Fig. 1: Gain control induced by axonal conduction velocity.
From: Myelin-induced gain control in nonlinear neural networks
a Diagram depicting an idealized, simplified representation of a neural network with poor myelination, in which neurons (black circles) are connected through axons (edges) expressing different levels of myelin (illustrated in shades and thickness of red). b Dynamics of a network of Poisson spiking neurons with low (c = 0.5 m/s) conduction velocity. A raster plot of the network spiking activity shown alongside the network mean firing rate above shows the response of the network to a spatially correlated (i.e., evenly applied to all neurons) stochastic stimulus S(t). The histogram corresponds to the firing rate distribution of the network (right red insert). c Diagram of a neural network with higher myelination (illustrated in shades and thickness of blue). d For the same stimulus S(t), if conduction velocity is increased (c = 50 m/s) to reflect higher myelination, the response of the network is amplified and mean firing rates increase (blue line). This also manifests as a change in the network firing rate distribution, which is now heavily skewed (right blue insert). In (a, b), axonal conduction delays τij = lij/c are Gamma distributed with shape k = 2 and scale θ = 4/c ms and axonal length distribution lij. Except from conduction velocity (i.e., (c), all other parameters are identical). The network is fully (i.e., all-to-all) connected and synaptic weights are both positive and identical. e Illustration of the mechanism of gain control. Changes in conduction velocity lead to a net change in normalized firing rate and response to stimuli. The red line corresponds to c = 0.5 m/s while the blue line corresponds to c = 50 m/s. f The membrane potential statistics for high (blue histogram; c = 50 m/s) and low (red histogram; c = 0.5 m/s) conduction velocity differ. The other parameters in the model (cf. Methods section) used for these exemplar simulations are N = 100, \({J}_{ij}=\bar{J}=0.9\), ρ = 1, I = 0 and D = 0.05. The activation function is nonlinear with parameters β = 2, h = 0.5.
