Hierarchy between forelimb premotor and primary motor cortices and its manifestation in their firing patterns

Reviewer #1 (Public review):

This study examined the interaction between two key cortical regions in the mouse brain involved in goal-directed movements, the rostral forelimb area (RFA) - considered a premotor region involved in movement planning, and the caudal forelimb area (CFA) - considered a primary motor region that more directly influences movement execution. The authors ask whether there exists a hierarchical interaction between these regions, as previously hypothesized, and focus on a specific definition of hierarchy - examining whether the neural activity in the premotor region exerts a larger functional influence on the activity in the primary motor area than vice versa. They examine this question using advanced experimental and analytical methods, including localized optogenetic manipulation of neural activity in either region while measuring both the neural activity in the other region and EMG signals from several muscles involved in the reaching movement, as well as simultaneous electrophysiology recordings from both regions in a separate cohort of animals.

The findings presented show that localized optogenetic manipulation of neural activity in either RFA or CFA resulted in similarly short-latency changes in the muscle output and in firing rate changes in the other region. However, perturbation of RFA led to a larger absolute change in the neural activity of CFA neurons. The authors interpret these findings as evidence for reciprocal, but asymmetrical, influence between the regions, suggesting some degree of hierarchy in which RFA has a greater effect on the neural activity in CFA. They go on to examine whether this asymmetry can also be observed in simultaneously recorded neural activity patterns from both regions. They use multiple advanced analysis methods that either identify latent components at the population level or measure the predictability of firing rates of single neurons in one region using firing rates of single neurons in the other region. Interestingly, the main finding across these analyses seems to be that both regions share highly similar components that capture a high degree of variability of the neural activity patterns in each region. Single units' activity from either region could be predicted to a similar degree from the activity of single units in the other region, without a clear division into a leading area and a lagging area, as one might expect to find in a simple hierarchical interaction. However, the authors find some evidence showing a slight bias towards leading activity in RFA. Using a two-region neural network model that is fit to the summed neural activity recorded in the different experiments and to the summed muscle output, the authors show that a network with constrained (balanced) weights between the regions can still output the observed measured activities and the observed asymmetrical effects of the optogenetic manipulations, by having different within-region local weights. These results put into question whether previous and current findings that demonstrate asymmetry in the output of regions can be interpreted as evidence for asymmetrical (and thus hierarchical) inputs between regions, emphasizing the challenges in studying interactions between any brain regions.

Strengths:

The experiments and analyses performed in this study are comprehensive and provide a detailed examination and comparison of neural activity recorded simultaneously using dense electrophysiology probes from two main motor regions that have been the focus of studies examining goal-directed movements. The findings showing reciprocal effects from each region to the other, similar short-latency modulation of muscle output by both regions, and similarity of neural activity patterns without a clear lead/lag interaction, are convincing and add to the growing body of evidence that highlight the complexity of the interactions between multiple regions in the motor system and go against a simple feedforward-like network and dynamics. The neural network model complements these findings and adds an important demonstration that the observed asymmetry can, in theory, also arise from differences in local recurrent connections and not necessarily from different input projections from one region to the other. This sheds an important light on the multiple factors that should be considered when studying the interaction between any two brain regions, with a specific emphasis on the role of local recurrent connections, that should be of interest to the general neuroscience community.

Weaknesses:

While the similarity of the activity patterns across regions and lack of a clear leading/lagging interaction are interesting observations that are mostly supported by the findings presented (however, see comment below for lack of clarity in CCA/PLS analyses), the main question posed by the authors - whether there exists an endogenous hierarchical interaction between RFA and CFA - seems to be left largely open. The authors note that there is currently no clear evidence of asymmetrical reciprocal influence between naturally occurring neural activity patterns of the two regions, as previous attempts have used non-natural electrical stimulation, lesions, or pharmacological inactivation. The use of acute optogenetic perturbations does not seem to be vastly different in that aspect, as it is a non-natural stimulation of inhibitory interneurons that abruptly perturbs the ongoing dynamics. Furthermore, the main finding that supports a hierarchical interaction is a difference in the absolute change of firing rates as a result of the optogenetic perturbation, a finding that is based on a small number of animals (N = 3 in each experimental group), and one which may be difficult to interpret. As the authors nicely demonstrate in their neural network model, the two regions may differ in the strength of local within-region inhibitory connections. Could this theoretically also lead to a difference in the effect of the artificial light stimulation of the inhibitory inter-neurons on the local population of excitatory projection neurons, driving an asymmetrical effect on the downstream region? Moreover, the manipulation was performed upon the beginning of the reaching movement, while the premotor region is often hypothesized to exert its main control during movement preparation, and thus possibly show greater modulation during that movement epoch. It is not clear if the observed difference in absolute change is dependent on the chosen time of optogenetic stimulation and if this effect is a general effect that will hold if the stimulation is delivered during different movement epochs, such as during movement preparation.

