Receptor Saturation Modeling for Synaptic DMC

Synaptic communication is a natural Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. In particular, it features highly specialized mechanisms to enable inter-symbol interference (ISI)-free and energy efficient communication. The understanding of synaptic MC is furthermore critical for disruptive innovations in the context of brain-machine interfaces. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver arising from the competition of postsynaptic receptors for neurotransmitters. Saturation renders the system behavior nonlinear and is commonly neglected in existing analytical models. In this work, we propose a novel model for receptor saturation in terms of a nonlinear, state-dependent boundary condition for Fick's diffusion equation. We solve the resulting boundary-value problem using an eigenfunction expansion of the Laplace operator and the incorporation of the receiver memory as feedback system into the corresponding state-space description. The presented solution is numerically stable and computationally efficient. Furthermore, the proposed model is validated with particle-based stochastic computer simulations.