  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.
