Protein filaments and their geometrical organization are crucial for cell mechanics, and their failure is related to diseases ranging from sickle cell anemia to Alzheimer’s to cancer. While such stakes would suggest a well-defined design to the engineer, sub-cellular filamentous structures are often surprisingly disordered, and very variable from one cell to the next. Physically, this disorder can be traced back to complicated random aggregation processes involving particles with intricate structures far from equilibrium. To help understand this paradoxical combination of reliability and randomness in the cell’s architecture, I plan on theoretically characterizing robust, generic organizational principles for biofilaments on multiple, interrelated scales, from the whole cell to individual proteins.
I will first consider disordered assemblies of actin filaments and molecular motors that contract in vivo. These systems self-organize to induce cell motility according to different mechanisms than ordered structures, and I will ask which of these non-conventional mechanisms dominates their activity. This problem crucially involves the mesoscopic structure of the filament assembly, which I will consider next. Going beyond existing naive equilibrium models, this second study will focus on the out-of-equilibrium competition between filament growth and aggregation, which experiments have recently shown to dominate actin gel structure. Finally, I will question the foundations of these two first studies by asking why protein filaments are so abundant; indeed, they form even in situations where their presence harms the cell. To this end, I will show that irregular protein-like particles have a natural tendency towards filament formation, which relieves the geometrical frustration resulting from their ill-fitting shapes.
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