Abstract
Branching actin network growth is the primary engine driving cell motility. At the front of a motile cell, inside the lamellipodium, is a dense mesh of actin filaments pushing the membrane forward. The structure of the mesh is believed to be largely regulated by three processes: branching of new filaments off of existing ones, capping of filament tips stopping filament growth, and filament growth. Filaments inside the lamellipodium have been observed to organize into a strict orientation pattern where filaments are angled approximately −35/35 degrees from the direction normal to the membrane. It has been previously hypothesized that the three processes above are sufficient to generate the unique orientation pattern.We derive and analyze an integro-differential PDE for the angular density of branching actin network by incorporating the three constituent processes. Our analysis implies that there exist multiple equilibrium angular distributions, which strongly suggests additional process that regulates actin filament orientation.
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