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| One of the most fascinating characteristics of biological systems is their ability of self-organization and pattern formation: Many biological processes lead to emergence of various chemical and mechanical, spatially heterogeneous structures from homogenous or chaotic systems. One prominent example is embryonic development, where a tissue sphere develops step by step into an organism of complex shape and function. Another example are biomembranes, which emerge as complex structures from initially chaotically distributed molecules.
During the last decades, advanced molecular biological methods allowed to identify various molecules involved in the biological processes of pattern formation. However, the question of how these molecules create patterns and structures often remains unanswered. An increasing amount of experimental results suggests an interplay between chemical and mechanical processes in biological patterning.
We develop new mathematical models to investigate biological patterning processes, taking into account biomechanical aspects of tissues and membranes. Models are based on minimization of free energy leading to nonlinear PDE systems of fourth order, related to the Willmore flow. Parametric finite element simulations allow us to avoid several limitations of experiments and to test different biological hypotheses. We demonstrate that even simple mechano-chemical interplays may lead to spontaneous pattern formation in biological surfaces. |
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