Exact distribution of the vesicle burst size in synaptic transmission

Abstract

AbstractThe transfer of electro-chemical signals from the pre-synaptic to the post-synaptic terminal of a neuronal or neuro-muscular synapse is the basic building block of neuronal communication. When triggered by an action potential the pre-synaptic terminal releases neurotransmitters in the synaptic cleft through vesicle fusion. The number of vesicles that fuse, i.e., the burst size, is stochastic, and widely assumed to be binomially distributed. However, the burst size depends on the number of release-ready vesicles, a random variable that depends upon a stochastic replenishment process, as well as stochastic inter-spike intervals of action potentials. The burst size distribution suitably averaged over these two stochastic processes was not known in the literature. Here we analytically obtain the exact probability distribution of the number of vesicles released in the synaptic cleft, in the steady state reached during stimulation by a spike train of action potentials. We show that this distribution is binomial, with modified parameters, only when stimulated by constant frequency signals. Other forms of input, e.g. Poisson-distributed action potentials, lead to distributions that are non-binomial. The general formula valid for arbitrary distributions of the input inter-spike interval, may be employed to study neuronal transmission under diverse experimental conditions. We corroborate our theoretical predictions through comparison with the burst size distributions obtained from electrophysiological recordings from MNTB-LSO synapses of juvenile mice. We also confirm our theoretically predicted frequency dependence of mean burst size by comparing with experimental data from hippocampal and auditory neurons.