A Mixed-Culture Biofilm Model with Cross-Diffusion

Area of Science:

• Microbiology
• Mathematical Biology
• Biophysics

Background:

• Biofilms are complex microbial communities crucial in various environments.
• Existing deterministic models often oversimplify ecological interactions within biofilms.
• Understanding interspecies dynamics is key to predicting biofilm behavior.

Purpose of the Study:

• To propose a novel deterministic continuum model for mixed-culture biofilms.
• To incorporate interdependent species movement via a degenerate cross-diffusion system.
• To compare two distinct derivations of the proposed model.

Main Methods:

• Developing a deterministic continuum model with cross-diffusion.
• Deriving the model from both discrete lattice equations and continuous mass balances.
• Conducting numerical simulations for competition, allelopathy, and aerobic/anaerobic systems.

Main Results:

• Both derivations yield the same partial differential equation (PDE) model under specific closure assumptions.
• Cross-diffusion significantly influences the local spatial distribution of microbial biomass.
• Overall system biomass and other lumped quantities remain unaffected by cross-diffusion.

Conclusions:

• The proposed cross-diffusion model offers a more nuanced representation of mixed-culture biofilms.
• Cross-diffusion is critical for understanding spatial structuring within biofilms.
• The model provides a generalized framework applicable to diverse biofilm ecological scenarios.