  In synaptic molecular communication, the activation of postsynaptic receptors
by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion
process and, hence, inherently random. It is currently not fully understood how
this randomness impacts downstream signaling in the target cell and,
ultimately, neural computation and learning. The statistical characterization
of the reaction-diffusion process is difficult because the reversible
bi-molecular reaction of NTs and receptors renders the system nonlinear.
Consequently, existing models for the receptor occupancy in the synaptic cleft
rely on simplifying assumptions and approximations which limit their practical
applicability. In this work, we propose a novel statistical model for the
reaction-diffusion process governing synaptic signal transmission in terms of
the chemical master equation (CME). We show how to compute the CME efficiently
and verify the accuracy of the obtained results with stochastic particle-based
computer simulations (PBSs). Furthermore, we compare the proposed model to two
benchmark models proposed in the literature and show that it provides more
accurate results when compared to PBSs. Finally, the proposed model is used to
study the impact of the system parameters on the statistical dependence between
binding events of NTs and receptors. In summary, the proposed model provides a
step forward towards a complete statistical characterization of synaptic signal
transmission.