Another finding that is not clearly interpretable is in the analysis of the population activity using CCA and PLS. The authors show that shifting the activity of one region compared to the other, in an attempt to find the optimal leading/lagging interaction, does not affect the results of these analyses. Assuming the activities of both regions are better aligned at some unknown ground-truth lead/lag time, I would expect to see a peak somewhere in the range examined, as is nicely shown when running the same analyses on a single region's activity. If the activities are indeed aligned at zero, without a clear leading/lagging interaction, but the results remain similar when shifting the activities of one region compared to the other, the interpretation of these analyses is not clear.

Reviewer #2 (Public review):

Summary:

While technical advances have enabled large-scale, multi-site neural recordings, characterizing inter-regional communication and its behavioral relevance remains challenging due to intrinsic properties of the brain such as shared inputs, network complexity, and external noise. This work by Saiki-Ishkawa et al. examines the functional hierarchy between premotor (PM) and primary motor (M1) cortices in mice during a directional reaching task. The authors find some evidence consistent with an asymmetric reciprocal influence between the regions, but overall, activity patterns were highly similar and equally predictive of one another. These results suggest that motor cortical hierarchy, though present, is not fully reflected in firing patterns alone.

Strengths:

Inferring functional hierarchies between brain regions, given the complexity of reciprocal and local connectivity, dynamic interactions, and the influence of both shared and independent external inputs, is a challenging task. It requires careful analysis of simultaneous recording data, combined with cross-validation across multiple metrics, to accurately assess the functional relationships between regions. The authors have generated a valuable dataset simultaneously recording from both regions at scale from mice performing a cortex-dependent directional reaching task.

Using electrophysiological and silencing data, the authors found evidence supporting the traditionally assumed asymmetric influence from PM to M1. While earlier studies inferred a functional hierarchy based on partial temporal relationships in firing patterns, the authors applied a series of complementary analyses to rigorously test this hierarchy at both individual neuron and population levels, with robust statistical validation of significance.

In addition, recording combined with brief optogenetic silencing of the other region allowed authors to infer the asymmetric functional influence in a more causal manner. This experiment is well designed to focus on the effect of inactivation manifesting through oligosynaptic connections to support the existence of a premotor to primary motor functional hierarchy.

Subsequent analyses revealed a more complex picture. CCA, PLS, and three measures of predictivity (Granger causality, transfer entropy, and convergent cross-mapping) emphasized similarities in firing patterns and cross-region predictability. However, DLAG suggested an imbalance, with RFA capturing CFA variance at a negative time lag, indicating that RFA 'leads' CFA. Taken together these results provide useful insights for current studies of functional hierarchy about potential limitations in inferring hierarchy solely based on firing rates.

While I would detail some questions and issues on specifics of data analyses and modeling below, I appreciate the authors' effort in training RNNs that match some behavioral and recorded neural activity patterns including the inactivation result. The authors point out two components that can determine the across-region influence - 1) the amount of inputs received and 2) the dependence on across-region input, i.e., the relative importance of local dynamics, providing useful insights in inferring functional relationships across regions.

Weaknesses:

(1) Trial-averaging was applied in CCA and PLS analyses. While trial-averaging can be appropriate in certain cases, it leads to the loss of trial-to-trial variance, potentially inflating the perceived similarities between the activity in the two regions (Figure 4). Do authors observe comparable degrees of similarity, e.g., variance explained by canonical variables? Also, the authors report conflicting findings regarding the temporal relationship between RFA and CFA when using CCA/PLS versus DLAG. Could this discrepancy be due to the use of trial-averaging in former analyses but not in the latter?

