It has been suggested that the lateral intraparietal area (LIP) of macaques plays a fundamental role in sensorimotor decision-making. We examined the neural code in LIP at the level of individual spike trains using a statistical approach based on generalized linear models. We found that LIP responses reflected a combination of temporally overlapping task- and decision-related signals. Our model accounts for the detailed statistics of LIP spike trains and accurately predicts spike trains from task events on single trials. Moreover, we derived an optimal decoder for heterogeneous, multiplexed LIP responses that could be implemented in biologically plausible circuits. In contrast with interpretations of LIP as providing an instantaneous code for decision variables, we found that optimal decoding requires integrating LIP spikes over two distinct timescales. These analyses provide a detailed understanding of neural representations in LIP and a framework for studying the coding of multiplexed signals in higher brain areas.
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We thank J. Yates, K. Latimer and L. Cormack for discussions, K. Eastman for assistance with data collection, and C. Rorex and S. Winston for technical support. This project was supported by grants from the National Eye Institute (EY017366 to A.C.H.) and the National Institute of Mental Health (MH099611 to J.W.P. and A.C.H.), by the Sloan Foundation (J.W.P.), McKnight Foundation (J.W.P.), and a National Science Foundation CAREER award (IIS-1150186 to J.W.P.).
The authors declare no competing financial interests.
Integrated supplementary information
(a) Peri-stimulus time variance (PSTV) histogram (thin line), and PSTH (think line) plotted simultaneously. These are targets-ON trials conditioned on coherence and decision. Both traces are computed with 50 ms boxcar moving average and smoothed with a Gaussian of 50 ms standard deviation. Note that the estimated mean and variance are close to each other, consistent with Poisson variability. (b) Population summary of PSTV power explained analogous to Fig. 3b. On average, 84.1% of the power is captured by the rate model.
We use the time-rescaling theorem to transform the observed spike trains and check if the transformed interval statistics resulting from post-spike filter are consistent with the Poisson assumption. (a) Quantile-quantile plot of time-rescaled interval distribution. Diagonal represents Poisson process model assumptions. (b) Subsamples of adjacent time-rescaled inter-spike intervals. Note the uniformity of the intervals resulting from the model with the post-spike filter. The post-spike filter decorrelates the consecutive intervals, which is consistent with the Poisson assumption, indicated by the reduction of correlation coefficient (R) values.
We compare an alternative nonlinearity with (soft rectification/threshold linear function). Each column represents a neuron corresponding to Fig. 5. (a) Exponential function (black) and empirical predicted nonlinearity on test-data (red). Empirical nonlinearities are estimated by first partitioning the net linear output for each time bin into eight equal-quantile buckets, then estimating the expected spike count conditioned on each bucket. The expected means are plotted at the mean net linear drive within each bucket. (b) Threshold linear function (black) and empirical predicted nonlinearity on test-data (red). Note the systematic deviation towards an exponential nonlinearity. (c) To check for multiplicative interactions, we divided the net linear input into two components, one from saccade-locked kernels and the rest. Then, we compared model prediction to that expected from multiplicative interaction between those two components. Each colored trace represents conditioning on different amounts of contribution from the saccade-locked kernels. Solid line is the true multiplicative effect predicted from the model (with exponential nonlinearity), while dotted lines are empirical rate prediction from the data.
Supplementary Figure 4 Nonlinearity comparison with cross-validated log-likelihoods for exponential and linear rectification.
Positive cross-validated log-likelihood difference implies exponential model better fits the data. We used Fano factor as a measure of neural variability, to test for a relation between variability and the quality of the fit with an exponential nonlinearity. There is a noticeable trend (correlation coefficient -0.44) indicating that underdispersed neurons (Fano factor less than 1) are better modeled with an exponential nonlinearity, while overdispersed neurons are often better modeled with linear rectification.
Majority of neurons showed a long self-exciting tail in the post-spike filter (Supplementary Fig. 7). We quantify how much information the tail contributes to, and test if there is a trial length scale modulation of gain. The post-spike filter used throughout the paper consists of ten 1 ms bins to model fast response components, in addition to ten raised cosine bases stretched logarithmically over 250 ms; here we also consider a model with shorter post-spike filter which has 7 temporal bases over 100 ms, and a model with longer post-spike filter which has 25 temporal bases over 5 s, which is long enough to cover the entire trial. (a) Resulting fits for 3 example cells, comparing short/medium/long spans for post-spike filter basis functions. Inset shows 5 seconds scale. (b) Spike prediction accuracy comparison across 3 models averaged over 80 neurons. Errorbar indicates standard error. Our "original" model used throughout the paper explained 7.9% more information per spike compared to short filter model (p < 10−10), and the long filter model explained 0.7% more information (p < 0.001). Thus, longer post-spike effect is negligible, and there is no systematic trial time scale gain modulation.
(Left) Kernels corresponding to each event. Thinner line shows the corresponding weight for the model with post-spike filter. Note that Fig. 2 is fit with a rank-2 constraint on the motion coherence kernels. Here we show the unconstrained kernel in the middle panel. (Right) Post-spike filter (blue), which is represented as a sum of weighted temporal basis functions (gray).
Each column represents a different kernel. The motion coherence kernels are convolved with a 500 ms boxcar for easier interpretation. (Top 9 rows) Each row shows one of the 9 example cells. They are sorted by decoding performance: The top cell is the best performing, followed by example neurons performing at 11%, 22%, …, 89% percentile. (Bottom row) Population average for all 80 neurons. Average kernel was transformed with exponential nonlinearity to represent gain. These fits are from models with the post-spike filter.
In Fig. 4, we only showed best and median predicted trials. Here are randomly selected trials per coherence strength for which the monkey was correct. Each column represents a cell corresponding to Fig. 5 and each row corresponds to a coherence level. Light blue lines are predictions from the model with the post-spike filter. Although the fine time scale predictions are significantly better with the post-spike filter, we avoided showing the post-spike filter prediction in Fig 4, because it is difficult to visually assess the quality of fit. This is because a typical sharp self-excitatory gain appears after each spike, which also makes it difficult to smooth without inducing deceiving results.
(Top row) Individual traces of the kernel shapes of the population. Difference corresponds to Fig. 7a. (Bottom row) Dimensionality analysis corresponding to Supplementary Table 1. The first few dimensions explain most of the variance. Note that the difference of IN and OUT kernel has the tightest subspace.
(Top) Raised cosine basis functions spaced in 50 ms steps. (Bottom) 10 single bin boxcars followed by log-time scaled raised cosine basis functions. This is only used for the post-spike filter.
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Park, I., Meister, M., Huk, A. et al. Encoding and decoding in parietal cortex during sensorimotor decision-making. Nat Neurosci 17, 1395–1403 (2014). https://doi.org/10.1038/nn.3800
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