Figure 3: The principle of filament guiding at curved edges in the Monte-Carlo simulations. (a) Filament front (grey filled circle) reaches border from open motility supporting area. Without the border, the position 1 would be attained. In the guiding process, this is shifted to position 2 while ensuring that the total distance moved between positions 0 and 2 is equal to sliding velocity times the simulation time step . (b) Continued guiding along the wall. A new sliding direction is drawn from a Gaussian (with SD as in (1)) under the assumption that the wall is not present. Even if the new position will be outside the wall, the filament front is first moved a distance to that position (2). The filament is then shifted to position 3 on the border in a process that maintains the sliding distance, , between positions 0 and 3. (c) The process if the random update in sliding direction moves the filament away from the border. Note, that the ratio is unrealistically large in this example for enhanced clarity in description of the guiding process.