(2) A key strength of the current study is the precise tracking of forelimb muscle activity during a complex motor task involving reaching for four different targets. This rich behavioral data is rarely collected in mice and offers a valuable opportunity to investigate the behavioral relevance of the PM-M1 functional interaction, yet little has been done to explore this aspect in depth. For example, single-trial time courses of inter-regional latent variables acquired from DLAG analysis can be correlated with single-trial muscle activity and/or reach trajectories to examine the behavioral relevance of inter-regional dynamics. Namely, can trial-by-trial change in inter-regional dynamics explain behavioral variability across trials and/or targets? Does the inter-areal interaction change in error trials? Furthermore, the authors could quantify the relative contribution of across-area versus within-area dynamics to behavioral variability. It would also be interesting to assess the degree to which across-area and within-area dynamics are correlated. Specifically, can across-area dynamics vary independently from within-area dynamics across trials, potentially operating through a distinct communication subspace?

(3) While network modeling of RFA and CFA activity captured some aspects of behavioral and neural data, I wonder if certain findings such as the connection weight distribution (Figure 7C), across-region input (Figure 7F), and the within-region weights (Figure 7G), primarily resulted from fitting the different overall firing rates between the two regions with CFA exhibiting higher average firing rates. Did the authors account for this firing rate disparity when training the RNNs?

(4) Another way to assess the functional hierarchy is by comparing the time courses of movement representation between the two regions. For example, a linear decoder could be used to compare the amount of information about muscle activity and/or target location as well as time courses thereof between the two regions. This approach is advantageous because it incorporates behavior rather than focusing solely on neural activity. Since one of the main claims of this study is the limitation of inferring functional hierarchy from firing rate data alone, the authors should use the behavior as a lens for examining inter-areal interactions.

Reviewer #3 (Public review):

This study investigates how two cortical regions that are central to the study of rodent motor control (rostral forelimb area, RFA, and caudal forelimb area, CFA) interact during directional forelimb reaching in mice. The authors investigate this interaction using
(1) optogenetic manipulations in one area while recording extracellularly from the other,
(2) statistical analyses of simultaneous CFA/RFA extracellular recordings, and
(3) network modeling.
The authors provide solid evidence that asymmetry between RFA and CFA can be observed, although such asymmetry is only observed in certain experimental and analytical contexts.

The authors find asymmetry when applying optogenetic perturbations, reporting a greater impact of RFA inactivation on CFA activity than vice-versa. The authors then investigate asymmetry in endogenous activity during forelimb movements and find asymmetry with some analytical methods but not others. Asymmetry was observed in the onset timing of movement-related deviations of local latent components with RFA leading CFA (computed with PCA) and in a relatively higher proportion and importance of cross-area latent components with RFA leading than CFA leading (computed with DLAG). However, no asymmetry was observed using several other methods that compute cross-area latent dynamics, nor with methods computed on individual neuron pairs across regions. The authors follow up this experimental work by developing a two-area model with asymmetric dependence on cross-area input. This model is used to show that differences in local connectivity can drive asymmetry between two areas with equal amounts of across-region input.

Overall, this work provides a useful demonstration that different cross-area analysis methods result in different conclusions regarding asymmetric interactions between brain areas and suggests careful consideration of methods when analyzing such networks is critical. A deeper examination of why different analytical methods result in observed asymmetry or no asymmetry, analyses that specifically examine neural dynamics informative about details of the movement, or a biological investigation of the hypothesis provided by the model would provide greater clarity regarding the interaction between RFA and CFA.

Strengths:

The authors are rigorous in their experimental and analytical methods, carefully monitoring the impact of their perturbations with simultaneous recordings, and providing valid controls for their analytical methods. They cite relevant previous literature that largely agrees with the current work, highlighting the continued ambiguity regarding the extent to which there exists an asymmetry in endogenous activity between RFA and CFA.

A strength of the paper is the evidence for asymmetry provided by optogenetic manipulation. They show that RFA inactivation causes a greater absolute difference in muscle activity than CFA interaction (deviations begin 25-50 ms after laser onset, Figure 1) and that RFA inactivation causes a relatively larger decrease in CFA firing rate than CFA inactivation causes in RFA (deviations begin <25ms after laser onset, Figure 3). The timescales of these changes provide solid evidence for an asymmetry in the impact of inactivating RFA/CFA on the other region that could not be driven by differences in feedback from disrupted movement (which would appear with a ~50ms delay).

The authors also utilize a range of different analytical methods, showing an interesting difference between some population-based methods (PCA, DLAG) that observe asymmetry, and single neuron pair methods (granger causality, transfer entropy, and convergent cross mapping) that do not. Moreover, the modeling work presents an interesting potential cause of "hierarchy" or "asymmetry" between brain areas: local connectivity that impacts dependence on across-region input, rather than the amount of across-region input actually present.

