Modeling phototaxis and planktonic cell behavior in phototrophic biofilms

We propose a continuous, multidimensional model of planktonic cell invasion in phototrophic biofilms that incorporates phototaxis as a key mechanism driving directed movement along light gradients. The model integrates a volume-filling term into the invasion equation, allowing for the description of phototactic behavior. A light-dependent sensitivity function captures both positive and negative phototaxis, modeling cell movement toward favorable light conditions and away from harmful ones. The biofilm is modeled as a homogeneous, viscous, incompressible fluid, with velocity described by Darcy’s law. The governing equations are solved numerically, and simulations are conducted to emphasize the crucial role of phototaxis in influencing biofilm dynamics. Planktonic cells are attracted to areas with optimal light intensity, where they accumulate, stimulating the growth of sessile phototrophs and promoting biofilm development. The interaction between random diffusion and phototactic movement governs the distribution of phototrophic biomass. Under high-light stress conditions, photoinhibition reduces phototrophic growth and reverses phototaxis, causing planktonic cells to move away from the light source, slowing overall biofilm development. Biofilm density significantly influences light availability within the biofilm. Greater biofilm densities increase light attenuation, which, depending on light conditions, either reduces overall phototrophic growth or provides protection against excessive light exposure. These findings are essential for understanding biofilm behavior in natural environments and can guide the optimization of biofilm-based processes in fields like wastewater treatment and bioremediation.