Study of the Bacterial "Conversations" and Pattern Formation in the Quorum Sensing System using Numerical Simulation

Cell-to-cell communication processes in the bacterial world can be considered as a collective bacterial behavior, which is coordinated by chemical signaling molecules (autoinducers, quorum sensing molecules, or pheromones). This complex biological process is termed the quorum sensing mechanism, which is considered a density-dependent bacterial communication system. As the bacterial culture grows, signal molecules are released into the extracellular milieu and accumulate, changing water fluidity. Under such threshold conditions, swimming bacterial suspensions impose a coordinated water movement on a length scale of the order of 10 to 100 micrometers compared with a bacterial size of the order of 3 micrometers. Here, we propose a non-local hydrodynamics of the quorum state and wave-like pattern formation using the forced Burgers equation with Kwak transformation. Such an approach resulted in the conversion of the Burgers equation paradigm into a reaction-diffusion system. The examination of the dynamics of the quorum sensing system, both analytically as well as numerically, results in similar long-time dynamical behaviour. Moreover, we find out the range kinematics viscosity of the living fluid, which is one of the significant parameters for pattern formation in the system. AMS Subject Classification: 92B05, 65N06, 65Z05. Doi: 10.28991/HEF-SP2022-01-03 Full Text: PDF