Quorum Sensing and Nonlocal Hydrodynamics of Swimming Bacteria

Abstract

Water fluidity is modified, in a non trivial manner, by the presence ofbacteria, above a threshold number density. At such threshold conditionssuspensions of swimming bacteria impose a coordinated water movementon a length scale of the order of (10 − 100)m with bacterial size of theorder of 3m. This observation leads to fundamental questions relating tothe mechanism of cell-cell communication among bacteria, presently knownas quorum sensing. Hydrodynamic model of ”swimming” bacteria or bac-terial colonies seems to be one of the most comprehensive alternate modelin defining possible quorum sensing mechanism. Here the densely packedbacteria may be viewed as a”bacterial fluid” or ”living fluid” similar to thatof dense granular systems. Lega and Passot initially assumed a two-phasehydrodynamic equations taken the bacteria and water as two interpene-trating and interacting continuum. However, by considering the relativelyhigh bacterial density, given the fact that no water motion is observed (un-der isothermal conditions and in the sense of displacement sheer viscosity,while rotational bulk viscosity may be present) in absence of the bacteria,we assume the dynamics of the suspended bacteria is governed by bacterialdynamics. Under these conditions bacteria and water appear to move asa single fluid at hydrodynamic scale. We propose that ”bacterial fluid”is consistently described by weakly non-local hydrodynamics where kine-matic viscosity is generated due to self- induced noise. This viscosity leadsto form a metastable state of the actively moving bacteria. This meta-stablestate is necessary for the simultaneous activation of the bacteria to supportquorum, given the existence of non-local nature of stresses mediated byautoinducers. The stability of noisy Burger equation for this metastablesituation will be also studied in this approach.