Motor Cortex Embeds Muscle-like Commands in an Untangled Population Response

Abstract

Primate motor cortex projects to spinal interneurons and motoneurons, suggesting that motor cortex activity may be dominated by muscle-like commands. Observations during reaching lend support to this view, but evidence remains ambiguous and much debated. To provide a different perspective, we employed a novel behavioral paradigm that facilitates comparison between time-evolving neural and muscle activity. We found that single motor cortex neurons displayed many muscle-like properties, but the structure of population activity was not muscle-like. Unlike muscle activity, neural activity was structured to avoid "tangling": moments where similar activity patterns led to dissimilar future patterns. Avoidance of tangling was present across tasks and species. Network models revealed a potential reason for this consistent feature: low tangling confers noise robustness. Finally, we were able to predict motor cortex activity from muscle activity by leveraging the hypothesis that muscle-like commands are embedded in additional structure that yields low tangling.

Keywords: motor control; motor cortex; movement generation; neural dynamics; neural network; pattern generation; rhythmic movement.

Figure 1

Behavior, neural activity, and muscle activity during the cycling task. A. Schematic illustration of the task during forward cycling. A lush green landscape indicated that progress from one target to the next required cycling in the ‘forward’ direction, as indicated. B. Same for backward cycling. An arid orange landscape indicated that progress required cycling in the opposite, ‘backward’ direction. C. Behavioral data and spikes for individual trials during an example neural recording session. Data are shown for a single condition: forward / seven-cycle / bottom-start (monkey C). Trials are aligned to movement onset, and ordered from fastest to slowest. D. Behavioral data and raw EMG recorded from the trapezius for a single condition: backward / seven-cycle / bottom-start (monkey D). E. Behavioral and neural data from C after temporal scaling to align trials. F. Behavioral and EMG data from D after temporal scaling. G. Trial-averaged and filtered (25 ms Gaussian kernel) neural activity for the example neuron in C,E. Flanking envelopes show standard error of the mean (SEM; often these were no larger than the trace width). The shaded rectangle indicates the interval during which the monkey was actively cycling between targets. Background shading indicates vertical hand position: lightest at top and darkest at bottom. Small tick-marks indicate the completion of each cycle. H. Rectified, filtered (25 ms Gaussian kernel) and trial-averaged muscle activity for the example in D,F.

Figure 2

A. Vertical hand velocity, averaged across trials from a typical session (monkey C). Same format as in Fig 1G. Data are shown for seven-cycle movements for forward cycling (green, left column) and backward cycling (red, right column), and for both top-start and bottom-start movements. The latter have been shifted a half-cycle to visually align hand position between top- and bottom-start movements (light shading indicates the top of each cycle). Flanking traces show the SEM but are generally narrower than the trace width. B. Horizontal hand velocity from the same session, plotted using the same format. C. Activity of brachialis (monkey C) plotted using the same format. Flanking traces (barely visible) show the SEM. D. Activity of the medial triceps (monkey C). E. Activity of the trapezius (monkey D).

Figure 3

Firing rates of six example neurons recorded from motor cortex. Same format as for Figure 2. Flanking envelopes show the SEM. Cell names indicate area (M1 versus PMd) and monkey (C and D). All vertical calibrations are 40 spikes/s.

Figure 4

Visualization of population structure via PCA. A. PCA operates on a population of responses (six of 103 neurons are shown, monkey D). Green traces highlight the middle three ‘steady state’ cycles, which were used to find the PCs for the present analyses (subsequent analyses consider all times for all conditions). Data are shown for only one condition – forward cycling starting at the bottom – but PCs were computed based on both forward and backward cycling and both top- and bottom-start conditions. B. Projections onto the PCs capture the dominant signals in the data. Orange dashed lines highlight the ‘neural state’ at a single time. That state can be summarized either using the full vector of firing rates (A) or a reduced-dimensional vector containing the values of the projections onto the top PCs (B). C. Neural trajectories revealed by plotting the projection onto the second PC versus the projection onto the first PC (~35% of the total variance is captured in these two dimensions). This is equivalent to projecting the 103-dimensional neural trajectory onto the two dimensions defined by the PCs. Orange dot corresponds to the neural state at the same time as in A and B. D. Muscle trajectories captured by projecting the muscle population response onto its first two PCs (monkey D). Trajectories are shown for forward cycling (green) and backward cycling (red). Each panel overlays trajectories for top-start and bottom-start conditions (lighter and darker colored traces respectively). The same PCs were used to project data for both forward and backward cycling. E. Corresponding neural trajectories for the same monkey and conditions as in D. F. Corresponding hand-velocity trajectories. Trajectories were produced by applying PCA to horizontal and hand velocity traces across multiple sessions. This is exceedingly similar (but for a change of axes) to simply plotting average vertical velocity versus average horizontal velocity. G,H,I. PCA-based muscle, neural, and velocity trajectories for monkey C. Same format as D,E,F, but forward and backward cycling are overlaid.

