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

Abstract

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 1-3 , 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 4,5 . 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 6 . 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.How does the spiking activity of a neural population represent the sensory environment? The answer depends critically on the structure of neuronal correlations, or the tendency of groups of neurons to fire temporally coordinated spike patterns. The statistics of such patterns have been studied in a variety of brain areas, and their significance in the processing and representation of sensory information has been debated extensively 2,3,7-13 .Author Information Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.W.P. (E-mail: pillow@gatsby.ucl.ac.uk). Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Previous studies have examined visual coding by pairs of neurons 11 and the statistics of simultaneous firing patterns in larger neural populations 14,15 . However, no previous approach has addressed how correlated spiking activity in complete neural populations depends on the pattern of visual stimulation, or has answered the question of how such dependencies affect the encoding of visual stimuli. NIH Public AccessHere we introduce a model-based methodology for studying this problem. We describe the encoding of stimuli in the spike trains of a neural population with a generalized linear model (Fig. 1a), a generalization of th...

Distinct timescales of population coding across cortex

“…Our encoding model extended the approach taken by Pillow and colleagues 19,20 to calcium imaging data recorded in populations of neurons in a behaving animal. It allowed us to model for single neurons the time-dependent effects of all measured variables related to the task and the animal’s behavior simultaneously on neuronal activity during single trials.…”

“…The advantage of this GLM approach is that on a single trial basis, our model accounts for variability in the timing and magnitude of behavioral and stimulus-related predictors simultaneously. Furthermore, by including all simultaneously imaged neurons, the model can reveal some interactions of higher order, which is not possible with pairwise noise correlation measurements 20 .…”

“…We selected α = 0.95, allowing for a relatively small number of useful predictors to be selected by the model out of a large number of potentially correlated predictors as in pure L1 regularization, while at the same time avoiding issues with degeneracies that can arise if the correlations between predictors are very strong 40 . Additional penalty factors (×10) were applied to the coupling predictors to reduce the number of selected coupling predictors to the smallest number necessary to increase model performance 20 . The value of the shrinkage parameter for the elastic net was chosen by three-fold cross validation on the training data.…”

“…To take these variables into account and to help isolate signals related to stimulus and choice, we developed an encoding model (generalized linear model - GLM). This model incorporated all measured task-related variables as predictors of each neuron’s activity 19,20 (Fig. 2a, Extended Data Fig.…”

“…To examine the structure of functional interactions in population activity 18,23–27 , we modified our encoding model to predict a given neuron’s activity based on the past activity of each of the other imaged neurons (“coupling predictors”; activity from up to ~2 s in the past, within defined lag ranges). These coupling predictors were included in a single model along with the task-related predictors described above 20 (“task predictors”; Fig. 3a–c).…”