Emergence of sector and spiral patterns from a two-species mutualistic cross-feeding model

The ubiquitous existence of microbial communities marks the importance of understanding how species interact within the community to coexist and their spatial organization. We study a two-species mutualistic cross-feeding model through a stochastic cellular automaton on a square lattice using kinetic Monte Carlo simulation. Our model encapsulates the essential dynamic processes such as cell growth, and nutrient excretion, diffusion and uptake. Focusing on the interplay among nutrient diffusion and individual cell division, we discover three general classes of colony morphology: co-existing sectors, co-existing spirals, and engulfment. When the cross-feeding nutrient is widely available, either through high excretion or fast diffusion, a stable circular colony with alternating species sector emerges. When the consumer cells rely on being spatially close to the producers, we observe a stable spiral. We also see one species being engulfed by the other when species interfaces merge due to stochastic fluctuation. By tuning the diffusion rate and the growth rate, we are able to gain quantitative insights into the structures of the sectors and the spirals.