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# Long-term stability of single neuron activity in the motor system

## Abstract

How an established behavior is retained and consistently produced by a nervous system in constant flux remains a mystery. One possible solution to ensure long-term stability in motor output is to fix the activity patterns of single neurons in the relevant circuits. Alternatively, activity in single cells could drift over time provided that the population dynamics are constrained to produce the same behavior. To arbitrate between these possibilities, we recorded single-unit activity in motor cortex and striatum continuously for several weeks as rats performed stereotyped motor behaviors—both learned and innate. We found long-term stability in single neuron activity patterns across both brain regions. A small amount of drift in neural activity, observed over weeks of recording, could be explained by concomitant changes in task-irrelevant aspects of the behavior. These results suggest that long-term stable behaviors are generated by single neuron activity patterns that are themselves highly stable.

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## Data availability

All data have been used previously by Dhawale et al.43. See https://github.com/KrisJensen/stability_paper_code for instructions on how to download the subset of data used for this paper.

## Code availability

The code used to train all models, perform all analyses, and generate all figures is available online: https://github.com/KrisJensen/stability_paper_code.

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## Acknowledgements

We are grateful to K. Hardcastle, C. Pehlevan, T.-C. Kao, G. Hennequin and M. Schimel for their feedback on the manuscript. This work was supported by a Gates Cambridge scholarship and Nordea-fonden (K.T.J.); a Helen Hay Whitney Foundation Postdoctoral Fellowship, the Zuckerman STEM Leadership Program postdoctoral fellowship, and the Weizmann Institute of Science - National Postdoctoral Award for Advancing Women in Science (N.K.H.); a Life Sciences Research Foundation and Charles A. Kings Foundation postdoctoral fellowship (A.K.D.); an EMBO postdoctoral fellowship ALTF1561-2013 and an HFSP postdoctoral fellowship LT 000514/2014 (S.B.E.W.); and National Institutes of Health grants R01-NS0993231 and R01-NS105349 (B.P.Ö.).

## Author information

Authors

### Contributions

B.P.Ö., K.T.J., A.K.D. and N.K.H. conceived the study. A.K.D. and S.B.E.W. collected the data. K.T.J. and N.K.H. analyzed the data. K.T.J., N.K.H. and B.P.Ö. interpreted the data and wrote the manuscript. All authors reviewed the manuscript.

### Corresponding author

Correspondence to Bence P. Ölveczky.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Neuroscience thanks the anonymous reviewers for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 RNN parameter interpolation.

(a) Mean correlation between the initial conditions (left), recurrent weight matrices (center), and readout weight matrices (right) of the simulated RNNs as a function of time difference for the stable and drifting networks. Shading indicates standard deviation across 10 repetitions of training and interpolation.

### Extended Data Fig. 2 Kinematics of all animals.

(a) Heatmaps showing the forelimb trajectories of each animal on every trial across all days. x-axes indicate time within trial and y-axes indicate trial number from first (top) to last (bottom). Each column corresponds to a single animal (first three: DLS, last three: MC). The rows illustrate the trajectories of the right forelimb parallel and perpendicular to the floor, followed by the left forelimb parallel and perpendicular to the floor. The second animal from the left corresponds to the example used in Figs. 3a, 5a and b. (b) Heatmaps showing the z-scored velocity of each animal on every trial across all days for the animals in a. The rows illustrate the velocity of the right forelimb parallel and perpendicular to the floor followed by the left forelimb parallel and perpendicular to the floor.

### Extended Data Fig. 3 Similarity as a function of time difference for all neurons.

We computed the PETH correlation as a function of time difference for all neurons, taking the average across all pairs of days separated by the same time difference for each neuron. This figure shows the average similarity as a function of time difference for neurons recorded in DLS (left) or MC (right) during the lever-pressing task (a) and the wet-dog shake behavior (b). Upper panels indicate all neurons recorded for at least 3 days, lower panels indicate neurons which were recorded for at least 14 (a) or 10 (b) days and therefore included in Fig. 4c or 6c. Neurons were sorted by recording duration.

