Characterization of Cooperators in Quorum Sensing with 2D Molecular Signal Analysis

TL;DR

This paper develops an analytical model for quorum sensing in bacteria within a 2D environment, considering stochastic molecular propagation and distribution of bacteria, providing new insights into cooperative behavior and its control.

Contribution

It introduces a stochastic geometry-based model for QS signal propagation and cooperation probability in 2D, improving upon prior deterministic models.

Findings

Analytical expressions for channel response and cooperation probability.

Poisson distribution best approximates the number of cooperators.

Model aligns well with particle-based simulation results.

Abstract

In quorum sensing (QS), bacteria exchange molecular signals to work together. An analytically-tractable model is presented for characterizing QS signal propagation within a population of bacteria and the number of responsive cooperative bacteria (i.e., cooperators) in a two-dimensional (2D) environment. Unlike prior works with a deterministic topology and a simplified molecular propagation channel, this work considers continuous emission, diffusion, degradation, and reception among randomly-distributed bacteria. Using stochastic geometry, the 2D channel response and the corresponding probability of cooperation at a bacterium are derived. Based on this probability, new expressions are derived for the moment generating function and different orders of moments of the number of cooperators. The analytical results agree with the simulation results obtained by a particle-based method. In addition, the Poisson and Gaussian distributions are compared to approximate the distribution of the number of cooperators and the Poisson distribution provides the best overall approximation. The derived channel response can be generally applied to any molecular communication model where single or multiple transmitters continuously release molecules into a 2D environment. The derived statistics of the number of cooperators can be used to predict and control the QS process, e.g., predicting and decreasing the likelihood of biofilm formation.