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: intrinsic growth arrest (e.g., due to sporulation), pressure from other cells, and nutrient access. We find that memoryless growth arrest still results in superlinear (accelerating) spreading, but at a reduced rate. In contrast, pressure-limited growth results in linear (constant-speed) spreading in the long-time limit. We characterize how the expansion speed depends on the maximum growth rate, the limiting pressure value, and the effective fluid friction. Interestingly, nutrient-limited growth results in a phase transition: depending on the nutrient supply and how efficiently nutrient is converted to biomass, the spreading can be either superlinear or sublinear (decelerating). We predict the phase boundary in terms of these parameters and confirm with simulations. Thus, our results suggest that when an expansion slowdown is observed, its dominant cause is likely nutrient depletion. More generally, our work suggests that cell-level growth limitations can be inferred from population-level dynamics, and it offers a methodology for connecting these two scales.

💡 Research Summary

In this work the authors develop a continuum active‑fluid framework to ask whether the dominant mechanism that limits microbial colony expansion can be inferred from the macroscopic spreading dynamics. They consider three distinct growth‑limiting scenarios—(i) a memoryless, time‑dependent growth arrest such as sporulation, (ii) pressure‑limited growth in which the local mechanical pressure suppresses the division rate, and (iii) nutrient‑limited growth in which the division rate depends on the local concentration of a diffusing nutrient. Assuming radial symmetry, constant cell density inside the colony, and a sharp colony edge, they reduce the full multi‑component fluid equations to a single ordinary differential equation for the colony radius R(t) coupled to either an algebraic relation (case i), a pressure‑velocity relation (case ii), or a diffusion‑consumption equation (case iii).

For the first case, the authors introduce a sporulation rate k and a maximal growth rate g. The total number of actively growing cells C₁(t) obeys dC₁/dt = (g‑k)C₁, giving C₁(t)=C₁(0) e^{(g‑k)t}. Substituting into the mass‑balance equation yields R(t)∝