polymers

 

  1. •Semiflexible polymers - worm like chain model

Many of the biologically relevant polymers like DNA, actin filament, microtubule etc. have finite bending rigidity. Their mechanical properties are well captured by the worm-like-chain (WLC) model, which describes the polymer as a space curve that resist bending. We studied the mechanical properties of finite-length WLC polymers as a function of stiffness in different ensembles and
in presence of various boundary conditions.

The polymer properties depend on which ensemble the measurements are done. In constant-extension ensemble, with increasing stiffness parameter, the polymer makes a crossover from flexible to rigid phase much like a first order phase transition. There is an intermediate regime of stiffness where the free energy has three minima and both phases are stable [Phys. Rev. Lett. 89, 065502 (2002)]. This leads to a non-monotonic force-extension curve.

In a follow up paper [Phys. Rev. E 76, 021603 (2007)] I showed that the multiple minima in the free energy is robust with respect to changing boundary orientations, however, the detailed structure of the free energy profile gets modified. In this paper, a mapping of the WLC model, to a quantum particle moving on the surface of an unit sphere, is used to obtain the statistical and mechanical properties of the polymer under various boundary conditions and ensembles. The results show excellent agreement with Monte-Carlo simulations.