., the eigenvectors) and presenting them in a way that shows the correspondence between the motor-unit weights across the components (e.g., show the PCs as bar graphs).Robustness of the motoneuronal synergies can then potentially be demonstrated through high similarity values between the PC vectors from the different conditions.If the k-means step is retained, the authors should better justify why this is done.If each motor unit can belong only to a single synergy, then why not just apply clustering on the spike discharge rates or rely solely on correlation measures?
(2) After performing PCA, the authors presented another analysis based on pairwise correlation of motor-unit discharge rates to further strengthen the observations of GL-SOL and GM-SOL synergies as demonstrated in the PCA analysis.Since each motor unit can be activated by multiple and different common inputs (as assumed in the authors' simulations), the lack of correlations between any two motor units does not necessarily imply that they are not co-activated in any one of the motoneuronal synergy.Correlation-based analysis is thus "less sophisticated" in a way than PCA-based analysis, because the former implicitly assumes that each motor unit belongs only to one synergy.I can see the value of including correlation results in this work, but the authors can better justify why this step is included after PCA.I suggest using the correlation results to benchmark the PCA results, especially in the simulation part.To what extent can co-activation patterns be revealed only by PCA but not by correlations?
(3) The authors pointed out one potential limitation of the classic muscle synergy model (lines 88-89; 630-632) in that it assumes that all motoneurons innervating a muscle receive the same common inputs.I can see this as one possible

05-Feb-2023
interpretation of the classic model (which does not appear to be explicitly acknowledged in Cheung & Seki 2021, as claimed on line 632).But it is also true that the classic model aims only to describe the EMGs of individual muscles at the wholemuscle level, and has nothing to say concerning which motor units are recruited in what order whenever the muscle is activated through one or multiple synergies.Very importantly, the classic model does not need this "implicit assumption" to work.For instance, in the classic model, the EMG of a muscle can be the summation of contributions from two different muscle synergies, and each synergy may recruit two different collections of motor units belonging to this same muscle to result in the final EMG of this muscle.

MINOR COMMENTS
(1) Lines 112-113: Can clarify that hd-EMGs were recorded during isometric conditions at three different ankle angles.
(2) Lines 268-270: Can further clarify how each isolated motor unit was attributed to an individual muscle (GM, GL, or SOL).Was this based solely on the anatomical positions of the channels that contributed to the isolated unit?
(4) Lines 320-321: It is a bit unclear why the criterion stated here is good for finding the 10-s window for cross-correlation.
(5) Fig. 2 & Fig. 4: Were the signs of any identified PCs flipped according to a certain criterion?(6) Line 439: It would be informative to report the average and range of the number of motor units identified per subject, for each of the three ankle angles.

26-Jun-2023 1st Authors' Response to Referees
Both reviewers recognize the contribu on of the manuscript and have raised a number of issues which should be addressed before it is ready for publica on.

Senior Editor:
As you will note, the Referees were posi vely disposed towards the intent and the execu on of the project.As also emphasised by the Reviewing Editor however, there are certain aspects of the presenta on that detract from the poten al impact of this work.Most conspicuous among these is the applica on of a clustering algorithm to the motor unit weights.It is emphasised by both referees that neither the logic nor the conceptual basis for this step appear convincing.In the event that you opt to revise your submission, I would ask that you pay par cular a en on to this issue.Dear editors and reviewers, we thank you for your feedback and your comments that helped us to improve the manuscript.Please note that in addi on to addressing your comments, we improved some analyses and updated the associated results.Specifically, motor units are now matched using single-differen al EMG signals instead of EMG signals recorded with a monopolar montage.We believe that this new analysis increases the accuracy of the matching by sampling the spa al distribu on of motor unit ac on poten als within the grid with greater spa al selec vity.Addi onally, we ran the principal component analysis on all the iden fied motor units instead of matched motor units only.By doing so, we increased the sta s cal power of the analysis by increasing the number of par cipants (12 instead of 7) and the total number of iden fied motor units (34 ± 17 instead of 15 ± 7 per par cipant) considered in the analysis.We believe that our conclusions are strengthened by the updated results.All comments and sugges ons of the reviewers have been taken into account in this revision, as detailed in the point-by-point replies provided in the following.