Weaknesses:

There is no attempt to examine neural dynamics that are specifically relevant/informative about the details of the ongoing forelimb movement (e.g., kinematics, reach direction). Thus, it may be preemptive to claim that firing patterns alone do not reflect functional influence between RFA/CFA. For example, given evidence that the largest component of motor cortical activity doesn't reflect details of ongoing movement (reach direction or path; Kaufman, et al. PMID: 27761519) and that the analytical tools the authors use likely isolate this component (PCA, CCA), it may not be surprising that CFA and RFA do not show asymmetry if such asymmetry is related to the control of movement details. An asymmetry may still exist in the components of neural activity that encode information about movement details, and thus it may be necessary to isolate and examine the interaction of behaviorally-relevant dynamics (e.g., Sani, et al. PMID: 33169030).

The idea that local circuit dynamics play a central role in determining the asymmetry between RFA and CFA is not supported by experimental data in this paper. The plausibility of this hypothesis is supported by the model but is not explored in any analyses of the experimental data collected. Given the focus on this idea in the discussion, further experimental investigation is warranted.

Author response:

We thank the reviewers for their constructive feedback here, which will both improve the present manuscript, and help us update our approach as we continue to examine interregional interactions in the motor system. Below we address the concerns raised in the Public Reviews.

Public Reviews:

Reviewer #1 (Public review):

This study examined the interaction between two key cortical regions in the mouse brain involved in goal-directed movements, the rostral forelimb area (RFA) - considered a premotor region involved in movement planning, and the caudal forelimb area (CFA) - considered a primary motor region that more directly influences movement execution. The authors ask whether there exists a hierarchical interaction between these regions, as previously hypothesized, and focus on a

specific definition of hierarchy - examining whether the neural activity in the premotor region exerts a larger functional influence on the activity in the primary motor area than vice versa. They examine this question using advanced experimental and analytical methods, including localized optogenetic manipulation of neural activity in either region while measuring both the neural activity in the other region and EMG signals from several muscles involved in the reaching movement, as well as simultaneous electrophysiology recordings from both regions in a separate cohort of animals.

The findings presented show that localized optogenetic manipulation of neural activity in either RFA or CFA resulted in similarly short-latency changes in the muscle output and in firing rate changes in the other region. However, perturbation of RFA led to a larger absolute change in the neural activity of CFA neurons. The authors interpret these findings as evidence for reciprocal, but asymmetrical, influence between the regions, suggesting some degree of hierarchy in which RFA has a greater effect on the neural activity in CFA. They go on to examine whether this asymmetry can also be observed in simultaneously recorded neural activity patterns from both regions. They use multiple advanced analysis methods that either identify latent components at the population level or measure the predictability of firing rates of single neurons in one region using firing rates of single neurons in the other region. Interestingly, the main finding across these analyses seems to be that both regions share highly similar components that capture a high degree of variability of the neural activity patterns in each region. Single units' activity from either region could be predicted to a similar degree from the activity of single units in the other region, without a clear division into a leading area and a lagging area, as one might expect to find in a simple hierarchical interaction. However, the authors find some evidence showing a slight bias towards leading activity in RFA. Using a two-region neural network model that is fit to the summed neural activity recorded in the different experiments and to the summed muscle output, the authors show that a network with constrained (balanced) weights between the regions can still output the observed measured activities and the observed asymmetrical effects of the optogenetic manipulations, by having different within-region local weights. These results put into question whether previous and current findings that demonstrate asymmetry in the output of regions can be interpreted as evidence for asymmetrical (and thus hierarchical) inputs between regions, emphasizing the challenges in studying interactions between any brain regions.

Strengths:

The experiments and analyses performed in this study are comprehensive and provide a detailed examination and comparison of neural activity recorded simultaneously using dense electrophysiology probes from two main motor regions that have been the focus of studies examining goal-directed movements. The findings showing reciprocal effects from each region to the other, similar short-latency modulation of muscle output by both regions, and similarity of neural activity patterns without a clear lead/lag interaction, are convincing and add to the growing body of evidence that highlight the complexity of the interactions between multiple regions in the motor system and go against a simple feedforward-like network and dynamics. The neural network model complements these findings and adds an important demonstration that the observed asymmetry can, in theory, also arise from differences in local recurrent connections and not necessarily from different input projections from one region to the other. This sheds an important light on the multiple factors that should be considered when studying the interaction between any two brain regions, with a specific emphasis on the role of local recurrent connections, that should be of interest to the general neuroscience community.