### Extended Data Fig. 4 Stability as a function of time difference for different recording durations.

(a) We performed analyses as in Fig. 4c, plotting the neural similarity as a function of time difference for neurons recorded for at least N days, with N ranging from 5 to 17 (c.f. N = 14 in Fig. 4c). Error bars indicate standard error across units, and dashed lines indicate controls as in Fig. 4c. (b) As in a, now for the wet-dog shake behavior instead of the lever-pressing task (c.f. Fig. 6c).

### Extended Data Fig. 5 Latent stability and neural decoding.

It has previously been reported that stable neural activity can be identified in a common latent space even when there is a turnover of recorded neurons43. As we show in Fig. 2e, this can be consistent with either stable or drifting single unit activity. While we have already shown a high degree of similarity for single neurons, here we investigate whether ‘aligning’ the neural activity between sessions can identify a common subspace with even higher similarity. These analyses require simultaneous recording of a large population of neurons, which in general was not the case in our dataset (c.f. Fig. 3c). Instead, we considered a single week of recording in a single animal with recordings from DLS (day 8-14 in Fig. 3c), where we simultaneously recorded 16 neurons firing at least 10 spikes during the task on each day. (a) We first computed the similarity as a function of time difference as the correlation between single neuron PETHs, averaged across neurons (black line). We then proceeded to align the neural activity on each pair of days using CCA and computed the similarity in the resulting aligned space as the average correlation across all dimensions. This CCA-aligned similarity was generally lower than the similarity averaged over individual neurons, suggesting that the neuron-aligned coordinate system is more stable than the CCA-aligned alternative (note that CCA performs a greedy alignment rather than finding the optimal alignment, which would provide an upper bound on the single neuron similarity). Shadings indicate standard error across all pairs of days with a given time difference. (b) We proceeded to consider population decoding of behavior from neural activity, using the same data as in a. We fitted a linear model to predict the trajectories of the left and right forelimbs from neural activity on each day using crossvalidated ridge regression, and we tested the models on data from all other days. Here, we plot the performance as a function of time difference, averaged across the vertical and horizontal dimensions and both forelimbs. Line and shading indicate mean and standard error across pairs of days with a given time difference. (c) We proceeded to compute stability indices for the data in b to see whether there was a significant negative trend. We bootstrapped the individual datapoints (before taking the mean) 10,000 times and estimated stability indices from each surrogate dataset. The distribution over the resulting stability indices was not significantly smaller than 0 (one-sided p = 0.48). (d) While the analysis in a suggests that the single neurons provide a good coordinate system for stable representations, it does not address the question of whether an aligned low-dimensional manifold can provide better decoding43. We therefore proceeded to train a population decoding model as in b, but where the decoder was trained on the top 10 PCs from a single day and tested on the top 10 PCs from every other day after alignment via CCA43 (blue dashed line). We found that decoding performance from this aligned latent space was almost identical to the decoding performance from raw neural activity (black line). This provides further evidence that the stable aligned dynamics identified in previous work are the result of stable single unit tuning curves. Shading indicates standard error across pairs of days with a given time difference. (e) Finally, we considered how the relationship between kinematics and neural activity changed over time at a single neuron level. We used the GLM discussed in Fig. 5e to predict neural activity from behavior. This GLM was trained on the first day of recording for each neuron and tested on each subsequent day. The figure shows the correlation between the predicted firing rate and true spike count as a function of time difference, averaged across all neurons which were recorded for at least a week and had a training correlation of at least 0.1. Blue indicates neurons recorded from DLS (n = 58 units), red from MC (n = 61 units), and shadings indicate standard errors across neurons. Dashed lines indicate the average correlation across neurons from hold-one-out crossvalidation on all trials from the first day of recording.

### Extended Data Fig. 6 Exponential model fits and stability indices.

(a) Plots of PETH similarity against time difference for four example units (colors) together with exponential fits illustrating a range of different decay rates, same-day similarities, and durations of recording. Note that one of these example units (cyan) exhibits an apparent increase in stability over time due to the noisy nature of the data. Indeed, in a perfectly stable model (such as the stable RNN in Fig. 2e), neurons will be as likely to exhibit such an increase as they are to exhibit a decrease in similarity over time, leading to a median stability index of 0. Such noise is mitigated by increasing recording durations. (b) Distribution of the mean error of each model fit across the population of neurons recorded from MC (red) or DLS (blue). Vertical dashed lines indicate quartiles of the distributions. (c) Stability indices for all neurons recorded from DLS (left; blue) or MC (right; red) during the lever-pressing task. Solid lines indicate exponential fits as in Fig. 4e. As the time difference increases, the variance decreases (due to the increase in data), and the median stability index gradually increases (c.f. solid lines). (d) As in c, for the WDS behavior.

