Jonathan W. Pillow

Spatio-temporal correlations and visual signalling in a complete neuronal population

Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.

Spike-triggered neural characterization

Response properties of sensory neurons are commonly described using receptive fields. This description may be formalized in a model that operates with a small set of linear filters whose outputs are nonlinearly combined to determine the instantaneous firing rate. Spike-triggered average and covariance analyses can be used to estimate the filters and nonlinear combination rule from extracellular experimental data. We describe this methodology, demonstrating it with simulated model neuron examples that emphasize practical issues that arise in experimental situations.

Prediction and Decoding of Retinal Ganglion Cell Responses with a Probabilistic Spiking Model

Sensory encoding in spiking neurons depends on both the integration of sensory inputs and the intrinsic dynamics and variability of spike generation. We show that the stimulus selectivity, reliability, and timing precision of primate retinal ganglion cell (RGC) light responses can be reproduced accurately with a simple model consisting of a leaky integrate-and-fire spike generator driven by a linearly filtered stimulus, a postspike current, and a Gaussian noise current. We fit model parameters for individual RGCs by maximizing the likelihood of observed spike responses to a stochastic visual stimulus. Although compact, the fitted model predicts the detailed time structure of responses to novel stimuli, accurately capturing the interaction between the spiking history and sensory stimulus selectivity. The model also accounts for the variability in responses to repeated stimuli, even when fit to data from a single (nonrepeating) stimulus sequence. Finally, the model can be used to derive an explicit, maximum-likelihood decoding rule for neural spike trains, thus providing a tool for assessing the limitations that spiking variability imposes on sensory performance.

Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model

We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the models validity using time-rescaling and density evolution techniques.

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

A better way to explain neuronal activity A brain region called the lateral intraparietal (LIP) area is involved in primate decision-making. The dominant model to explain neuronal firing in LIP assumes that neurons slowly accumulate sensory evidence in favor of one choice or another. Latimer et al. hypothesized that neurons instead exhibit rapid steps or jumps in their firing rate, reflecting discrete changes in the animals decision state. They recorded from LIP neurons in macaque monkeys performing a motion-discrimination task. LIP spike trains in most cells involved discrete stepping dynamics rather than slow evidence integration dynamics. Science, this issue p. 184 Macaque cortical neurons exhibit rapid “jumps” in spike rate, reflecting discrete changes in the animal’s decision state. 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.

Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Perceptual Completion across the Vertical Meridian and the Role of Early Visual Cortex

Perceptual completion can link widely separated contour fragments and interpolate illusory contours (ICs) between them. The mechanisms underlying such long-range linking are not well understood. Here we report that completion is much poorer when ICs cross the vertical meridian than when they reside entirely within the left or right visual hemifield. This deficit reflects limitations in cross-hemispheric integration. We also show that the sensitivity to the interhemispheric divide is unique to perceptual completion: a comparable task which did not require completion showed no across-meridian impairment. We propose that these findings support the existence of specialized completion mechanisms in early visual cortical areas (V1/V2), since those areas are likely to be more sensitive to the interhemispheric divide.

Modeling the impact of common noise inputs on the network activity of retinal ganglion cells

Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies. Two candidate mechanisms of synchronized firing include direct coupling and shared noisy inputs. In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, recent experimental work indicates that direct electrical or synaptic coupling is weak, but shared synaptic input in the absence of modulated stimuli is strong. However, previous modeling efforts have not accounted for this aspect of firing in the parasol cell population. Here we develop a new model that incorporates the effects of common noise, and apply it to analyze the light responses and synchronized firing of a large, densely-sampled network of over 250 simultaneously recorded parasol cells. We use a generalized linear model in which the spike rate in each cell is determined by the linear combination of the spatio-temporally filtered visual input, the temporally filtered prior spikes of that cell, and unobserved sources representing common noise. The model accurately captures the statistical structure of the spike trains and the encoding of the visual stimulus, without the direct coupling assumption present in previous modeling work. Finally, we examined the problem of decoding the visual stimulus from the spike train given the estimated parameters. The common-noise model produces Bayesian decoding performance as accurate as that of a model with direct coupling, but with significantly more robustness to spike timing perturbations.

Encoding and decoding in parietal cortex during sensorimotor decision-making

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.

Dissociated functional significance of decision-related activity in the primate dorsal stream

During decision making, neurons in multiple brain regions exhibit responses that are correlated with decisions. However, it remains uncertain whether or not various forms of decision-related activity are causally related to decision making. Here we address this question by recording and reversibly inactivating the lateral intraparietal (LIP) and middle temporal (MT) areas of rhesus macaques performing a motion direction discrimination task. Neurons in area LIP exhibited firing rate patterns that directly resembled the evidence accumulation process posited to govern decision making, with strong correlations between their response fluctuations and the animal’s choices. Neurons in area MT, in contrast, exhibited weak correlations between their response fluctuations and choices, and had firing rate patterns consistent with their sensory role in motion encoding. The behavioural impact of pharmacological inactivation of each area was inversely related to their degree of decision-related activity: while inactivation of neurons in MT profoundly impaired psychophysical performance, inactivation in LIP had no measurable impact on decision-making performance, despite having silenced the very clusters that exhibited strong decision-related activity. Although LIP inactivation did not impair psychophysical behaviour, it did influence spatial selection and oculomotor metrics in a free-choice control task. The absence of an effect on perceptual decision making was stable over trials and sessions and was robust to changes in stimulus type and task geometry, arguing against several forms of compensation. Thus, decision-related signals in LIP do not appear to be critical for computing perceptual decisions, and may instead reflect secondary processes. Our findings highlight a dissociation between decision correlation and causation, showing that strong neuron-decision correlations do not necessarily offer direct access to the neural computations underlying decisions.