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Propulsion by growing actin networks is a universal mechanism used in manydifferent biological systems. Although the core molecular machinery for actinnetwork growth is well preserved in most cases, the geometry of the propelledobstacle can vary considerably. In recent years, filament orientationdistribution has emerged as an important observable characterizing thestructure and dynamical state of the growing network. Here we derive severalcontinuum equations for the orientation distribution of filaments growingbehind stiff obstacles of various shapes and validate the predicted steadystate orientation patterns by stochastic computer simulations based on discretefilaments. We use an ordinary differential equation approach to demonstratethat for flat obstacles of finite size, two fundamentally different orientationpatterns peaked at either +35/-35 or +70/0/-70 degrees exhibit mutuallyexclusive stability, in agreement with earlier results for flat obstacles ofvery large lateral extension. We calculate and validate phase diagrams as afunction of model parameters and show how this approach can be extended toobstacles with piecewise straight contours. For curved obstacles, we arrive ata partial differential equation in the continuum limit, which again is in goodagreement with the computer simulations. In all cases, we can identify the sametwo fundamentally different orientation patterns, but only within anappropriate reference frame, which is adjusted to the local orientation of theobstacle contour. Our results suggest that two fundamentally different networkarchitectures compete with each other in growing actin networks, irrespectiveof obstacle geometry, and clarify how simulated and electron tomography datahave to be analyzed for non-flat obstacle geometries.

Mesoscopic model for filament orientation in growing actin networks: the role of obstacle geometry