Figure 5

Illustration and validation of the tangling metric. A. Muscle trajectories during the middle five cycles for two conditions: seven-cycle / bottom-start / forward (green) and seven-cycle / bottom-start / backward (red). Arrows illustrate a pair of highly tangled states. Arrows point in the direction of the derivative (the path of the trajectory). The state at time t is maximally tangled with the state at time t₁′, yielding Q_EMG (t)=3898. Tangling was computed in eight dimensions. B. Same as A but for neural trajectories. The state at time t becomes maximally tangled with the state at time t₂′, but this maximum is lower than for the muscles. C. Same but for network trajectories from an artificial recurrent network. The network was trained to produce the activity of all muscles for the times / conditions illustrated in A. D. Scatterplot, with one point per time/condition, of network tangling versus muscle tangling. Orange arrow denotes tangling for time t, corresponding to the time for which tangling was assessed in panels A and C. E. The consistency of the effect in panel D is demonstrated across 247/216 networks, each trained to produce the pattern of muscle activity from monkey D (red) or monkey C (blue). Tangling is summarized by the 90^th percentile value (which highlights how high tangling can become). Lines denote 90^th percentile tangling for the empirical muscle populations.

Figure 6

Trajectory tangling for multiple datasets. A. Scatterplot of motor-cortex-trajectory tangling versus muscle-trajectory tangling (monkey D). Each point shows tangling for one moment (one time during one condition). Points are show for all times during movement (sampled every 25 ms) for all twenty conditions. Blue line indicates unity slope. Gray / orange triangles indicate 90% percentile tangling. B. Same as A but for monkey C. C. Neural versus muscle populations could be distinguished based on tangling. For a given number of recordings, we drew that many neurons and muscles and computed tangling for each subpopulation. 500 such draws were made for each subpopulation size. The vertical axis gives the percentage of instances where the neural sub-population was correctly identified based on lower tangling. Flanking standard errors are based on binomial statistics. D. Tangling for S1 neural population trajectories versus muscle trajectories (monkey D). E. Scatterplot of motor-cortex-trajectory tangling versus muscle-trajectory tangling during reaching (monkey A). Each point corresponds to one time during one of eight conditions. F. Same as E but for monkey B. G. Scatterplot of motor-cortex-trajectory tangling versus muscle-trajectory tangling in three mice (black, blue, and green symbols) during both locomotion and lever pulling. Illustration in inset by E. Daubert. H. Comparison of tangling in motor cortex and visual cortex. Motor cortex data are from the cycling task as in panels A and B. V1 data were recorded using natural scenes. Because V1 data contains no corresponding muscle activity, tangling is quantified by the 90^th percentile values. Error bars show the standard error computed via bootstrap: the distribution of tangling values was resampled 200 times, and we computing the sampling distribution of the 90^th percentile values.

Figure 7

Leveraging the observation of low tangling to predict the neural population response. A. Illustration of how the same output can be embedded in a larger trajectory with varying degrees of tangling. Top gray traces: A desired two-dimensional output [cos t; sin 2t] Plotted in state space, the output trajectory is a figure eight, and contains a central point that is maximally tangled. Adding a third dimension (βsin t) reduces tangling at that central point. The figure-eight can still be decoded via projection onto two dimensions, in which case the third dimension falls in the null-space of the decode. B. Noise robustness of recurrent networks trained to follow the internal trajectory [cos t; sin 2t; βsin t]. By varying β, we trained multiple networks that could all produce the same figure-eight output, but had varying degrees of trajectory tangling. For each network, noise tolerance was the largest magnitude of state noise for which the network still produced the figure-eight output. For each value of β we trained 20 networks, each with a different random weight initialization. Error bars show the SEM across such networks. C. Similarity of the predicted and empirical motor-cortex population responses (monkey D). Blue trace: prediction yielded by optimizing the cost function in Equation 2. Light blue dot indicates similarity at initialization. Dashed lines show benchmarks as described in the text. Gray shading indicates 95% confidence interval on the upper benchmark, computed across multiple random divisions of the population. D. Same but for monkey C. E. Projection of the predicted population response (after optimization was complete) onto the top two principal components. Data are for monkey D. Green / red traces show trajectories for three cycles of forward / backward cycling respectively. F. Same but for monkey C.

Figure 8

Muscle-like signals coexist with signals that contribute to low tangling. Data are for monkey D. A. Three-dimensional subspace capturing trajectories that encode trapezius activity; i.e., can be linearly read out to approximate trapezius activity. Blue arrow indicates the readout direction, defined by the weights identified via linear regression. Axes correspond to the first two PCs and a third dimension that ensures the space spans the readout direction. Trajectories are shown for four conditions: forward (green) and backward (red) seven-cycle movements, starting at the top and bottom (lighter and darker traces). Lighter ‘shadow’ traces at bottom show the projection onto just the first two PCs (perspective has been added). B. Projections, for the four conditions plotted in A, onto the readout direction. Thin black trace plots the true activity of the trapezius. Axis spans the time of movement. C,D. Same as A,B but for the medial biceps. Only the third (vertical) axis is different. E,F. Same but for the medial triceps.