Weaknesses:

While the similarity of the activity patterns across regions and lack of a clear leading/lagging interaction are interesting observations that are mostly supported by the findings presented (however, see comment below for lack of clarity in CCA/PLS analyses), the main question posed by the authors - whether there exists an endogenous hierarchical interaction between RFA and CFA - seems to be left largely open.

The authors note that there is currently no clear evidence of asymmetrical reciprocal influence between naturally occurring neural activity patterns of the two regions, as previous attempts have used non-natural electrical stimulation, lesions, or pharmacological inactivation. The use of acute optogenetic perturbations does not seem to be vastly different in that aspect, as it is a non-natural stimulation of inhibitory interneurons that abruptly perturbs the ongoing dynamics.

We do believe that our optogenetic inactivation identifies a causal interaction between the endogenous activity patterns in the excitatory projection neurons that are largely silenced, and the endogenous activity that is affected in a downstream region. To clarify, the effect in the downstream region results directly from the silencing of activity in the excitatory projection neurons that connect RFA and CFA.

Here we have performed a causal intervention common in biology: a loss-of-function experiment. Such experiments generally reveal that a causal interaction of some sort is present, but often do not clarify much about the nature of the interaction, as is true in our case. By showing that the silencing of endogenous activity in one motor cortical region causes a significant change to the endogenous activity in another, we establish a causal relationship between these activity patterns.

This is analogous to knocking out the gene for a transcription factor and observing causal effects on the expression of other genes that depends on it.

Moreover, our experiments are, to our knowledge, the first that localize a causal relationship to endogenous activity in motor cortical regions at a particular point during motor behavior. Stimulation experiments generate spiking in excitatory projection neurons that is not endogenous. Lesion and pharmacological or chemogenetic inactivation have long-lasting effects, and so their consequences on firing in other regions cannot be attributed to a short-latency influence of activity at a particular point during movement. Moreover, the involvement of motor cortex in motor learning and movement preparation/initiation complicates the interpretation of these consequences vis-à-vis movement execution, as disturbance to processes on which execution depends can impede execution itself.

That said, we would agree that the form of the causal interaction between RFA and CFA remains largely unaddressed by our results. These results do not expose how the silenced activity patterns affect activity in the downstream region, just as transcription factor gene knockouts do not expose how the effect on transcription occurs. To show evidence for specific interaction dynamics between RFA and CFA, a different sort of experiment would be necessary. See Jazayeri and Afraz, Neuron, 2017 for more on this issue.

Furthermore, the main finding that supports a hierarchical interaction is a difference in the absolute change of firing rates as a result of the optogenetic perturbation, a finding that is based on a small number of animals (N = 3 in each experimental group), and one which may be difficult to interpret.

Though N = 3 in this case, we do show statistical significance. Moreover, using three replicates is not uncommon in biological experiments that require a large technical investment, including those in rodents.

As the authors nicely demonstrate in their neural network model, the two regions may differ in the strength of local within-region inhibitory connections. Could this theoretically also lead to a difference in the effect of the artificial light stimulation of the inhibitory interneurons on the local population of excitatory projection neurons, driving an asymmetrical effect on the downstream region?

We (Miri et al., Neuron, 2017) and others (Guo et al., Neuron, 2014) have shown that the effect of this inactivation on excitatory neurons in CFA is a near-complete silencing (90-95% within 20 ms). Thus there is not much room for the effects on projection neurons in RFA to be much larger. As part of other work currently in review, we have verified that the effects on RFA projection neuron firing are not larger.

Moreover, the manipulation was performed upon the beginning of the reaching movement, while the premotor region is often hypothesized to exert its main control during movement preparation, and thus possibly show greater modulation during that movement epoch. It is not clear if the observed difference in absolute change is dependent on the chosen time of optogenetic stimulation and if this effect is a general effect that will hold if the stimulation is delivered during different movement epochs, such as during movement preparation.

We agree that the dependence of RFA-CFA interactions on movement phase would be interesting to address in subsequent experiments. While a strong interpretation of past lesion results might lead to a hypothesis that premotor influence on primary motor cortex is local to, or stronger during, movement preparation as opposed to execution, at present there is to our knowledge no empirical support from interventional experiments for this hypothesis. Moreover, existing results from analysis of activity in premotor and primary motor cortex have produced conflicting results on the strength of interaction between these regions during preparation. Compare for example Bachschmid-Romano et al., eLife, 2023 to Kaufman et al., Nature Neuroscience, 2014.

