The Influence of Synaptic Weight Distribution on Neuronal Population Dynamics

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.Author Summary: Neurons communicate via action potentials. Typically, depolarizations caused by presynaptic firing are small, such that many synaptic inputs are necessary to exceed the firing threshold. This is the assumption made by standard mathematical approaches such as the Fokker-Planck formalism. However, in some cases the synaptic weight can be large. On occasion, a single input is capable of exceeding threshold. Although this phenomenon can be studied with computational simulations, these can be impractical for large scale brain simulations or suffer from the problem of insufficient knowledge of the relevant parameters. Improving upon the standard Fokker-Planck approach, we develop a hybrid approach combining semi-analytical with computational methods into an efficient technique for analyzing the effect that rare and large synaptic weights can have on neural network activity. Our method has both neurobiological as well as methodological implications. Sparse but powerful synapses provide networks with response celerity, enhanced bandwidth and stability, even when the networks are matched for average input. We introduce a measure characterizing this response. Furthermore, our method can characterize the sub-threshold membrane potential distribution and spiking statistics of very large networks of distinct but homogeneous populations of 10s to 100s of distinct neuronal cell types throughout the brain.