Fig. 4: Coupling encapsulates population structure.

a Comparison of the log likelihoods of the model constructed using only external inputs as predictors against those of a model that also included effects of spike-history (brown), against a model with both spike-history and inter-neuronal coupling (maroon). Each circle denotes an individual neuron. Inset shows the cumulative distribution of the contribution of spike history and neuron-neuron coupling, calculated as the reduction in variance explained by the model after removing those filters. Black curve shows the distribution of the variance explained by the full model. b Top left: Spike history filter of an example neuron. Bottom left: Model with spike history filter accurately captures the autocorrelation function of the neuron. Top right: Bidirectional coupling filters between an example pair of neurons. Bottom right: Coupling filters capture the cross-correlation between the pair, whereas spike-history filters alone do not. c Top: Structure of the peak-to-trough amplitude of cross-correlation between the activity of all pairs of simultaneously recorded neurons from an example monkey. Neurons are ordered according to the weight of their contribution to the first principal component of the population activity. Coupled model (bottom), but not the uncoupled model (middle), captures the structure of cross-correlation of the full population. d Left: The strength of the coupling filters between all pairs of neurons in the population shown in c. Strength of the filter was computed by taking the total area under the filter. A strength greater than one corresponds to excitatory coupling whereas less than one corresponds to inhibitory coupling. The diagonal elements correspond to the strength of the spike-history filter (self-coupling) as a special case. Right: Details of the coupling (off-diagonal) and spike-history filters of a subset of the neural population, highlighting the diversity in the filter profiles across neuronal pairs. e Top: Frequency distribution over the coupling strengths between all pairs of neurons, pooled across monkeys. A vast majority of the neurons were weakly coupled (note the log scale of the frequency axis). Bottom: Each coupling filter was expressed as a weighted sum of seven exponential basis functions with different decay constants ([6, 12, 24, 48, 96, 192, 384] milliseconds). Data points show the average magnitude of weighting of the different basis functions across all coupling filters, pooled across monkeys. Black line denotes the best fit power-law relationship. Error bars denote ± 1 SEM (n = 244). f Strength of coupling decreased as a function of distance between the electrodes from which the neurons were recorded. Points above and below the black line correspond to excitatory and inhibitory couplings respectively. Source data are provided as a Source data file.