Research

1. Semiflexible Networks and the Cytoskeleton

    The elasticity of polymer gels is a well established subject that relies fundamentally on the notion of entropic elasticity. A piece of polymer chain between two cross-linking points where it is attached to other polymers is described as a simple random walk. Under an applied strain this polymer gel stores elastic energy in the form of an increased free energy due to entropy reduction of the random walk polymers. Remarkably, stretching the random walk polymers between network nodes leads to a force of purely entropic origin coming from the fact that there are fewer random walks consistent with the stretched configuration of the nodes than there are consistent with relaxed configuration. This is the underlying idea behind the theory of the elasticity of rubbery materials. There are many reviews and pedagogical discussions of these ideas.  A beautiful introduction to the subject can be found in Giant Molecules: Here, There, and Everywhere... by Alexander Grosberg and Alexei Khokhlov. You can get the book from Amazon.  In the picture below you can see the random shape of a (particular) flexible polymer as it lies on a surface. The elasticity of networks of such flexible polymers is fairly well understood using the ideas of entropic elasticity along with the assumption that the material deforms in an affine or self-averaging manner.

On the left is an electron micrograph of N5 DNA. The scale bar at the bottom is 300nm long. From Sen et al. Virology Journal 2, 27 (2005). On the right is a schematic image of affine vs. nonaffine deformation. In the case of affine deformation, each sub-volume shown in green and grey deforms in the same way as the entire material (light blue) under a uniformly imposed shear (green arrows).

    Semiflexible networks, on the other hand, have a very different microscale architecture. These networks are constructed for stiff filaments that are densely cross-linked on the scale of their thermal persistence length so that they take essentially straight paths between consecutive cross-links.  In the deformed state of the gel, these filaments can store elastic energy in both stretching (as in the case of flexible polymers) and in bending.