Quorum sensing (QS) is a signaling mechanism that pathogenic bacteria use to communicate and synchronize the production of exofactors to attack their hosts. Understanding and controlling QS is an important step towards a possible solution to the growing problem of antibiotic resistance. QS is a cooperative effort of a bacterial population in which some of the bacteria do not participate. This phenomenon is usually studied using game theory and the non-participating bacteria are modeled as cheaters that exploit the production of common goods (exofactors) by other bacteria. Here, we take a different approach to study the QS dynamics of a growing bacterial population. We model the bacterial population as a growing graph and use spectral graph theory to compute the evolution of its synchronizability. We also treat each bacterium as a source of signaling molecules and use the diffusion equation to compute the signaling molecule distribution. We formulate a cost function based on Lagrangian dynamics that combines the time-like synchronization with the space-like diffusion of signaling molecules. Our results show that the presence of non-participating bacteria improves the homogeneity of the signaling molecule distribution preventing thus an early onset of exofactor production and has a positive effect on the optimization of QS signaling and on attack synchronization.
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