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Transición de frentes viajantes a crecimiento limitado por difusión en poblaciones en expansión

Louis Brezin, Kyle J Shaffer, Kirill S Korolev

|February 23, 2026

Abstract:

Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as the square root of time. These sublinear fronts preserve an invariant shape, with an effective diffusion constant that diverges at the transition to linear spreading. The model applies to dense cellular aggregates of nonmotile cells consuming a diffusible nutrient. The sublinear spread results from biomass redistribution slowing due to nutrient depletion, a phenomenon supported experimentally but often neglected. Our results provide a potential explanation for the linear rather than quadratic increase of colony area with time, which has been observed for many microbes.

Palabras clave:

biología matemática biofísica dinámica celular ecuaciones de reacción-difusión frentes viajantes crecimiento limitado por difusión colonias microbianas agotamiento de nutrientes redistribución de biomasa propagación sublineal

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