Phenotypic switching of populations of cells in a stochastic environment

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.Comment: 17 pages, 6 figure

Formation and Dissolution of Bacterial Colonies

Many organisms form colonies for a transient period of time to withstand environmental pressure. Bacterial biofilms are a prototypical example of such behavior. Despite significant interest across disciplines, physical mechanisms governing the formation and dissolution of bacterial colonies are still poorly understood. Starting from a kinetic description of motile and interacting cells we derive a hydrodynamic equation for their density on a surface. We use it to describe formation of multiple colonies with sizes consistent with experimental data and to discuss their dissolution.Comment: 3 figures, 1 Supplementary Materia

Scaling of the chiral magnetic effect in quantum diffusive Weyl semimetals

We investigate the effect of short-range spin-independent disorder on the chiral magnetic effect (CME) in Weyl semimetals. Based on a minimum two-band model, the disorder effect is examined in the quantum diffusion limit by including the Drude correction and the correction due to the Cooperon channel. It is shown that the Drude correction renormalizes the CME coefficient by a factor to a finite value that is independent of the system size. Furthemore, due to an additional momentum expansion involved in deriving the CME coefficient, the contribution of Cooperon to the CME coefficient is governed by the quartic momentum term. As a result, in contrast to the weak localization and weak anti-localization effects observed in the measurement of conductivity of Dirac fermions, we find that in the limit of zero magnetic field, the CME coefficients of finite systems manifest the same scaling of localization even in three dimension. Our results indicate that while the chiral magnetic current due to slowly oscillating magnetic fields can exist in clean systems, its observability will be limited by suppression due to short-range disorder in condensed matters.Comment: 13 pages, 4 figure, to appear in Phys. Rev.