A Chemical Master Equation Model for Synaptic Molecular Communication

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.