Competition between chiral self-replicators is mediated by surface growth dynamics

Phase separation and self-assembly of chiral components underlie many biological and industrial processes. We study how chirality of the components impacts these processes. Motivated by recent experiments with microbes, we focus on two-dimensional growth of auto-catalytic or self-replicating agents. The dynamics, described by a chiral reaction-diffusion equation, recapitulate experimental findings in homochiral populations. We predict very unusual behavior when there are two distinct chiral components. Depending on the relative chirality of each, the population evolves to a stable mixed state with both components or a homochiral state where one component goes extinct. To explain our results, we derive an effective theory that couples component competition and growth front dynamics. The theory reduces to a chiral extension of the KPZ equation coupled to a Burgers’ equation with multiplicative noise. The solution of these equations exhibits bulges and dips on the surface at boundaries between domains with different chirality. These undulations in turn alter the motion of the domain boundaries and determine composition and spatial structure. Our findings suggest a new class of surface growth phenomena and can explain the rapid evolution of chirality in biological populations.