The influence of synaptic weight distribution on neuronal population dynamics

PLoS Comput Biol. 2013 Oct;9(10):e1003248. doi: 10.1371/journal.pcbi.1003248. Epub 2013 Oct 24.

Abstract

The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials / physiology
  • Computer Simulation
  • Models, Neurological*
  • Neurons / physiology*
  • Synapses / physiology*

Grant support

The Allen Institute for Brain Science funded the research but had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.