That said, this lesion interpretation would predict the same asymmetry we have observed from perturbations at the beginning of a reach – a larger effect of RFA on CFA than vice versa.

Another finding that is not clearly interpretable is in the analysis of the population activity using CCA and PLS. The authors show that shifting the activity of one region compared to the other, in an attempt to find the optimal leading/lagging interaction, does not affect the results of these analyses. Assuming the activities of both regions are better aligned at some unknown groundtruth lead/lag time, I would expect to see a peak somewhere in the range examined, as is nicely shown when running the same analyses on a single region's activity. If the activities are indeed aligned at zero, without a clear leading/lagging interaction, but the results remain similar when shifting the activities of one region compared to the other, the interpretation of these analyses is not clear.

Our results in this case were definitely surprising. Many share the intuition that there should be a lag at which the correlations in activity between connected regions will be strongest. Similarity in alignment across lags might be expected if communication between regions occurs over a range of latencies as a result of dependence on a broad diversity of synaptic paths that connect neurons. In the Discussion, we offer an explanation of how to reconcile these findings with the seemingly different picture presented by DLAG.

Reviewer #2 (Public review):

Summary:

While technical advances have enabled large-scale, multi-site neural recordings, characterizing inter-regional communication and its behavioral relevance remains challenging due to intrinsic properties of the brain such as shared inputs, network complexity, and external noise. This work by Saiki-Ishikawa et al. examines the functional hierarchy between premotor (PM) and primary motor (M1) cortices in mice during a directional reaching task. The authors find some evidence consistent with an asymmetric reciprocal influence between the regions, but overall, activity patterns were highly similar and equally predictive of one another. These results suggest that motor cortical hierarchy, though present, is not fully reflected in firing patterns alone.

Strengths:

Inferring functional hierarchies between brain regions, given the complexity of reciprocal and local connectivity, dynamic interactions, and the influence of both shared and independent external inputs, is a challenging task. It requires careful analysis of simultaneous recording data, combined with cross-validation across multiple metrics, to accurately assess the functional relationships between regions. The authors have generated a valuable dataset simultaneously recording from both regions at scale from mice performing a cortex-dependent directional reaching task.

Using electrophysiological and silencing data, the authors found evidence supporting the traditionally assumed asymmetric influence from PM to M1. While earlier studies inferred a functional hierarchy based on partial temporal relationships in firing patterns, the authors applied a series of complementary analyses to rigorously test this hierarchy at both individual neuron and population levels, with robust statistical validation of significance.

In addition, recording combined with brief optogenetic silencing of the other region allowed authors to infer the asymmetric functional influence in a more causal manner. This experiment is well designed to focus on the effect of inactivation manifesting through oligosynaptic connections to support the existence of a premotor to primary motor functional hierarchy.

Subsequent analyses revealed a more complex picture. CCA, PLS, and three measures of predictivity (Granger causality, transfer entropy, and convergent cross-mapping) emphasized similarities in firing patterns and cross-region predictability. However, DLAG suggested an imbalance, with RFA capturing CFA variance at a negative time lag, indicating that RFA 'leads' CFA. Taken together these results provide useful insights for current studies of functional hierarchy about potential limitations in inferring hierarchy solely based on firing rates.

While I would detail some questions and issues on specifics of data analyses and modeling below, I appreciate the authors' effort in training RNNs that match some behavioral and recorded neural activity patterns including the inactivation result. The authors point out two components that can determine the across-region influence - 1) the amount of inputs received and 2) the dependence on across-region input, i.e., the relative importance of local dynamics, providing useful insights in inferring functional relationships across regions.

Weaknesses:

(1) Trial-averaging was applied in CCA and PLS analyses. While trial-averaging can be appropriate in certain cases, it leads to the loss of trial-to-trial variance, potentially inflating the perceived similarities between the activity in the two regions (Figure 4). Do authors observe comparable degrees of similarity, e.g., variance explained by canonical variables? Also, the authors report conflicting findings regarding the temporal relationship between RFA and CFA when using CCA/PLS versus DLAG. Could this discrepancy be due to the use of trial-averaging in former analyses but not in the latter?

We certainly agree that the similarity in firing patterns is higher in trial averages than on single trials, given the variation in single-neuron firing patterns across trials. Here, we were trying to examine the similarity of activity variance that is clearly movement dependent, as trial averages are, and to use an approach that mirrors those applied in much of the existing literature. We would also agree that there is more that can be learned about interactions from trial-by-trial analysis.

