Diffusion-Based Molecular Communication Channel in Presence of a Probabilistic Absorber: Single Receptor Model and Congestion Analysis

Abstract

In this paper, a diffusion-based molecular communication channel is modeled in presence of a probabilistic absorber. The probabilistic absorber is an absorber which absorbs molecules upon collision with probability q. With random walk analysis, the discrete probability function of particle location in presence of a probabilistic absorber can be found. Then a continuous probability function is fitted to this Markov-based results with introducing several fitting parameters to the known probability function of particle location in an unbounded environment without an absorbing barrier. With this approach, a single receptor is modeled as an M/M/1/1 queue in which q represents the complementary blocking probability and the mean service time is the mean trafficking time. Therefore, we are able to model the stochastic nature of ligand-receptor binding which comes from the incapability of a receptor to receive all molecules in its space; Also known as receptor occupancy. Proper consideration of the absorption effect leads to the accurate calculation of the concentration at the desired site, which is definitely less than the concentration obtained when neglecting it. These findings can have a crucial role in designing drug delivery systems in which determining the optimal rate of the drug transmitting nanomachines is critical to avoid toxicity while maintaining effectiveness.

Saturating Receiver and Receptor Competition in Synaptic DMC: Deterministic and Statistical Signal Models

“…Finally, to ensure the existence of the inverse transformation in (21), the eigenfunctions in (25) have to be bi-orthogonal, yielding the following expression for the scaling factor [39]…”

“…3) State-Space Description: We conclude this section by deriving an equivalent formulation of ( 27), (21) in terms of an SSD. The state-space representation will subsequently allow us in Section III-C to incorporate the nonlinear effects due to receptor saturation that we have avoided in this section by setting κ a = 0.…”

“…The state-space representation will subsequently allow us in Section III-C to incorporate the nonlinear effects due to receptor saturation that we have avoided in this section by setting κ a = 0. To derive the SSD, the expansion coefficients ȳµ in (27) and the synthesis equation (21) for y are transformed into discrete time using an impulse invariant transform [30]. This yields the following discrete-time SSD [29] ȳ i.e., the smaller D, κ a 0 , κ d , and κ e C E are, the smoother signal y(x, t) is and the larger may T be chosen.…”

“…, respectively, and contain Q values of fµ and φµ from (28). Output equation (30) is the discrete-time equivalent of the synthesis equation in (21), where the summation is replaced by a multiplication with matrix…”

“…Saturation at the molecular receiver has been considered in the MC literature also in the context of targeted drug delivery [19]- [21] and experimental studies [22]- [24]. In none of these works, however, the impact of receptor saturation on the spatial distribution of solute molecules is modeled explicitly.…”