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New tools for the mechanics of biofilaments
Many biological objects present themselves as elongated slender structures. One may for instance mention proteins, polymers, DNA, bacterial fibres, fungi, stems, roots, arteries or neurons to cite but a few. It so happens that these bio-filaments are often organised as bundles of sub-filaments. The interplay of the growth and mechanical properties of these sub-entities generates the subtle geometric and mechanical properties of the global structure.
In this presentation, I will cover recent advances and point out exciting challenges in three key problems. How to infer the mechanical properties of the filament from their microscopic structure ? How to infer the macroscopic properties of spring like filaments ? How to effortlessly decide the stability of various equilibria ? We will see that these problems raise interesting mathematical questions but also that they are of direct practical relevance. Some of our examples will be drawn from biology and others from man-made structures, all of them will involve nonlinear equations and stratagems for handling them.