It is possible that the activity components identified by DLAG as being asymmetric somehow are not reflected strongly in trial averages. In our Discussion we offer another potential explanation related to the differences in what is calculated in DLAG and CCA/PLS.

We also note here that all of the firing pattern predictivity analysis we report (Figure 6) was done on single-trial data, and in all cases the predictivity was symmetric. Thus, our results in aggregate are not consistent with symmetry purely being an artifact of trial averaging.

(2) A key strength of the current study is the precise tracking of forelimb muscle activity during a complex motor task involving reaching for four different targets. This rich behavioral data is rarely collected in mice and offers a valuable opportunity to investigate the behavioral relevance of the PM-M1 functional interaction, yet little has been done to explore this aspect in depth. For example, single-trial time courses of inter-regional latent variables acquired from DLAG analysis can be correlated with single-trial muscle activity and/or reach trajectories to examine the behavioral relevance of inter-regional dynamics. Namely, can trial-by-trial change in inter-regional dynamics explain behavioral variability across trials and/or targets? Does the inter-areal interaction change in error trials? Furthermore, the authors could quantify the relative contribution of across-area versus within-area dynamics to behavioral variability. It would also be interesting to assess the degree to which across-area and within-area dynamics are correlated. Specifically, can acrossarea dynamics vary independently from within-area dynamics across trials, potentially operating through a distinct communication subspace?

These are all very interesting questions. Our study does not attempt to parse activity into components predictive of muscle activity and others that may reflect other functions. Distinct components of RFA and CFA activity may be involved in distinct interactions between them.

(3) While network modeling of RFA and CFA activity captured some aspects of behavioral and neural data, I wonder if certain findings such as the connection weight distribution (Figure 7C), across-region input (Figure 7F), and the within-region weights (Figure 7G), primarily resulted from fitting the different overall firing rates between the two regions with CFA exhibiting higher average firing rates. Did the authors account for this firing rate disparity when training the RNNs?

The key comparison in Figure 7 is shown in 7F, where the firing rates are accounted for in calculating the across-region input strength. Equalizing the firing rates in RFA and CFA would effectively increase RFA rates. If the mean firing rates in each region were appreciably dependent on across-region inputs, we would then expect an off-setting change in the RFA→CFA weights, such that the RFA→CFA distributions in 7F would stay the same. We would also expect the CFA→RFA weights would increase, since RFA neurons would need more input. This would shift the CFA→RFA (blue) distributions up. Thus, if anything, the key difference in this panel would only get larger.

We also generally feel that it is a better approach to fit the actual firing rates, rather than normalizing, since normalizing the firing rates would take us further from the actual biology, not closer.

(4) Another way to assess the functional hierarchy is by comparing the time courses of movement representation between the two regions. For example, a linear decoder could be used to compare the amount of information about muscle activity and/or target location as well as time courses thereof between the two regions. This approach is advantageous because it incorporates behavior rather than focusing solely on neural activity. Since one of the main claims of this study is the limitation of inferring functional hierarchy from firing rate data alone, the authors should use the behavior as a lens for examining inter-areal interactions.

As we state above, we agree that examining interactions specific to movement-related activity components could be illuminating. Since it remains a challenge to rigorously identify a subset of activity patterns specifically related to driving muscle activity, any such analysis would involve an additional assumption. It remains unclear how well the motor cortical activity that decoders use for predicting muscle activity matches the motor cortical activity that actually drives muscle activity in situ.

Reviewer #3 (Public review):

This study investigates how two cortical regions that are central to the study of rodent motor control (rostral forelimb area, RFA, and caudal forelimb area, CFA) interact during directional forelimb reaching in mice. The authors investigate this interaction using

(1) optogenetic manipulations in one area while recording extracellularly from the other,

(2) statistical analyses of simultaneous CFA/RFA extracellular recordings, and

(3) network modeling.

The authors provide solid evidence that asymmetry between RFA and CFA can be observed, although such asymmetry is only observed in certain experimental and analytical contexts.

The authors find asymmetry when applying optogenetic perturbations, reporting a greater impact of RFA inactivation on CFA activity than vice-versa. The authors then investigate asymmetry in endogenous activity during forelimb movements and find asymmetry with some analytical methods but not others. Asymmetry was observed in the onset timing of movement-related deviations of local latent components with RFA leading CFA (computed with PCA) and in a relatively higher proportion and importance of cross-area latent components with RFA leading than CFA leading (computed with DLAG). However, no asymmetry was observed using several other methods that compute cross-area latent dynamics, nor with methods computed on individual neuron pairs across regions. The authors follow up this experimental work by developing a twoarea model with asymmetric dependence on cross-area input. This model is used to show that differences in local connectivity can drive asymmetry between two areas with equal amounts of across-region input.