REFEREE COMMENTS
Referee #1: This study inves gated the robustness of motor neuron synergies, i.e., groups of motor neurons belonging to motor neuron pools of mul ple muscles and sharing the same common input, across task condi ons.First, the use of principal component analysis (PCA) on the smoothed discharge rates of mul ple motor units to iden fy the number of independent common inputs and of cross-correla on to iden fy pairs of motor units receiving the same common input were validated using simulated data.Then, PCA and crosscorrela on analyses were applied to the smoothed discharge rates of motor units iden fied in gastrocnemius lateralis (GL), gastrocnemius medialis (GM), and soleus (SOL) from highdensity surface electromyographic recordings during genera on of isometric plantarflexion torque at three different ankle angles.Even if the task involved a single degree of freedom, PCA allowed to iden fy two motor neuron synergies with most of the motor units assigned to each synergy maintaining a significant cross-correla on across angles.
The inves ga on of motor neuron synergies is cri cal to gain insights in the neural implementa on of a modular control architecture.This study is novel and important because it demonstrates for the first me the robustness of motor neuron synergies across different task condi ons, suppor ng the hypothesis that such synergies represent a set of invariant modules that may reduce the computa onal burden of movement control.There is, however, one key aspect of the conceptual framework used to interpret the results and to define one of the steps of the analysis of both simulated and experimental data that is unnecessary and poten ally misleading.
Classifying each motor neuron as belonging to one motor neuron synergies, and consequently applying a clustering algorithm on the weights of each motor unit in the two first principal components, is jus fied under the assump on that each motor neuron belongs to only one synergy.While this is a reasonable possibility, there is no reason not to also consider the possibility that each motor neurons may belong to more than one synergy.Indeed, this possibility is implemented in the simula on, where 60% of the motor neurons received both common inputs.Then, if each motor neurons may have synap c weights of different magnitudes for both common inputs, there is no need and no jus fica on for a classifica on of each motor neuron.If the representa on of the motor neurons in the twodimensional space of synap c weights (or equivalently of the weight of the two principal components) is not concentrated in specific por ons of the space, clustering becomes arbitrary.Indeed, in many of the cases illustrated in Fig. 4 (e.g., for P#1, P#5, P#14), the distribu on of the motor units appears rather uniform in a broad region of space.Clearly one can apply a clustering algorithm to a uniform distribu on and classify its elements, but this opera on likely does not provide any addi onal informa on on the property of that distribu on.In fact, the key insight and important result of the study, the iden fica on of two motor unit synergies, does not depend on the poten ally unsupported observa on of dis nct clusters.We thank the reviewer for this important insight.We agree that motor neurons could receive mul ple inputs from common drivers.This is indeed at the basis of the concept of synergies at the motor neuron level.The reviewer is right that clustering the weights of the motor neurons can be misleading.To address this comment, we have removed the clustering analysis and we now focus our results on the principal component analysis applied on all the iden fied motor units.Despite considering more motor neurons and par cipants than in the original version (see general comment above), we iden fied the same number of synergies, i.e., two.To replace the analysis based on the clustering, we have calculated the angle between vectors displayed in the two-dimensional biplots.As shown with the simula on, the larger the difference between the distribu on of correlated inputs to two motor neurons, the larger the angle between the two vectors.The adjusted R 2 of linear fits between these angles and the differences in ra o of common input 1 ranged between 0.91 and 0.92 for the three condi ons of our simula on.We observed a significant main effect of muscle on experimental data.Specifically, our analysis highlights that the angles between motor neurons innerva ng the GL or the GM are significantly smaller than those between motor neurons innerva ng the SOL.Addi onally, we did not observe a significant main effect of the ankle angle nor an interac on between angle and muscles.This confirms our hypothesis that the two synergies mostly separate motor units from GL and GM across ankle angles, while motor neurons from the SOL are spread within the biplots.
