Three-dimensional buckling model reveals the evolution of energy-driven biofilm wrinkle morphologies

On solid substrates, biofilms develop rich wrinkle morphologies during its growth. Based on the thin film buckling theory, we established a local three-dimensional biofilm/substrate buckling model, and explored the effects of mechanical forces, elastic modulus of the substrate, and biofilm thickness on the wrinkle morphology. We simulated the wrinkle evolution in various patterns of <i>Bacillus subtilis</i> biofilm growing on agar substrates with different stiffness and found that the biofilm wrinkling process is the process of internal energy release. The stiffness of the substrate changes the wrinkling time of the biofilm; The biofilm wrinkle morphology (patterns II, III, and IV) <i>U</i>_internal and <i>U</i>_internal/<i>U</i>₀ decrease with nutrient consumption, and the biofilm evolves towards lower energy consumption. In the early stages of biofilm growth (patterns I, II, and III), the harder the agar substrate, the larger the <i>U</i>_friction and <i>U</i>_friction/<i>U</i>₀, which is less conducive to biofilm expansion.