  Synaptic communication is studied by communication engineers for two main
reasons. One is to enable novel neuroengineering applications that require
interfacing with neurons. The other reason is to draw inspiration for the
design of synthetic molecular communication systems. Both of these goals
require understanding of how the chemical synaptic signal is sensed and
transduced at the synaptic receiver (Rx). While signal reception in synaptic
molecular communication (SMC) depends heavily on the kinetics of the receptors
employed by the synaptic Rxs, existing channel models for SMC either
oversimplify the receptor kinetics or employ complex, high-dimensional kinetic
schemes limited to specific types of receptors. Both approaches do not
facilitate a comparative analysis of different types of natural synapses. In
this paper, we propose a novel deterministic channel model for SMC which
employs a generic three-state receptor model that captures the characteristics
of the most important receptor types in SMC. The model is based on a transfer
function expansion of Fick's diffusion equation and accounts for release,
diffusion, and degradation of neurotransmitters as well as their reversible
binding to finitely many generic postsynaptic receptors. The proposed SMC model
is the first that allows studying the impact of the characteristic dynamics of
the main postsynaptic receptor types on synaptic signal transmission. Numerical
results indicate that the proposed model indeed exhibits a wide range of
biologically plausible dynamics when specialized to specific natural receptor
types.