Overall, this work provides a useful demonstration that different cross-area analysis methods result in different conclusions regarding asymmetric interactions between brain areas and suggests careful consideration of methods when analyzing such networks is critical. A deeper examination of why different analytical methods result in observed asymmetry or no asymmetry, analyses that specifically examine neural dynamics informative about details of the movement, or a biological investigation of the hypothesis provided by the model would provide greater clarity regarding the interaction between RFA and CFA.

Strengths:

The authors are rigorous in their experimental and analytical methods, carefully monitoring the impact of their perturbations with simultaneous recordings, and providing valid controls for their analytical methods. They cite relevant previous literature that largely agrees with the current work, highlighting the continued ambiguity regarding the extent to which there exists an asymmetry in endogenous activity between RFA and CFA.

A strength of the paper is the evidence for asymmetry provided by optogenetic manipulation. They show that RFA inactivation causes a greater absolute difference in muscle activity than CFA interaction (deviations begin 25-50 ms after laser onset, Figure 1) and that RFA inactivation causes a relatively larger decrease in CFA firing rate than CFA inactivation causes in RFA (deviations begin <25ms after laser onset, Figure 3). The timescales of these changes provide solid evidence for an asymmetry in the impact of inactivating RFA/CFA on the other region that could not be driven by differences in feedback from disrupted movement (which would appear with a ~50ms delay).

The authors also utilize a range of different analytical methods, showing an interesting difference between some population-based methods (PCA, DLAG) that observe asymmetry, and single neuron pair methods (granger causality, transfer entropy, and convergent cross mapping) that do not. Moreover, the modeling work presents an interesting potential cause of "hierarchy" or "asymmetry" between brain areas: local connectivity that impacts dependence on across-region input, rather than the amount of across-region input actually present.

Weaknesses:

There is no attempt to examine neural dynamics that are specifically relevant/informative about the details of the ongoing forelimb movement (e.g., kinematics, reach direction). Thus, it may be preemptive to claim that firing patterns alone do not reflect functional influence between RFA/CFA. For example, given evidence that the largest component of motor cortical activity doesn't reflect details of ongoing movement (reach direction or path; Kaufman, et al. PMID: 27761519) and that the analytical tools the authors use likely isolate this component (PCA, CCA), it may not be surprising that CFA and RFA do not show asymmetry if such asymmetry is related to the control of movement details.

An asymmetry may still exist in the components of neural activity that encode information about movement details, and thus it may be necessary to isolate and examine the interaction of behaviorally-relevant dynamics (e.g., Sani, et al. PMID: 33169030).

To clarify, we are not claiming that firing patterns in no way reflect the asymmetric functional influence that we demonstrate with optogenetic inactivation. Instead, we show that certain types of analysis we might expect to reflect such influence, in fact, do not. Indeed, DLAG did exhibit asymmetries that matched those seen in functional influence (at least qualitatively), though other methods we applied did not.

As we state above, we do think that there is more that can be gleaned by looking at influence specifically in terms of activity related to movement. However, if we did find that movement-related activity exhibited an asymmetry matching that of functional influence in cases where overall activity exhibited symmetry, our results imply that the activity not related to movement would exhibit an opposite asymmetry, such that the overall balance is symmetric. This would itself be surprising. We also note that the components identified by CCA and PLS show substantial variation across reach targets, indicating that they are not only reflecting condition-invariant components. These analyses used over 90% of the total activity variance, suggesting that both condition-dependent and condition-invariant components are included.

The idea that local circuit dynamics play a central role in determining the asymmetry between RFA and CFA is not supported by experimental data in this paper. The plausibility of this hypothesis is supported by the model but is not explored in any analyses of the experimental data collected. Given the focus on this idea in the discussion, further experimental investigation is warranted.

While we do not provide experimental support for this hypothesis, the data we present also do not contradict this hypothesis. Here we used modeling as it is often used – to capture experimental results and generate hypotheses about potential explanations. We feel that our Discussion makes clear where the hypothesis derives from and does not misrepresent the lack of experimental support. We expect readers will take our engagement with this hypothesis with the appropriate grain of salt. The imaginable experiments to support such a hypothesis would constitute another substantial study requiring numerous controls – a whole other paper in itself.