Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth.
In contrast to their name, biofilms are not always flat and homogeneous but instead often exhibit complex structural heterogeneity. It has been suggested that nonhomogeneous geometry is selected in order to increase biofilm growth rate. A previous study (Dockery and Klapper (2002) SIAM J. Appl. Math., 62, 853-869) of a model biofilm system in a static bulk fluid demonstrated that under some circumstances a flat biofilm-bulk fluid interface is linearly unstable to perturbation due to growth induced forces. Computations indicated that subsequent nonlinear evolution results in fingers and mushrooms of biofilm similar to structures observed in actual biofilms. However, the important complementary issue of biological functionality was not considered. Here a weakly nonlinear analysis of the simple growing biofilm layer model in Dockery and Klapper (2002, SIAM J. Appl. Math., 62, 853-869) is presented. It is argued that, at least in the case of biofilms free of external mechanical stress, overall growth is in fact generally inhibited by the presence of growing perturbations in the linear stage. Hence a more complex explanation of function is necessary.