A sequential decision making model of bacterial growth via quorum sensing

Quorum sensing is a mechanism used by bacteria to coordinate the expression of certain exofactors which are more beneficial at higher cell densities. It has been argued that quorum sensing is a way for bacteria to control gene expression where some performance metric is being optimized. Herein, bacterial growth via quorum sensing is studied under the lens of optimal control theory. Under the assumption of perfect state observation, it is shown that quorum sensing is an optimal control strategy for an infinite horizon discounted reward function.