The manuscript and the figures 2, 4 and 5 have been updated.
On the contrary, considering the fact that motor neurons may belong to more than one motor neuron synergies, makes motor neuron synergies a plausible model for the implementa on of muscle synergies and avoids presen ng motor neuron synergies and muscle synergies as two contras ng views.Synergies defined at the muscle levels do not prescribe any specific neural implementa on, as muscle synergy models describe the genera on of muscle pa erns at a func onal rather than at a neural implementa on level.Thus, synergies at the muscle level do not require the "implicit assump on" that "all motor neurons innerva ng a muscle (i.e., a motor neuron pool) receive the same common inputs" (lines 88-89, 631-632), as they do not model the genera on of muscle pa erns at the motor unit level.The reviewer is right.We updated both the introduc on and the discussion sec ons to realign the frameworks of muscle and motor neuron synergies.Thus, motor neuron synergies are presented as a change of scale to describe the distribu on of common inputs across groups of motor neurons that enables the nervous system to reduce the dimension of the neural control of movement.
You can now read: (P.3, L.84): "This concept of synergies (or motor modules) has been mainly demonstrated at the muscle level by combining the recording of mul ple muscles with bipolar electromyography and factoriza on algorithms (Tresch et al., 1999;d'Avella et al., 2003;Ting et al., 2015;Yaron et al., 2020).The recent development of algorithms that iden fy the discharge ac vity of ac ve motor units revealed a new dimensionality of movement control, where synergies are considered at the motor neuron level.These motor neuron synergies can cover subsets of motor neurons within each muscle or across por ons of different muscles (Hug et al., 2022)."(P.25, L.622): "The fact that the central nervous system may group motor units from synergis c muscles to reduce the dimensionality of the neural control of movements has been supported for decades by the theory of muscle synergies (Tresch & Jarc, 2009;Dominici et al., 2011;Bizzi & Cheung, 2013;Ting et al., 2015;Takei et al., 2017).Of note, these synergies have been described at the muscle level.However, several studies have highlighted similar levels of correla on between the firing ac vi es of motor units origina ng from two synergis c muscles as from the same muscle (Del Vecchio et al., 2022;Hug et al., 2022b).Thus, recent studies have proposed to take advantage of the large sampling of motor unit ac vity from decomposed HD-EMG signals to extend the synergy concept to the motor neuron level (Madarshahian et al., 2021;Tanzarella et al., 2021;Del Vecchio et al., 2022;Hug et al., 2022;Hug et al., 2023)."*** Referee #2: In this study, the authors seek to uncover invariant pa erns of motoneuronal co-ac va ons across the three muscles belonging to the triceps surae (medial (GM) and lateral (GL) heads of gastrocnemius and soleus (SOL)).Prior studies of motor modularity usually involve analysis of mul -muscle EMGs with muscle synergies defined at the whole-muscle level.Here, by uncovering common inputs to motor units belonging to poten ally different muscles, the authors extend the motor modularity concept to the motoneuronal level.High-density EMGs (64 channels) were recorded during an isometric task with the ankle fixed at three different angles.A er the motor unit spikes were decomposed from the hd-EMG, a procedure based on the principal component analysis (PCA), validated by simula ons, was used to reveal how mul ple motor units were co-ac vated by common inputs.The authors found two motoneuronal synergies, involving GL-SOL and GM-SOL, that recruited the same motoneurons across the three ankle angles.These synergies are interpreted to be plausible modules of lower-limb motor control.
Overall, this is a very well wri en paper that addresses a mely, important ques on in motor neuroscience.It demonstrates how motor modularity may be produc vely studied at the motorneuronal level.The methods adopted here may also become a framework for later hd-EMG studies that inves gate motorneuronal synergies.But to further enhance the paper's poten al impact, the authors are suggested to further clarify the following points in their revision.

