旅行波向扩散限制生长的转变在扩展种群中
Transition from traveling fronts to diffusion-limited growth in expanding populations
AI总结：
该研究通过分析反应-扩散方程，揭示了扩展种群中旅行波向扩散限制生长转变的机制，解释了菌落面积随时间线性增长的原因。
摘要：
反应-扩散方程描述了各种在空间上扩展的过程，这些过程以恒定速度移动的旅行波展开。我们引入并求解了一个模型，除了这样的波外，该模型还支持以时间平方根速度前进的解。这些亚线性波保持不变的形状，具有在转向线性扩展时发散的有效扩散常数。该模型适用于非移动细胞密集的细胞团，这些细胞消耗可扩散的营养物质。亚线性扩展是由于生物量重新分布因营养耗尽而减慢，这一现象已通过实验得到支持，但常被忽视。我们的结果为线性而非二次增长的菌落面积与时间的关系提供了可能的解释，这一现象在许多微生物中已被观察到。
英文摘要：
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.
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