A potpourri of results on molecular communication with active transport

Abstract

Molecular communication (MC) is a model of information transmission where the signal is transmitted by information-carrying molecules through their physical transport from a transmitter to a receiver through a communication channel. Prior efforts have identified suitable "information molecules" whose efficacy for signal transmission has been studied extensively in diffusive channels (DC). Although easy to implement, DCs are inefficient for distances longer than tens of nanometers. In contrast, molecular motor-driven nonequilibrium or active transport can drastically increase the range of communication and may permit efficient communication up to tens of micrometers. In this paper, we investigate how active transport influences the efficacy of molecular communication, quantified by the mutual information between transmitted and received signals. We consider two specific scenarios: (a) active transport through relays and (b) active transport through a mixture of active and diffusing particles. In each case, we discuss the efficacy of the communication channel and discuss their potential pitfalls.

Figures (5)

• Figure 1: Schematic diagram of the model. sarkar2023efficacy
• Figure 2: (a) Schematic of the one relay lattice. The red site is the relay. (b) $I_1$ and $I_3$ vs. system size for channels with one relay. The relay is kept at the midpoint of the 1D channel.
• Figure 3: (a) Schematic diagram of relays. The site coloured red is the relay site. (i) A molecule (labeled in brown) approaches the relay site. Its left and right hopping rates are equal, in this case: $k_L=0.5$, $k_R=0.5$. (ii) The molecule reaches the relay site, and its hopping rates change to $k_L=0$ and $k_R=1$. (iii) The molecule is pushed by the relay into the next site, where its hopping rates changes back to $k_L=0.5$ and $k_R=0.5$. (b) A contour plot showing the variation of I, the MI between transmitter-receiver, with $n_2$ and $n_3$, where $n_2$ is the number of DCs of length 2 and $n_3$ is the number of DCs of length 3 in the channel. (c) Variation of MI between source-sink with inter-relay distance for different lengths of the 1D lattice. (d) Variation of MI between source-sink with number of relays for different lengths of the 1D lattice. (e) Variation of MI between source-sink with inter-relay distance for different $\left< \tau_F \right>$, with $L=256$. Inset shows variation of threshold length $L_0$ with $\left< \tau_F \right>$. Here, $L_0$ is the threshold inter-relay distance $L/(N_{relay}+1)$ at which $I$ falls below 0.1 in (d).
• Figure 4: Plot of $\ln(-\ln I)$ vs. $\ln n$, which shows that channels made of single-length DCs of lengths 2, 3, 5, 10 all follow the stretched exponential function given in Eq. \ref{['eq: 6']}. A straight line is fitted to the simulation data, with the slope, $m$ and intercept $c$ given in the legend.
• Figure 5: (a) MI vs. active fraction for channels of different lengths, with $k_R=1$ for active particles. The best fit shows that above an active fraction, MI $\sim$$f_a^3$. The inset shows a schematic showing active particles labeled green, with passive particles labeled brown. (b) The joint probability distribution function, $P(\tau_F, \tau_D)$ for different active fractions, $f_a$. (i) $f_a = 0$, (ii) $f_a = 0.1$, (iii) $f_a = 1$. (c) Cluster size distribution for different active fractions $f_a$. (d) Kymographs from stochastic simulations. Kymographs show molecular trajectories for different active fractions, (i) $f_a=0$, (ii) $f_a=0.1$, and (iii) $f_a=1$, all for $L=256$.