Modeling Phototaxis and Planktonic Cell Behavior in Phototrophic Biofilms

We propose a continuous multidimensional multispecies model of planktonic cell invasion in phototrophic biofilms that incorporates phototaxis as a key mechanism driving directed movement along light gradients. The biofilm is modeled as a homogeneous, viscous, incompressible fluid, with the velocity field governed by a Darcy-type law. The phototactic behavior of planktonic cells is integrated in the model by considering a reaction-advection-diffusion equation including a diffusive and tactic flux with a volume-filling term. Cell movement toward favorable light conditions and away from harmful ones is modeled through a light-dependent sensitivity function capturing both positive and negative phototaxis. Planktonic cells are attracted to regions with optimal light intensity, where they accumulate as an effect of phototactic behavior, and might switch their phenotype from planktonic to sessile, contributing to biofilm expansion. Numerical simulations highlight the crucial role of phototaxis in biofilm dynamics, showing how the balance between random diffusion and phototactic movement regulates biomass distribution and, consequently, oxygen and organic carbon dynamics. Under high-light stress conditions, photoinhibition reverses phototaxis, causing planktonic cells to move away from the light source, reducing overall biofilm development. Higher biofilm densities increase light attenuation, which, depending on light conditions, either reduces overall phototrophic growth or provides protection against excessive light exposure. Finally, biofilm geometry influences light attenuation and phototrophic growth, with its effects depending on incident light conditions and biofilm density. Overall, the proposed multispecies framework provides a mechanistic tool to investigate how phototactic motility, light conditions, biofilm properties, and microbial interactions jointly regulate phototrophic biofilm development.