Fig. 4: Mechanistic modelling suggests slow neurotransmission and feedback inhibition.
From: Causal evidence of a line attractor encoding an affective state
a, Diagram of strong but sparse connectivity among x1 neurons (1), or dense interconnectivity within subnetwork (2) (left). Right, the empirical distribution of the strength of pairwise functional connectivity between x1 neurons (green) and from x1 to x2 neurons (red). n = 99 pairs, n = 7 mice. b, Cartoon illustrating different elements of an excitatory network that can determine network-level persistent activity. c, Model simulation result showing the network time constant (τn) by varying the subnetwork connectivity (σ) in the range of 0 to 20% density values and τs in the range of 0 to 20 s. Blue portions show configurations that result in unstable networks with runaway excitation. d, Magnified version of c (the region left of the dashed line) showing glutamatergic networks with a synaptic conductance time constant (τs) in range of 0.01 to 0.6 s. e, Network time constant (τn) against density of integration subnetwork for slow neurotransmitter (τs: 10, 15 and 20 s). τn varies monotonically with density for large values of τs. f, As in e but for glutamatergic networks (τs: 0.01, 0.1, 0.2 and 0.3 s). g, Cartoon showing the modified VMHvl circuit with fast feedback inhibition incorporated. h, Plot of network time constant (τn) against density of integration subnetwork for a slow neurotransmitter network with τs = 20s, for different values of strength of inhibition (inhibitory gain, ginh: 1.25, 5 and 10) (left). Right, as on the left but for a glutamatergic network with ts = 0.1 s. i, Model simulation of a slow neurotransmitter network with fast feedback inhibition (ts: 20 s, 36% density of subnetwork connectivity). Top, the input (20 s ISI) provided to the model, Bottom, spiking activity in the network. The first 200 neurons (20%) comprise the interconnected integration subnetwork. j, Ca2+ activity convolved from firing rate (Methods) of the integration subnetwork (top) and the remaining neurons (bottom). k, As in i but for a fast transmitter network (ts: 0.1 s, 36% density of subnetwork connectivity). l, As in j but for a fast transmitter network (ts: 0.1 s, 36% density of subnetwork connectivity). a.u., arbitrary units.
