Reorganization between preparatory and movement population responses in motor cortex

Abstract

Neural populations can change the computation they perform on very short timescales. Although such flexibility is common, the underlying computational strategies at the population level remain unknown. To address this gap, we examined population responses in motor cortex during reach preparation and movement. We found that there exist exclusive and orthogonal population-level subspaces dedicated to preparatory and movement computations. This orthogonality yielded a reorganization in response correlations: the set of neurons with shared response properties changed completely between preparation and movement. Thus, the same neural population acts, at different times, as two separate circuits with very different properties. This finding is not predicted by existing motor cortical models, which predict overlapping preparation-related and movement-related subspaces. Despite orthogonality, responses in the preparatory subspace were lawfully related to subsequent responses in the movement subspace. These results reveal a population-level strategy for performing separate but linked computations.

Figure 1. Illustration of neural states and across-condition correlations for three hypothetical neurons during two successive computations.

(a) Activity of three hypothetical neurons involved in the first of two successive computations. Each axis represents the firing rate of one neuron and each dot represents the neural state for one of six conditions. The activity of the three neurons occupies a subspace (green line) of the full space of possible states. The heatmap shows the cross-condition correlation matrix: large values indicate that the relevant pair of neurons has activity that covaries across conditions. (b) Population structure for the independent strategy. Responses occupy a different neural subspace from that in a and the correlation structure is changed completely. Further, there is no particular relationship between the ordering of conditions in b versus that in a. (c) Population structure for the overlapping strategy. The across-condition pattern of neural activity changes across the computations: the set of dots is now in a different order. However, the subspace occupied by neural activity remains the same and the correlation structure is thus preserved. (d) Population structure for the orthogonal-but-linked strategy. Neural activity occupies a different subspace and thus the correlation structure changes. Yet, unlike the situation in b, the ordering of conditions is lawfully related to that in a. In this example the ordering is identical, but activity is in a new subspace. (e–g) Firing rates as a function of time for neuron 2 for the three types of population structure described above. The colour of each trace indicates the condition identity. In time, the first half of each trace corresponds to the first computation and the second half corresponds to the second computation. Regardless of the type of population structure, the response of this neuron changes in complex ways from one computation to the other.

Figure 2. Task and example neurons.

(a) Events in the delayed-reach task. Monkeys made reaches to one of eight possible targets displayed on a monitor. Dashed circles (not visible to the monkey) indicate the possible reach-target locations. (b) Reach trajectories and velocity profiles for monkey B. Thick traces denote the average trajectory across all recording sessions, thin traces denote the average trajectories for 15 randomly chosen sessions. (c) Responses of four example neurons. Each trace is the trial-averaged firing rate during a reach in one of the eight directions. Trace colour indicates reach direction (shown in b). Red dot indicates target onset time. Green dot indicates movement onset time. Grey horizontal bars denote the 300ms preparation and movement epochs. Black vertical bars denote 20 spikes per sec. (d) Correlation matrices for the four example neurons during preparatory (left) and movement (right) epochs.

Figure 3. Preparatory-epoch and movement-epoch correlation structure for all neurons.

(a) Preparatory-epoch (left) and movement-epoch (right) correlation matrices for all neurons for monkey B (top) and monkey A (bottom). Each entry in the matrix gives the degree to which the response pattern was similar for the two neurons during that epoch. The order of neurons is the same for the preparatory-epoch matrix and the movement-epoch matrix. (b) The correlation for each neuron pair during the movement epoch plotted against the correlation for the same pair during the preparatory epoch. (c) Histogram of epoch-preference index, which quantifies the strength of neural activity during the preparatory epoch compared with the strength of neural activity during the movement epoch (see text). Positive values indicate that a neuron is more selective during the preparatory epoch and negative values indicate that a neuron is more selective during the movement epoch. The distributions are not significantly bimodal (Hartigan's dip test; dip statistic monkey B=0.024; P=0.89, and dip statistic monkey A=0.036; P=0.48).

Figure 4. Percentage of variance explained by preparatory and movement principal components (prep-PCs and move PCs).

