Exact distribution of the quantal content in synaptic transmission

During electro-chemical signal transmission through synapses, triggered by an action potential (AP), a stochastic number of synaptic vesicles (SV), called the quantal content, release neurotransmitters in the synaptic cleft. It is widely accepted that the quantal content probability distribution is a binomial based on the number of ready-release SVs in the pre-synaptic terminal. But the latter number itself fluctuates due to its stochastic replenishment, hence the actual distribution of quantal content is unknown. We show that exact distribution of quantal content can be derived for general stochastic AP inputs in the steady-state. For fixed interval AP train, we prove that the distribution is a binomial, and corroborate our predictions by comparison with electrophysiological recordings from MNTB-LSO synapses of juvenile mice. For a Poisson train, we show that the distribution is non-binomial. Moreover, we find exact moments of the quantal content in the Poisson and other general cases, which may be used to obtain the model parameters from experiments.