Figure 8.

Preserved constraints on firing rate vectors allow prediction of a neuron’s sensory tuning based on spontaneous activity, and a geometrical interpretation of these constraints. (A) Prediction of a neuron’s receptive field from correlations with simultaneously recorded neurons during spontaneous activity, and from the receptive fields of these other neurons. Here, w denotes a vector of weights, optimized to maximize prediction of the target neuron’s activity during spontaneous activity, and r denotes the receptive field vectors of N other neurons. (B,C) Actual and predicted receptive fields for a representative neuron. On average, predicted and actual receptive fields showed a correlation of 0.62 (see text for details). (D,E) General relationship between correlation matrix and cluster orientation. (D) shows a set of simulated spike count vectors with the correlation matrix shown in (E); the values of the correlation matrix provide information about the orientation of the cluster relative to the coordinate axes. (F) Cartoon illustrating the geometrical interpretation of our findings. The gray area illustrates the space of all rate vectors theoretically possible in the absence of relationships between neurons. The black outline represents the space of spontaneous events; this is shown elongated and of small volume to illustrate strong constraints at the population level. Responses to individual stimuli occupy smaller subsets within this (colored blobs; the irregular shape illustrates possible non-Gaussianity of these clusters). The orientations of the spaces for individual stimuli (corresponding to noise correlation matrices) are approximately aligned with the space of spontaneous events. The mean response to each stimulus also lies within the space of spontaneous events (see Supplementary Figure 10).