Curvature tensor and collective behavior in a population of bacteria

Abstract

In this work, from a geometric point of view, we analyze the SET model (Schweitzer, Ebeling and Tilch) of the mobility of a bacterium. Biological systems are out of thermodynamic equilibrium and they are subject to complex external or internal influences that can be modeled in the form of noise or fluctuations. In this sense, due to the stochasticity of the variables, we study the probability of finding a bacteria with a speed v in the interval (v; v +dv) or, from a population point of view, we can interpret the probability density function as associated with finding a bacterium with a speed v in the interval (v; v +dv). We carry out this study from the stationary probability density solution of the Fokker-Planck equation and using the structure of the statistical manifold related with the stationary probability density, we study the curvature tensor in terms of two coordinates associated with the state of mobility of the bacteria and the environmental conditions. Taking as reference the geometric interpretations found in the framework of equilibrium thermodynamics, our results suggest that bacteria have an effective repulsive interaction that increases with mobility. These results are compatible with the behavior of populations of bacteria that form biofilms when their mobility decreases.