Distinguishable spreading dynamics in microbial communities

A packed community of exponentially proliferating microbes will spread in size exponentially. However, due to nutrient depletion, mechanical constraints, or other limitations, exponential proliferation is not indefinite, and the spreading slows. Here we theoretically explore a fundamental question: is it possible to infer the dominant limitation type from the spreading dynamics? Using a continuum active fluid model, we consider three limitations to cell proliferation: nutrient access, pressure from other cells, and intrinsic metabolic timing such as a sporulation pathway. We find that each leads to different spreading dynamics: a purely intrinsic timer corresponds to exponential spread at a slower rate, pressure limitation corresponds to linear spread, and nutrient limitation corresponds to a phase transition that gives either exponential or sublinear spread. These results suggest that mechanistic, cell-level growth limitations can be inferred from phenomenological, population-level dynamics, and they offer a quantitative roadmap for connecting these two scales.