Statistical and Biological Physics

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Length Regulation Drives Self-Organization in Filament-Motor Mixtures

Moritz Striebel, Fridtjof Brauns, and Erwin Frey

Cytoskeletal structures play essential roles in many cellular processes, including intracellular transport, cell division and cell motility. The formation and regulation of these structures involves many types proteins that associate with the cytoskeletal filaments, to regulate their nucleation and polymerization, to crosslink them, and to exert mechanical forces on them.

Past studies on the collective organization of many filaments have focused on the mechanical interactions between filaments and force-generating (cross-linking) motors. In contrast, studies on length regulation have exclusively focused on the single filaments and did not address collective effects.

In our work we focus on collective length regulation in a conceptual model for a filament motor mixture. Importantly, we explicitly account for the diffusive redistribution of cytosolic tubulin units and depolymerizing motors. We derive a hydrodynamic description of the collective dynamics of tubulin, motors and filaments. Employing a linear stability analysis, we discover a long wavelength spatial instability that is driven by diffusive redistribution of tubulin mass. Thereby we were able to show that cytosolic redistribution of microtubule associated proteins in combination with microtubule length regulation can drive self-organisation of large scale filament assemblies. This instability mechanism is operational in a large parameter regime, including physiological parameters. Importantly and surprisingly, the self-organization mechanism is driven by filament-length regulation alone, in the absence of any mechanical interactions between filaments.

This finding opens up the possibility for a currently unstudied self-organization pathway for cytoskeletal filament assemblies. Using our theoretical framework we make predictions which can be tested experimentally to get further insight in the role of resource limitation for cytoskeletal self-organization.