Copeland Raymond, Yunker Peter J
School of Physics, Georgia Institute of Technology, Atlanta, GA, United States of America.
Phys Biol. 2025 Jul 11;22(4):046003. doi: 10.1088/1478-3975/ade928.
Bacterial biofilms, surface-attached microbial communities, grow horizontally across surfaces and vertically above them. Although a simple heuristic model for vertical growth was experimentally shown to accurately describe the behavior of diverse microbial species, the biophysical implications and theoretical basis for this empirical model were unclear. Here, we demonstrate that this heuristic model emerges naturally from fundamental principles of active fluid dynamics. By analytically deriving solutions for an active fluid model of vertical biofilm growth, we show that the governing equations reduce to the same form as the empirical model in both early- and late-stage growth regimes. Our analysis reveals that cell death and decay rates likely play key roles in determining the characteristic parameters of vertical growth. The active fluid model produces a single, simple equation governing growth at all heights that is surprisingly simpler than the heuristic model. With this theoretical basis, we explain why the vertical growth rate reaches a maximum at a height greater than the previously identified characteristic length scale. These results provide a theoretical foundation for a simple mathematical model of vertical growth, enabling deeper understanding of how biological and biophysical factors interact during biofilm development.
细菌生物膜,即附着于表面的微生物群落,在表面水平生长并在其上方垂直生长。尽管一个简单的垂直生长启发式模型经实验证明能准确描述多种微生物物种的行为,但该经验模型的生物物理意义和理论基础尚不清楚。在此,我们证明这个启发式模型自然地源于活性流体动力学的基本原理。通过解析推导垂直生物膜生长活性流体模型的解,我们表明在早期和晚期生长阶段,控制方程都简化为与经验模型相同的形式。我们的分析表明,细胞死亡和衰变速率可能在决定垂直生长的特征参数方面起关键作用。活性流体模型产生一个单一的、简单的方程,该方程在所有高度上控制生长,其出人意料地比启发式模型更简单。基于这一理论基础,我们解释了为什么垂直生长速率在大于先前确定的特征长度尺度的高度处达到最大值。这些结果为垂直生长的简单数学模型提供了理论基础,有助于更深入地理解生物膜发育过程中生物和生物物理因素是如何相互作用的。