Comparisons between simulations and DiPDE.

<p>Panels (a)–(e) show results for excitatory, low-frequency, large amplitude current-based synapses of constant weight. Topmost panels show time evolution of the probability distribution of membrane potentials in the neuronal population obtained with Poisson input for with synaptic weight (maximum EPSP) mV and input rate Hz from, a) simulations of 10,000 leaky integrate-and-fire (LIF) neurons (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4" target="_blank">Methods</a>: Population Simulations for parameters used in simulations) , b) the numerical solution to the DiPDE <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e029" target="_blank">equation (3)</a>, and c) the Fokker-Planck (FP) equation. Middle panels: d) Output firing rates as a function of time. e) The distribution of the sub-threshold steady-state membrane potential after 200 ms. These discrete synaptic jumps are evident in the voltage distributions just after synaptic input is switched on. Bottom panels: f) Expected 95% intervals for spike counts obtained from DiPDE for simulation data shown in panels (a)–(e). g) Output firing rates obtained from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e345" target="_blank">equation (21)</a> for leaky integrate-and-fire (LIF) neurons and equivalent numerical simulations (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4" target="_blank">Methods</a>: Population Simulations for parameters used in simulations), for excitatory conductance-based synapses. Poisson input for with maximum depolarization achieved by a neuron starting from rest mV and input rate Hz. h) Output firing rates obtained from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#pcbi.1003248.e345" target="_blank">equation (21)</a> for exponential integrate-and-fire (EIF) neurons and equivalent numerical simulations (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003248#s4" target="_blank">Methods</a>: Population Simulations for parameters used in simulations), for excitatory conductance-based synapses without adaptation. Poisson input for with maximum depolarization achieved by a neuron starting from rest mV and input rate Hz.