MAJOR COMMENTS
(1) To iden fy the motorneuronal synergies from the smoothed discharge rates of the motor unit spikes, the authors relied on PCA, which necessarily assumes that each motor unit can be under the influence of more than one common input, and that this influence may either be excitatory or inhibitory.But then, a er PCA, the authors performed an addi onal step of plo ng the weights of every motor unit of the first two principal components on x and y coordinates, and then applied k-means on this plane to cluster each motor unit into a single motoneuronal synergy (lines 313-315).This step essen ally forces each motor unit to receive a single common input, thus making the PCA strength of allowing each data channel to be contributed by mul ple sources appearing superfluous.These analy c steps seem all the more curious when the authors explicitly noted that the assignment of motor units to clusters became inconsistent when the units receive balanced ac va ons from mul ple common inputs (e.g., lines 382-383).
Importantly, in light of the above methodological choices, the statement "74% of the motor units belonged to the same clusters across all the condi ons" (lines 477-479) should be qualified with the caveat that synergy robustness was observed only a er the addi onal step of assigning each motor unit into a single synergy.I suggest repor ng the actual principal components (PCs) (i.e., the eigenvectors) and presen ng them in a way that shows the correspondence between the motor-unit weights across the components (e.g., show the PCs as bar graphs).Robustness of the motoneuronal synergies can then poten ally be demonstrated through high similarity values between the PC vectors from the different condi ons.If the k-means step is retained, the authors should be er jus fy why this is done.If each motor unit can belong only to a single synergy, then why not just apply clustering on the spike discharge rates or rely solely on correla on measures?We thank the reviewer for this important insight.As reported in the first response to reviewer 1, we removed the clustering analysis to make the results more consistent with the framework of muscle/motor neuron synergies.We applied PCA on the full sample of iden fied motor units in the new version of the manuscript (see general comment above).Therefore, it is not possible to directly compare the distribu on of PC vectors across ankle angles, as the iden fied motor units may change.To replace the analysis based on the clustering, we have calculated the angle between vectors displayed in the two-dimensional biplots.As shown with the simula on, the larger the difference between the distribu on of correlated inputs to two motor neurons, the larger the angle between the two vectors represen ng these two motor neurons on the biplot.The adjusted R 2 of linear fits between these angles and the differences in ra o of common input 1 ranged between 0.91 and 0.92 for the three condi ons of our simula on.
We observed a significant main effect of the muscle on experimental data.Specifically, our analysis highlights that the angles between motor neurons innerva ng the GL or the GM are significantly smaller than those between motor neurons innerva ng the SOL.Addi onally, we did not observe a significant main effect of the angle nor an interac on between angle and muscles.
The updated results are reported in the method and result sec ons, and in figures 2, 4 and 5.
(2) A er performing PCA, the authors presented another analysis based on pairwise correla on of motor-unit discharge rates to further strengthen the observa ons of GL-SOL and GM-SOL synergies as demonstrated in the PCA analysis.Since each motor unit can be ac vated by mul ple and different common inputs (as assumed in the authors' simula ons), the lack of correla ons between any two motor units does not necessarily imply that they are not co-ac vated in any one of the motoneuronal synergy.Correla on-based analysis is thus "less sophis cated" in a way than PCA-based analysis, because the former implicitly assumes that each motor unit belongs only to one synergy.I can see the value of including correla on results in this work, but the authors can be er jus fy why this step is included a er PCA.I suggest using the correla on results to benchmark the PCA results, especially in the simula on part.To what extent can coac va on pa erns be revealed only by PCA but not by correla ons?
In the new version of the manuscript, the cross-correla on analysis is reported for matched motor units, which adds value to this analysis.It allows us to determine whether the distribu on of common inputs is stable between tasks.Specifically, we considered that two motor units with a consistent significant correla on between their smoothed discharge rates across the three ankle angles are likely to receive a significant level of common inputs.On the contrary, if two motor units exhibit consistent non-significant correla on, regardless of the ankle angle, or exhibit variable levels of correla on depending on the ankle angle, they are likely to mostly receive independent inputs, as supported by our simula on.We believe that this new analysis strengthens the observa on made with the PCA.These updated results are reported in the result sec ons, and in figure 6.
(3) The authors pointed out one poten al limita on of the classic muscle synergy model (lines 88-89; 630-632) in that it assumes that all motoneurons innerva ng a muscle receive the same common inputs.I can see this as one possible interpreta on of the classic model (which does not appear to be explicitly acknowledged in Cheung & Seki 2021, as claimed on line 632).But it is also true that the classic model aims only to describe the EMGs of individual muscles at the whole-muscle level, and has nothing to say concerning which motor units are recruited in what order whenever the muscle is ac vated through one or mul ple synergies.Very importantly, the classic model does not need this "implicit assump on" to work.For instance, in the classic model, the EMG of a muscle can be the summa on of contribu ons from two different muscle synergies, and each synergy may recruit two different collec ons of motor units belonging to this same muscle to result in the final EMG of this muscle.Our interpreta on of Fig 2E from Cheung and Seki (2021) was that inputs are distributed to the whole motor neuron pool.But we agree with the reviewer, and as reported in the second response to reviewer 1, we rephrased the introduc on and discussion sec ons to be er align the framework of muscle and motor neuron synergies.We now present the motor neuron synergies as a change of scale to describe the low dimensional control of groups of motor units.
You can now read: (P.3, L.84): "This concept of synergies (or motor modules) has been mainly demonstrated at the muscle level by combining the recording of mul ple muscles with bipolar electromyography and factoriza on algorithms (Tresch et al., 1999;d'Avella et al., 2003;Ting et al., 2015;Yaron et al., 2020).The recent development of algorithms that iden fy the discharge ac vity of ac ve motor units revealed a new dimensionality of movement control, where synergies are considered at the motor neuron level.These motor neuron synergies can cover subsets of motor neurons within each muscle or across por ons of different muscles (Hug et al., 2022)."(P.25, L.622): "The fact that the central nervous system may group motor units from synergis c muscles to reduce the dimensionality of the neural control of movements has been supported for decades by the theory of muscle synergies (Tresch & Jarc, 2009;Dominici et al., 2011;Bizzi & Cheung, 2013;Ting et al., 2015;Takei et al., 2017).Of note, these synergies have been described at the muscle level.However, several studies have highlighted similar levels of correla on between the firing ac vi es of motor units origina ng from two synergis c muscles as from the same muscle (Del Vecchio et al., 2022;Hug et al., 2022b).Thus, recent studies have proposed to take advantage of the large sampling of motor unit ac vity from decomposed HD-EMG signals to extend the synergy concept to the motor neuron level (Madarshahian et al., 2021;Tanzarella et al., 2021;Del Vecchio et al., 2022;Hug et al., 2022;Hug et al., 2023)."
We look forward to receiving your revised submission.
If you have any queries, please reply to this email and we will be pleased to advise.