(a) Percentage of preparatory-epoch data variance (red bars) and movement-epoch data variance (green bars) explained by the top ten prep-PCs. (b) Percentage of preparatory-epoch data variance and movement-epoch data variance explained by the top ten move-PCs. (c) Alignment index for neural, random and model data. For each pair, the two bars correspond to data from monkey B and A, or to simulated data sets based on real data from two monkeys. Bars labelled ‘random' correspond to the distribution of indices expected from random dimensions within the space occupied by the data. The last four pairs of bars were obtained from simulated data generated from a coding model, a pattern generator model, a non-normal RNN (RNN1) and a regularized RNN (RNN2). Stars for the neural data bars denote a significantly lower index relative to both random and to all models (P<0.001, one-tailed test). For random data and models, the bars show the median index across multiple bootstrap resamples and error bars denote the 95% confidence interval (based on the distribution obtained via bootstrap).

Figure 5. Separating preparation-related and movement-related aspects of the population response.

(a) Projections of the neural population responses onto the two-dimensional preparatory subspace (red traces) and the four-dimensional movement subspace (green traces). Light-to-dark colour shading corresponds to different reach conditions (right-to-left). (b) Percentage of variance explained by the preparatory (red) and movement (green) subspaces. The left pair of bars corresponds to variance captured during the preparatory epoch. The right pair of bars corresponds to variance captured during the movement epoch. Stars denote significantly higher variance (P<0.001, bootstrap one tailed test) with respect to random subspaces of the same dimensionality as the preparatory and movement subspaces (NS, not significant).

Figure 6. Activity in four subspaces in response to key task events.

Each trace corresponds to a different reach direction. (a) Responses during a 150 ms window beginning at target onset. Data are shown for the neural population response (monkey B) projected onto two dimensions of the preparatory subspace (top), for the neural population response projected onto two dimensions of the movement subspace (second from top), for the top two principal components of muscle activity (second from bottom) and for hand position (bottom). (b) Same as in a but for the response to the go cue (during a 250 ms window starting at the go cue and ending at approximately the onset of movement). (c) Same as in a but for a 200 ms window starting at movement onset.

Figure 7. Neural activity displays an orderly transition from the preparatory subspace to the movement subspace.

(a) Neural state trajectory during the transition from preparation to movement. Each trace plots the trajectory for one (of eight) reach directions. Axes correspond to the top preparatory dimension and the top two movement dimensions. Stars denote the neural state 200 ms before movement onset. Dotted lines denote the neural trajectories during the transition, over the next 200 ms, from the preparatory dimension to the movement dimensions. Solid lines denote the trajectories during the 50 ms following movement onset. (b) The same space as in a rotated to show only the two movement dimensions. (c) Quality of fit (R²) of the regression between the responses in the movement subspace (at the middle of movement epoch; 100 ms after movement onset) and the responses in the preparatory subspace (at the end of the preparatory epoch; 450 ms after target onset). (d) Leave-one-out cross-validation (LOOCV) for that same relationship. Stars in c and d denote a significantly higher R² than shuffled data (P<0.001, one-tailed test). The shuffled data were generated by randomly shuffling the preparatory-epoch responses across conditions. In both c and d, bars show the median and error bars denote the 95% confidence interval of the shuffled distribution with 1,000 random shuffles.

Figure 8. Feed-forward generator model.

(a) Diagram illustrating the model and the computation it performs. The model consists of two latent dynamic subspaces (preparatory and movement). The movement goal (that is, target location) is loaded into the preparatory subspace. That preparatory subspace possesses leaky integrator dynamics and the input thus produces a fixed point that is specific to each condition. At the start of the movement, the state established in the preparatory subspace is passed to the movement subspace via a feed-forward mechanism. This sets the initial state in the movement subspace, whose dynamics are modelled as an oscillator. The dynamics of the preparatory and movement subspaces are fixed; different movement-subspace trajectories result from being passed different preparatory states, which in turn result from different inputs. (b) Responses of two simulated neurons from the model using the same conventions as Fig. 2c. (c) Neural trajectories from the model during the transition from preparation to movement, plotted in the top preparatory dimension and the top two movement dimensions using the same conventions as Fig. 7a. (d) Rotated view of c to show only the two movement dimensions. (e,f) Same analysis as in Fig. 7c,d but for the model data.