### Extended Data Fig. 7 Results are not dependent on time-warping.

In this figure, we reproduce some of the key analyses of the paper after aligning trials by ‘trimming’ to a fixed duration rather than the time-warping used in the main text. (a) Neural similarity as a function of time difference for neurons recorded for at least 14 days in the lever-pressing task in either DLS (blue) or motor cortex (red). Note the similarity with Fig. 4c using time-warping. Lines and shading indicate mean and standard error across units. (b) Kinematic similarity in the lever-pressing task as a function of time difference across all animals. Solid line and shading indicate mean and standard error across animals after trimming. Dashed line indicates the mean after time-warping. Note that time-warping better aligns kinematics, which is the primary motivation for its use in the main text. (c) correlation between neural similarity and kinematic similarity on consecutive days (c.f. Fig. 5d). (d-f) As in a-c, now for the wet-dog shake behavior.

### Extended Data Fig. 8 Exponential fits for different subsampled recording durations.

Black lines indicate the mean across units of the neural similarity as a function of time difference for units recorded for at least 14 days during the lever-pressing task (c.f. Fig. 4c). We fitted exponential models to the mean data, considering only data up to and including increasing time differences (legend). As the subsampled ‘recording duration’ increases, so does the stability index learned in the exponential model for both neurons recorded in DLS (a) and MC (b). If the observed increase in stability with recording duration is due to latent processes with autocorrelations on the order of days, we would expect the neural similarity to decrease to some saturating baseline value, γ. We therefore also fitted a model to the average similarity across neurons as a function of time difference, which assumes a decay to such a baseline ($$\rho = \beta e^{\alpha \,\delta t} + \gamma$$; red dashed lines). This model yielded an asymptotic correlation of γ = 0.71 for DLS and γ = 0.58 for MC, suggesting a high degree of neural similarity at long timescales.

### Extended Data Fig. 9 Behavioral drift and inter-press intervals.

(a) Correlations between mean velocity profiles plotted against time difference for all pairs of days in each animal. Top row: lever-pressing task; bottom row: wet dog shakes. Blue indicates animals with recordings from DLS, red from MC. (b) Distribution of correlations between time difference and behavioral similarity across all animals, generated by a bootstrap analysis of the data in a. All animals exhibit a significant negative correlation between behavioral similarity and time difference in both the lever-pressing task and wet dog shake behavior (p < 0.001; one-sided bootstrap test). (c) Inter-press interval (IPI) for each animal, convolved with a 200-trial Gaussian filter. Time is normalized from 0 to 1 for each animal (n = 9365 ± 6886 trials, mean ± std). Black horizontal line indicates 700 ms. (d) We computed the IPI autocorrelation as a function of trial number and normalized time by the average number of trials per day for each animal (colored lines). Black line and shading indicate mean and standard error across animals. Task performance is only correlated over short timescales of 0.5-1 days despite behavioral drift on timescales of weeks (c.f. panel a). This suggests that behavioral changes are predominantly along ‘task-null’ directions that do not affect performance.

### Extended Data Fig. 10 Task-modulation of neurons in the lever-pressing task and wet-dog shake behavior.

(a) A PETH was computed across all trials for each neuron in 20 ms bins, and the time bin identified with the maximum deviation from the mean across all time bins. The corresponding z-score was computed, and the distribution of absolute values of these z-scores plotted across all DLS neurons for the lever-pressing task (black) and wet-dog shake behavior (blue). (b) As in a, now for neurons recorded from MC.

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Jensen, K.T., Kadmon Harpaz, N., Dhawale, A.K. et al. Long-term stability of single neuron activity in the motor system. Nat Neurosci 25, 1664–1674 (2022). https://doi.org/10.1038/s41593-022-01194-3

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• DOI: https://doi.org/10.1038/s41593-022-01194-3