Selected topics in transport phenomena: deterministic and probabilistic aspects

Spatiotemporal self-organization of fluctuating bacterial colonies

Eric Vanden-Eijnden

New York University

Because they are not bound by the standard laws of equilibrium thermodynamics, active materials such as bird flocks, motile bacteria, self-organizing bio-polymers, or man-made self-propelled particles have many more routes towards self-assembly and self-organization than systems whose dynamics satisfy detailed-balance. While much remains to be done to build a statistical mechanics theory of these non-equilibrium systems, some generic principles governing their behavior have started to emerge. Motility-induced phase separation (MIPS) is one example. MIPS arises naturally in systems of self-propelled particles whose locomotive speed decreases strongly at high density, through a feedback in which particles accumulate where they move slowly and vice-versa. In this talk, we build on these results and model an enclosed system of bacteria, whose MIPS is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population causes a dense bacterial colony to form, which then declines by local cell death, before dispersing to re-initiate the cycle. Adding fluctuations, we find that static colonies are now metastable, moving between spatial locations via rare and strongly nonequilibrium pathways, whereas the limit cycle becomes quasi-periodic such that after each redispersion event the next colony forms in a random location. These results, which resemble some aspects of the biofilm-planktonic life cycle, can be explained by combining tools from large deviation theory with a bifurcation analysis in which the global population density plays the role of control parameter. The analytical and numerical tools presented should also be useful in other non-equilibrium systems in which noise-driven self-organization occurs. This is joint work with Mike Cates and Tobias Grafke.