The force generated by biological membranes on a polymer rod and its response: statics and dynamics

We propose a theory for the force exerted by a fluctuating membrane on a polymer rod tip. Using statistical mechanical methods, the expression for the generated force is written in terms of the distance of the rod tip from the membrane "frame." We apply the theory in calculating the stall force and membrane displacement required to cease the growth of a growing fiber induced by membrane fluctuations, as well as the membrane force and membrane displacement required for rod/fiber buckling. We also consider the dynamics of a growing fiber tip under the influence of a fluctuation-induced membrane force. We discuss the importance of our results in various biological contexts. Finally, we present a method to simultaneously extract both the rigidity of the semiflexible rod and the force applied by, e.g., the membrane from the measurements of the bending fluctuations of the rod. Such a measurement of the force would give information about the thermodynamics of the rod polymerization that involves the usual Brownian ratchet mechanism.