Richard Carson Senior Editor
The Journal of Physiology ----------------REQUIRED ITEMS -You must start the Methods section with a paragraph headed Ethical Approval.If experiments were conducted on humans confirmation that informed consent was obtained, preferably in writing, that the studies conformed to the standards set by the latest revision of the Declaration of Helsinki, and that the procedures were approved by a properly constituted ethics committee, which should be named, must be included in the article file.If the research study was registered (clause 35 of the Declaration of Helsinki) the registration database should be indicated, otherwise the lack of registration should be noted as an exception (e.g.The study conformed to the standards set by the Declaration of Helsinki, except for registration in a database).For further information see: https://physoc.onlinelibrary.wiley.com/hub/human-experiments.
-The Journal of Physiology funds authors of provisionally accepted papers to use the premium BioRender site to create high resolution schematic figures.Follow this link and enter your details and the manuscript number to create and download figures.Upload these as the figure files for your revised submission.If you choose not to take up this offer we require figures to be of similar quality and resolution.If you are opting out of this service to authors, state this in the Comments section on the Detailed Information page of the submission form.The link provided should only be used for the purposes of this submission.Authors will be charged for figures created on this premium BioRender account if they are not related to this manuscript submission.

In summary:
-If n {less than or equal to} 30, all data points must be plotted in the figure in a way that reveals their range and distribution.A bar graph with data points overlaid, a box and whisker plot or a violin plot (preferably with data points included) are acceptable formats.
-If n > 30, then the entire raw dataset must be made available either as supporting information, or hosted on a not-for-profit repository e.g.FigShare, with access details provided in the manuscript.
-'n' clearly defined (e.g.x cells from y slices in z animals) in the Methods.Authors should be mindful of pseudoreplication.
-All relevant 'n' values must be clearly stated in the main text, figures and tables, and the Statistical Summary Document (required upon revision).
-The most appropriate summary statistic (e.g.mean or median and standard deviation) must be used.Standard Error of the Mean (SEM) alone is not permitted.
-Exact p values must be stated.Authors must not use 'greater than' or 'less than'.Exact p values must be stated to three significant figures even when 'no statistical significance' is claimed.
-Statistics Summary Document completed appropriately upon revision.----------------EDITOR COMMENTS Reviewing Editor: The major comments of both reviewers have been addressed in the revised manuscript.A small number of remaining issues have been identified which should be addressed.These include the interpretation of the new data presented and clarification around the terms 'clusters' and motor neuron synergies. -----------------

