Diffusion-Based Model for Synaptic Molecular Communication Channel

Abstract

Computational methods have been extensively used to understand the underlying dynamics of molecular communication methods employed by nature. One very effective and popular approach is to utilize a Monte Carlo simulation. Although it is very reliable, this method can have a very high computational cost, which in some cases renders the simulation impractical. Therefore, in this paper, for the special case of an excitatory synaptic molecular communication channel, we present a novel mathematical model for the diffusion and binding of neurotransmitters that takes into account the effects of synaptic geometry in 3-D space and re-absorption of neurotransmitters by the transmitting neuron. Based on this model we develop a fast deterministic algorithm, which calculates expected value of the output of this channel, namely, the amplitude of excitatory postsynaptic potential (EPSP), for given synaptic parameters. We validate our algorithm by a Monte Carlo simulation, which shows total agreement between the results of the two methods. Finally, we utilize our model to quantify the effects of variation in synaptic parameters, such as position of release site, receptor density, size of postsynaptic density, diffusion coefficient, uptake probability, and number of neurotransmitters in a vesicle, on maximum number of bound receptors that directly affect the peak amplitude of EPSP.

Sum Rate of MISO Neuro-Spike Communication Channel With Constant Spiking Threshold

“…Once a vesicle is released, neurotransmitters diffuse through the synaptic cleft to reach post-synaptic density (PSD) that contains receptors. As defined in [20], we consider a rectangular synaptic cleft for ith synapse with height H i and a square shaped PSD with side length L i on post-synaptic membrane. In [20], the pre-and post-synaptic membranes are assumed to have infinite dimension.…”

“…As defined in [20], we consider a rectangular synaptic cleft for ith synapse with height H i and a square shaped PSD with side length L i on post-synaptic membrane. In [20], the pre-and post-synaptic membranes are assumed to have infinite dimension. Then, the expected value of concentration of neurotransmitters in the synaptic cleft from ith pre-synaptic input at time t, C i (x, y, z, t), is given as,…”

“…The neurotransmitters that reach post-synaptic terminal bind to the receptors residing on the PSD. These receptors are assumed to be uniformly distributed on the PSD and a small effective volume, i.e., v i,r , is considered around rth receptor located in ith synapse such that the neurotransmitters that are inside this volume are likely to bind with the receptor [20]. The expected concentration of neurotransmitters inside v i,r , i.e., C vi,r (t), is calculated in [20] as…”

“…is the number of neurotransmitters found inside v i,r at time t and |v i,r | is the size of the effective volume. As shown in [20], T i,r (t) can be modeled by a binomial random variable, having expected value T i,r (t) = T i (t)P i,r (t).…”

“…Here, T i (t) ≤ T 0 is the expected total number of unbound neurotransmitters in the ith synaptic cleft at time t and P i,r (t) is the probability of finding a released neurotransmitter inside v i,r at time t. This probability is calculated in [20] as…”