Inference of the force pattern acting on a semiflexible filament from shape analysis

The study of the active forces acting on semiflexible filaments networks such as the cytoskeleton requires noninvasive tools able to explore the deformation of single filaments in their natural environment. We propose here a practical method based on the solution of the hydrodynamic beam equation in the presence of transverse forces. We found that the derivative of the local curvature presents discontinuities that match the location of the applied forces, in contrast to the smooth curvature function obtained for the case of compressing longitudinal forces. These patterns can be easily appreciated in a kymograph of the curvature, which also reflects the temporal behavior of the forces. We assessed the method performance with numerical simulations describing the deformation of single microtubules provoked by the action of intracellular active forces.