REFEREE COMMENTS
Referee #1: The authors have addressed my concerns by removing the clustering analysis and realigning the frameworks of muscle and motor neuron synergies.As they agree that the clustering analysis was not appropriate, I suggest also removing all references to "clusters" in the text (e.g. at lines 62, 95, 102, 649-652) and referring directly to "motor neuron synergies".

Referee #2:
In this revised version, the authors have updated their analysis of the motor neuron synergies with one based on biplots of the motor-unit weights from the principal components (the new Fig. 4) and finding the angles between all pairs of vectors on such biplots (the new Fig. 5).While the authors' effort on addressing the reviewers' comments by implementing such new analyses is much appreciated, some work on suitably interpreting these new results remain to be done.

MAJOR COMMENTS
(1) It is a bit unclear how the new results on Fig. 5 lead to the conclusion that muscles GL and GM "receive the highest proportion of common input" (line 489) (in fact, it is unclear what this very phrase means).If I understand correctly, a consistent small angle between the vectors of the motor-unit PC weights from the same muscle just means that within the same muscle, the proportion of inputs from the two common drives received by the motoneurons tend to be consistent across motor units.(For instance, if motor unit 1 of GL is driven by 4 activation units of drive 1 and 3 units of drive 2, motor unit 2 of GL likewise is driven by a similar proportion of activations from drives 1 and 2.) It is unclear what it means physiologically when the angles from GL and GM units are lower than those from SOL or any of the muscle pairs, and the implications of this finding are not discussed in Discussion section.Does this mean that GL and GM are controlled more like whole-muscles while the SOL motor units are controlled more individually?
(2) Related to the above point, the Discussion section has not been adequately updated in light of the findings of the new analysis.How do the biplot and vector-angle analyses (Fig. 4-5) support the finding that GL-SOL and GM-SOL are the two dominant common inputs?In fact, from the biplots on Fig. 4, it looks like for some subjects and DF angles, GL and GM were also prominently co-represented in a principal component (e.g., in P#5, DF20deg, both GL and GM have units with large PC1 weights).The Discussion section now still reads like one that is based on the PCA/clustering analysis of the previous version.The authors should elaborate on how their new analyses can be related to the conceptual findings.

MINOR COMMENT
In Fig. 4, the vectors denoting motor units from GM and SOL are shown in colors very close to each other (dark blue and light blue, respectively).It is a little difficult to distinguish vectors from the 3 muscles.I suggest using 3 contrasting colors for the three muscles.The major comments of both reviewers have been addressed in the revised manuscript.A small number of remaining issues have been identified which should be addressed.These include the interpretation of the new data presented and clarification around the terms 'clusters' and motor neuron synergies.
We thank the editors and reviewers for their feedback.We have answered their comments below.

