Statistical mechanics of individual semi-flexible filaments

There are many real macromolecules and assemblies that exhibit large chain stiffness, and as a consequence do not behave as Gaussian chains. Notable examples of such semiflexible chains occur in biological systems such as DNA, actin filaments, fibrils, microtubules and in some liquid crystalline polymers. Although the problem of obtaining the probability distribution for such filaments dates back to the 1950's, there has been a renewed interest recently due to the expansion of people interested in modelling biological semi-flexible networks. We have obtained a simple method of calculating this probability distribution using a single Lagrange multiplier to constrain the average length of the chain. Our paper on the problem can be found here.

Cross-linked networks of semi-flexible filaments

Cross-linked semi-flexible polymer networks are abundant in biology - particularly in cellular architechture. My focus at present is in developing simple theoretical models that aim to capture the interesting physics of these materials including:

Equilibrium shear modulus These networks exhibit dramatic non-linear elasticity, whereby the elastic shear modulus can increase by up to an order of magnitude over modest strains (see figure to the right). At present I am working on a model that examines the validity of assuming the cross-links in such a network move affinely. There is still much debate in the literature whether non-affine deformations play an important role. Using a model inspired by the theories of classical rubbers we are able to calculate the shear moduli and uniaxial (Young) moduli of affine networks that account for entropic stretching and mechanical stretching. A preprint of our paper is available here.