Modeling Thermal Fluctuations of Bio-Filaments With Elastic Rod Theory

Bio-filaments at sub-micron scales such as DNA perform their biological functions via well-regulated structural deformations that involve large twisting and bending. The strain energies associated with these deformations are of the order of the thermal kinetic energies of surrounding solvent molecules. Therefore, the bio-filaments at such small length scales also exhibit large fluctuations in their shape due to the random collisions of the solvent molecules with them. These thermal fluctuations may, on one hand, help the bio-filaments explore functionally desirable configuration space, while, on the other hand, hinder the regulation of their deformations by motor proteins. Nevertheless, it seems indispensable to model the thermal fluctuations to accurately study the dynamics of deformation of bio-filaments. This paper presents the first elastic rod formulation that incorporates the thermal fluctuations by modeling the impacts of solvent molecules as distributed stochastic force. For quasi-static fluctuations, this formulation leverages the simplicity of a rod formulation noted by Anker et al. [1] that allows solving it as an initial value problem (IVP) in single iteration, and yet capturing arbitrarily large (nonlinear) deformations with rigorous description of constitutive laws.