Referee #1:
The authors have addressed my concerns by removing the clustering analysis and realigning the frameworks of muscle and motor neuron synergies.As they agree that the clustering analysis was not appropriate, I suggest also removing all references to "clusters" in the text (e.g. at lines 62, 95, 102, 649-652) and referring directly to "motor neuron synergies".
The term 'clusters' has been removed from the manuscript.To clarify the terms used in the manuscript, we consider motor neuron synergies as groups of motor units exhibiting covariations in their discharge rates, likely due to their activation by common inputs, previously described as motor modules.

Referee #2:
In this revised version, the authors have updated their analysis of the motor neuron synergies with one based on biplots of the motor-unit weights from the principal components (the new Fig. 4) and finding the angles between all pairs of vectors on such biplots (the new Fig. 5).While the authors' effort on addressing the reviewers' comments by implementing such new analyses is much appreciated, some work on suitably interpreting these new results remain to be done.

MAJOR COMMENTS
(1) It is a bit unclear how the new results on Fig. 5 lead to the conclusion that muscles GL and GM "receive the highest proportion of common input" (line 489) (in fact, it is unclear what this very phrase means).If I understand correctly, a consistent small angle between the vectors of the motor-unit PC weights from the same muscle just means that within the same muscle, the proportion of inputs from the two common drives received by the motoneurons tend to be consistent across motor units.(For instance, if motor unit 1 of GL is driven by 4 activation units of drive 1 and 3 units of drive 2, motor unit 2 of GL likewise is driven by a similar proportion of activations from drives 1 and 2.) It is unclear what it means physiologically when the angles from GL and GM units are lower than those from SOL or any of the muscle pairs, and the implications of this finding are not discussed in Discussion section.Does this mean that GL and GM are controlled more like whole-muscles while the SOL motor units are controlled more individually?
We rephrased the sentence to explain that the smaller the angle formed between two vectors, the higher the proportion of common inputs between the two motor neurons.
P23, L598: 'The covariation of discharge rates between motor units from either GL or GM was particularly high, with a ratio of pairs with significant correlation for all three ankle angles reaching 94.1% and 88.4% for GL and GM, respectively.This is in agreement with the small angles between vectors identified from the PCA (Fig. 5).Together, these observations indicate that the majority of motor neurons innervating either GL or GM received the two main common inputs with a similar weighting.'Moreover, the complementary analysis of correlations of discharge rates between pairs of motor neurons showed that only a few pairs of motor units between GL and GM had a consistent significant correlation across conditions.This means that the nervous system may uncouple the behavior of motor neurons from each muscle.We revised the manuscript to better explain how this result might functionally impact the control of forces produces by these muscles.P23, L603: 'On the contrary, the degree of covariation of discharge rates between motor neurons from GL and GM was lower than for the other pairs of muscles, with 13% of pairs of motor neurons exhibiting significant correlation across all three ankle angles.This is in agreement with previous work that used methods at the muscle level, such as intermuscular coherence (Hug et al., 2021b;Rossato et al., 2022) or PCA (Mazzo et al., 2022), to assess the covariations of motor unit discharge rates in the triceps surae muscles.Similarly, pairs of motor units from the SOL appear to have lower covariations of discharge rates than from GL and GM.The nervous system may thus take advantage of the geometry and compartmentalization of this muscle (Bolsterlee et al., 2018) to control multiple sources of common input and produce forces in multiple directions (Segal et al., 1991;English et al., 1993).Such strategies have been observed in muscles controlling the individual fingers through multiple tendons (Keen & Fuglevand, 2004;Hockensmith et al., 2005;McIsaac & Fuglevand, 2007), or in the biceps brachii producing force for forearm supination and/or elbow flexion (Barry et al., 2009).' (2) Related to the above point, the Discussion section has not been adequately updated in light of the findings of the new analysis.How do the biplot and vector-angle analyses (Fig. 4-5) support the finding that GL-SOL and GM-SOL are the two dominant common inputs?In fact, from the biplots on Fig. 4, it looks like for some subjects and DF angles, GL and GM were also prominently co-represented in a principal component (e.g., in P#5, DF20deg, both GL and GM have units with large PC1 weights).The Discussion section now still reads like one that is based on the PCA/clustering analysis of the previous version.The authors should elaborate on how their new analyses can be related to the conceptual findings.
We now have updated the discussion to better link our results to the concepts of motor modules and muscle/motor neuron synergies.Specifically, i) we removed all the sentences arguing that the two synergies are grouping motor neurons from the GL/SOL and GM/SOL, and ii) we linked the invariance of motor neuron synergies across conditions to the existence of motor modules as building block for movement control.P24, L634: 'Here, PCA identified two principal components that explained the main variations of discharge rates of the identified motor neurons.It is worth noting that Gibbs et al. (1995) have already reported significant levels of synchronization between the discharge times of motor units from the gastrocnemius and the soleus muscles, consistent with our results outlining the projection of common inputs to the two muscles.
The results of this study support three of the hypotheses proposed by Hug et al. (2023) within the motor neuron synergies framework, namely that during movement 1) motor neurons receives common input in relatively large groups; 2) motor neuron synergies may significantly differ from the classical definition of motor neuron pools, such that synergies may span across muscles (i.e., GL and SOL, GM and SOL) and/or involve only a portion of a muscle (i.e., SOL); and 3) synergies represent motor modules used by the central nervous system to reduce the dimensionality of control.The latter observation is the main novelty of our study.Previous studies identified motor neuron synergies during isometric contractions performed at a single joint angle (Madarshahian et al., 2021;Del Vecchio et al., 2022;Hug et al., 2022) and, therefore, did not demonstrate their invariance across tasks, which is needed to prove a modular organization of movement control (d'Avella et al., 2003;d'Avella & Bizzi, 2005).'

