On population density estimation via quorum sensing

Microbial communities regulate various collective functions using a system of cell-cell communication known as quorum sensing. Quorum sensing allows bacteria to estimate the density of their local population, and coordinate gene expression accordingly. Understanding and modeling of quorum sensing regulation can pave the way to the design of nano-networks and, in particular, of communication and coordination schemes among large numbers of nano-machines that need to perform collective decisions based on their local density. In this paper, the performance of population density estimation via quorum sensing is investigated. The distribution of local autoinducers within each cell is derived in closed form, for an asymptotic scenario of large cell population. Based on it, the maximum likelihood estimator is derived, and is compared numerically to a low-complexity estimator. It is shown that the mean squared error of the low-complexity estimator closely approaches that of the maximum-likelihood estimator, and is thus suitable in computationally constrained nano-machines.