NEURONAL MODELING. Single-trial spike trains in parietal cortex reveal discrete steps during decision-making

Abstract

Neurons in the macaque lateral intraparietal (LIP) area exhibit firing rates that appear to ramp upward or downward during decision-making. These ramps are commonly assumed to reflect the gradual accumulation of evidence toward a decision threshold. However, the ramping in trial-averaged responses could instead arise from instantaneous jumps at different times on different trials. We examined single-trial responses in LIP using statistical methods for fitting and comparing latent dynamical spike-train models. We compared models with latent spike rates governed by either continuous diffusion-to-bound dynamics or discrete "stepping" dynamics. Roughly three-quarters of the choice-selective neurons we recorded were better described by the stepping model. Moreover, the inferred steps carried more information about the animal's choice than spike counts.

Fig. 1

(A) Schematic of moving-dot direction-discrimination task. The monkey views and discriminates the net direction of a motion stimulus of variable motion strength and duration, and indicates its choice by making a saccade to one of two choice targets 500 ms after motion offset. One choice target is in the response field of the neuron under study (RF; shaded patch on left); the other is outside it. (B) Ramping (diffusion-to-bound) model. Spike rate trajectories (solid traces) were sampled from a diffusion-to-bound process for each of three motion coherences (strong positive, zero, and strong negative). The model parameters include an initial spike rate, a slope for each coherence, noise variance, and an upper bound. We do not include a lower bound, consistent with the competing integrator (race) model of LIP (5). Spike trains (below) obey an inhomogeneous Poisson process for each spike rate trajectory. (C) Discrete stepping model. Spike rate trajectories (above) begin at an initial rate and jump “up” or “down” at a random time during each trial, and spike trains (below) are once again Poisson given the latent rate. The step times take a negative binomial distribution, which resembles the time-to-bound distribution under a diffusion model. Parameters include the spike rates for the three discrete states and two parameters governing the distribution over step timing and direction for each motion coherence. Both models were fit using the spike trains and coherences for each neuron, without access to the animal’s choices.

Fig. 2

Model-based analysis of spike responses from an example LIP neuron. (A) Spike rasters sorted by the monkey’s choice in or out of the RF of the neuron under study (black=“in-RF”, gray=“out-RF”), and their associated averages (PSTHs, below). Left: Conventional stimulus-aligned rasters with each trial aligned to the time of motion onset exhibit commonly-observed ramping in the PSTH. Blue and red triangles indicate the inferred time of an “up” or “down” step on each trial under the fitted stepping model. Yellow triangles indicate that no step was found during the trial, and are placed at the end of the trial segment we analyzed (200 ms after motion offset). Right: The same spike trains aligned to the inferred step time for each trial. Note that estimated step direction of the neuron does not always match the animal’s decision on each trial. (B) The distribution of inferred step times shown in A (histogram), and the distribution over step times under the fitted parameters (black trace). (C) The probability of an “up” step, for each coherence level. Error bars indicate 95% credible intervals.

Fig. 3

(A) Population average PSTH sorted by motion coherence computed from spike trains: (left) aligned to motion onset and sorted by motion strength; (middle) aligned to step times inferred under the stepping model and sorted by motion strength; (right) aligned to step times and sorted by both motion strength and inferred step direction. Simulated results from the stepping model (dashed lines) provide a close match to the real data under all types of alignment and conditioning. (B) Quantitative model comparison using divergence information criterion (DIC) reveals a superior fit of the stepping model over the ramping model for the majority of cells (31 out of 40). A DIC difference greater than ± 10 (gray region) is commonly regarded as providing “strong” support for one model over the other (20). We found substantially more cells with strong evidence for stepping over ramping (25 cells vs. 6 cells; median DIC difference = 22.1, sign test p < 0.001).

Fig. 4

Stepping model better explains variance of responses and can be used to decode choices. (A) Comparison of model fits to average population activity, sorted by stimulus strength. Motion coherence and direction are indicated by color (blue, in-RF; red, out-RF). Average spike rate (top) and spike count variance (bottom) for the population aligned to motion onset. The data (left) and simulations from the stepping model (center) and the diffusion-to-bound model (right) fits to all 40 cells are shown. Spike rates and variances were calculated with a 25 ms sliding window. (B) Population average choice probability aligned to stimulus onset (left), and average CP aligned to estimated step times (right). Grey region indicates one standard error of the mean. CPs were calculated with a sliding 25 ms window. Conventional alignment suggests a ramp in choice selectivity, while the model-based alignment indicates a rapid transition. (C) Conventional choice probability based on spike counts using responses 200–700 ms after motion onset versus model-based choice probability using the probability of stepping to the up state by the end of the same period. Model-based CP is greater than conventional CP in the population (Wilcoxon signed rank test, p < 0.05). Stepping models were fit using 10 fold cross validation. Error bars show the standard error of CPs, as computed on each training data set. Black points indicate cells with significant differences between model-based and conventional CP (Student’s t-test, p < 0.05), and grey indicates not significant.