Elasticity of a Filament with Kinks

Using the wormlike chain model, we analytically study the elasticity of a filament with kinks. We calculate the position probability density function and the force constant of a kinked filament with a general kink angle. Then, using the mathematical induction, we obtain the positional-orientational probability density function of a filament with regular kinks. For this filament, we compute the force constant in two different directions. In longitudinal direction of the filament, the force constant is proportional to the inverse of the number of the segments, i.e., 1 / m, while in transverse direction, it is proportional to \(1/m^3\).