Fluctuating elastic filaments under distributed loads

Filaments under distributed loads are common in biological systems. In this paper, we study the thermo-mechanical properties of an extensible thermally fluctuating elastic filament under distributed forces. The ground state of the filament is solved first, followed by an investigation of the thermal fluctuations around the ground state. We first consider a special case where the tangential component of the distributed force tau is uniform along the filament. For the force-extension relation in this case, we show that the filament is equivalent to one under end-to-end applied force F = tauL0/2 where L0 is the length of the filament. To study the thermal fluctuations under more general distributed loadings, the filament is first discretized into segments, and its energy is approximated up to quadratic order. Then the partition function of the discretized filament, or chain, is evaluated using multi-dimensional Gaussian integrals, from which free energy and other properties of the filament are derived. We show that a filament under distributed loads suffers larger thermal fluctuations than one with the end loads of the same magnitude. We also show that our results for a discretized filament agree with continuum theory for a continuous rod. Finally, we give some applications of our ideas to the stretching and fluctuation of DNA in non-uniform microfluidic channels.