Distributions of instantaneous excitatory synaptic weights with same mean input current.

<p>Top panels: a) Two self-similar Gaussian synaptic weight distributions. b) The distribution of the sub-threshold, steady-state membrane potential when the two Gaussian synaptic inputs are activated with either a low (solid curves) or a high input firing rate (dashed curves) adjusted such that the mean input currents are equal. The low-amplitude distribution always has twice the input rate of the high amplitude one. In the absence of a threshold, these synaptic input would depolarize by 12 mV and 30 mV respectively. As we use a threshold of 20 mV, these inputs lead to distinct results, with the first being driven primarily by variations in input and the second by the mean input. c) Output firing rates as a function of time. In b) and c), green curves correspond to the Gaussian distribution with mean (3 mV) and standard deviation (SD) of (1 mV) and blue curves correspond to the Gaussian distribution with mean (6 mV) and SD (2 mV). For equal currents, stronger synapses produce a quicker response and a higher equilibrium firing rate. Bottom panels: d) Semi-log plot of -function (Delta), Gaussian (Gauss), exponential (Exp), lognormal (LogN), bi-modal (BiMod) and power-law (PL) synaptic weight distributions, matched for mean weight (1 mV) (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4" target="_blank">Methods</a>: Matched distributions for the exact forms used for these distributions). e) Steady-state, sub-threshold voltage distributions and f) output firing rates for an input rate of 1,000 Hz. Heavier-tailed distributions produce quicker transients.