Emergent probability fluxes in confined microbial navigation

When the motion of a motile cell is observed closely, it appears erratic, and yet the combination of nonequilibrium forces and surfaces can produce striking examples of organization in microbial systems. While most of our current understanding is based on bulk systems or idealized geometries, it remains elusive how and at which length scale self-organization emerges in complex geometries. Here, using experiments and analytical and numerical calculations, we study the motion of motile cells under controlled microfluidic conditions and demonstrate that probability flux loops organize active motion, even at the level of a single cell exploring an isolated compartment of nontrivial geometry. By accounting for the interplay of activity and interfacial forces, we find that the boundary’s curvature determines the nonequilibrium probability fluxes of the motion. We theoretically predict a universal relation between fluxes and global geometric properties that is directly confirmed by experiments. Our findings open the possibility to decipher the most probable trajectories of motile cells and may enable the design of geometries guiding their time-averaged motion.

Asymptotic analysis of extended two-dimensional narrow capture problems

In this paper, we extend our recent work on two-dimensional diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux into each target. The latter determines the distribution of arrival or capture times into an individual target, conditioned on the set of events that result in capture by that target. A characteristic feature of strongly localized perturbations in two dimensions is that matched asymptotics generates a series expansion in ν = −1/ln ϵ rather than ϵ , 0 < ϵ ≪ 1, where ϵ specifies the size of each target relative to the size of the search domain. Moreover, it is possible to sum over all logarithmic terms non-perturbatively. We exploit this fact to show how a Taylor expansion in the Laplace variable s for fixed ν provides an efficient method for obtaining corresponding asymptotic expansions of the splitting probabilities and moments of the conditional first-passage-time densities. We then use our asymptotic analysis to derive new results for two major extensions of the classical narrow capture problem: optimal search strategies under stochastic resetting and the accumulation of target resources under multiple rounds of search-and-capture.

Stochastic Epigenetic Dynamics of Gene Switching

Epigenetic modifications of histones crucially affect the eukaryotic gene activity. We theoretically analyze the dynamical effects of histone modifications on gene switching by using the Doi-Peliti operator formalism of chemical reaction kinetics. The calculated probability flux in self-regulating genes shows a distinct circular flow around basins in the landscape of the gene state distribution, giving rise to hysteresis in gene switching. In contrast to the general belief that the change in the amount of transcription factor (TF) precedes the histone state change, the flux drives histones to be modified prior to the change in the amount of TF in the self-regulating circuits. The flux-landscape analyses elucidate the nonlinear nonequilibrium mechanism of epigenetic gene switching.

The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system

Dissipative chaotic dynamics and its onset/offset are determined by the intrinsic potential landscape and nonequilibrium probability flux flow.