Chemical Reactions-based Detection Mechanism for Molecular Communications

Abstract

In molecular communications, the direct detection of signaling molecules may be challenging due to the lack of suitable sensors and interference from co-existing substances in the environment. Motivated by examples in nature, we investigate an indirect detection mechanism using chemical reactions between the signaling molecules and a molecular probe to produce an easy-to-measure product at the receiver. The underlying reaction-diffusion equations that describe the concentrations of the reactant and product molecules in the system are non-linear and coupled, and cannot be solved in closed-form. To analyze these molecule concentrations, we develop an efficient iterative algorithm by discretizing the time variable and solving for the space variables in each time step. We also derive insightful closed-form solutions for a special case. The accuracy of the proposed algorithm is verified by particle-based simulations. Our results show that the concentration of the product molecules has a similar characteristic over time as the concentration of the signaling molecules. We analyze the bit error rate (BER) for a threshold detector and highlight that significant improvements in the BER can be achieved by carefully choosing the molecular probe and optimizing the detection threshold.

An Analytical Model for Molecular Communication over a Non-linear Reaction-Diffusion Medium

“…June 1, 2020 DRAFT equations is intractable, these works either use numerical simulations to back up the presented ideas or else simplify the reaction-diffusion process via idealized assumptions about chemical reactions. Authors in [39] provide an iterative numerical algorithm for solving reaction diffusion equations. In a recent work, a neural network is used as the decoder in a medium with chemical reactions [40].…”

“…We need to specify the diffusion coefficients, reaction rate λ, input signals f A and f B as well as the locations of the transmitters. Previous works in the literature commonly take the number released molecules to be either in the order of 10 −14 moles (which is 10 9 molecules) [27], [36], [37], [39], [41], or in the order of 10 −3 mole [34]. The reaction rates in these works are generally in the order of 1 to 10 8 mole −1 .m 3 .s −1 or equivalently 10 −23 to 10 −15 molecules −1 .m 3 .s −1 [34], [39], [42], [43].…”

“…The exact solution in each case is obtained by the finite difference method. The first simulation borrows its system parameters from [39] as follows: Figure 7 shows the perturbation solution up to the second order term. The solution is accurate for λ = 10 −15 and t ∈ [0, 15].…”

“…This observation is consistent with the theoretical analysis given in Appendix A, where the convergence rate of perturbation solution depends on the length of the time interval T . We also remark that in many prior works on chemical reactions in MC, the observation time T is rather small: [41] uses T ≤ 0.1s, [42] uses T ≤ 4s; [39] uses T ≤ 10s, while in other cases T is in taken of order µs [36], [37]. In the third simulation, we assume that a significantly larger number of molecules are released into the medium.…”

A Study of Chemical Reactions in Point-to-Point Diffusion-Based Molecular Communication

“…Reaction-diffusion equations are widely studied in mathematical biology as they model biological phenomena [23]. Unfortunately, chemical reaction-diffusion equations have no closed-form solution in general [24]. In other words, the concentration of molecules cannot be explicitly expressed in terms of the input signals, system parameters as well as the initial and boundary conditions.…”