MINOR COMMENT
In Fig. 4, the vectors denoting motor units from GM and SOL are shown in colors very close to each other (dark blue and light blue, respectively).It is a little difficult to distinguish vectors from the 3 muscles.I suggest using 3 contrasting colors for the three muscles.
The figure has been updated to increase the contrast between the colors of each muscle.

-
Please include an Abstract Figure file, as well as the figure legend text within the main article file.The Abstract Figure is a piece of artwork designed to give readers an immediate understanding of the research and should summarise the main conclusions.If possible, the image should be easily 'readable' from left to right or top to bottom.It should show the physiological relevance of the manuscript so readers can assess the importance and content of its findings.Abstract Figures should not merely recapitulate other figures in the manuscript.Please try to keep the diagram as simple as possible and without superfluous information that may distract from the main conclusion(s).Abstract Figures must be provided by authors no later than the revised manuscript stage and should be uploaded as a separate file during online submission labelled as File Type 'Abstract Figure'.Please ensure that you include the figure legend in the main article file.All Abstract Figures should be created using BioRender.Authors should use The Journal's premium BioRender account to export high-resolution images.Details on how to use and access the premium account are included as part of this email.

-
Please include an Abstract Figure file, as well as the figure legend text within the main article file.The Abstract Figure is a piece of artwork designed to give readers an immediate understanding of the research and should summarise the main conclusions.If possible, the image should be easily 'readable' from left to right or top to bottom.It should show the physiological relevance of the manuscript so readers can assess the importance and content of its findings.Abstract Figures should not merely recapitulate other figures in the manuscript.Please try to keep the diagram as simple as possible and without superfluous information that may distract from the main conclusion(s).Abstract Figures must be provided by authors no later than the revised manuscript stage and should be uploaded as a separate file during online submission labelled as File Type 'Abstract Figure'.Please ensure that you include the figure legend in the main article file.All Abstract Figures should be created using BioRender.Authors should use The Journal's premium BioRender account to export high-resolution 26-Jun-2023 images.Details on how to use and access the premium account are included as part of this email.