Fig. 5: Mechanisms for generating multiple timescales in local population activity.

a–c Network models consist of units (circles) arranged on a two-dimensional lattice (thin grey lines). Each target unit (large circle) receives inputs from 8 other units in the network (thick grey lines). The connectivity is random (a, b) or spatially arranged with each unit connected to its nearest neighbors (c). In the model with heterogeneous cell types (a), a local population at each lattice node (dashed circle) consists of two cell types, A and B, with distinct timescales (self-excitation probabilities p_s,A = 0.88 and p_s,B = 0.976). In the model with two local biophysical processes (b), each local population has a fast membrane time constant (modeled as p_s = 0.88) and a slow synaptic time constant (modeled as τ_synapse = 41 ms). The spatial network model (c) assumes only a single self-excitation timescale (p_s = 0.88) for each unit. d–f All models reproduce two distinct timescales in the autocorrelations of local population activity. In the model with two cell types (d), the timescales correspond to the self-excitation timescales of two unit types (τ_self,A, τ_self,B, pink lines). In the model with synaptic filtering (e), the timescales correspond to the self-excitation and synaptic timescales (τ_self, τ_synapse, blue lines). In the spatial network model (f), the unit’s autocorrelation exhibits multiple timescales and is well captured by the analytical derivation (purple). The fast autocorrelation decay corresponds to the self-excitation timescale (τ_self, blue). The slower decay is captured by the autocorrelation of recurrent inputs received by each unit in simulations (gray) and an analytical effective interaction timescale (τ_int, dashed line). g–i In the models with random connectivity, cross-correlations between the activity of local populations do not depend on the distance (d) between units on the lattice (two cell types in g; synaptic filtering in h). In contrast, in the spatial network model, cross-correlations depend on distance d and exhibit multiple timescales (i). The strength of cross-correlations decreases with distance, and slower interaction timescales dominate cross-correlations at longer distances. For all models: BP = 0.99, p_ext = 10⁻⁴. j Auto- and cross-correlations of V4 spiking activity recorded on different channels overlaid with correlations of synthetic data with MAP parameters (data from monkey G, FT; data from monkey N in Supplementary Fig. 9). The strength of cross-correlations is smaller than the auto-correlation and decreases with RF-center distance (d_RF,L > d_RF,S). k Posterior distributions of timescales from fitting correlations in j. Cross-correlations had slower timescales than the autocorrelation, and slower timescales dominated cross-correlations at larger RF-center distances. Statistics: two-sided Wilcoxon rank-sum test, *** indicate p < 10⁻¹⁰. Number of samples in each posterior N = 100. Correlations are plotted from the first time-lag (t = 2 ms). Source data are provided as a Source Data file.