Mathematics

It is well known that biofilaments at thermodynamic equilibrium under the action of forces and moments fluctuate around their minimum energy configuration due to Brownian motion. This remains true of filaments in networks and gels such as those of actin, spectrin, fibrin or other biopolymers. The thermal motion of these filaments at the microscopic scales manifests itself as entropic elasticity at the macroscopic scales. In this talk we present a theory to efficiently calculate the thermo-mechanical properties of fluctuating heterogeneous filaments and networks. The central problem is to evaluate the partition function and free energy of heterogeneous filaments and networks under the assumption that their energy can be expressed as a quadratic function in the kinematic variables. We analyze the effects of various types of boundary conditions on the fluctuations of filaments and show that our results are in agreement with recent work on homogeneous rods as well as experiments and simulations. We apply similar ideas to filament networks and calculate the area expansion modulus and shear modulus for hexagonal networks. We also apply our methods to study partially unfolded proteins and the consequences of unfolding on the macroscopic behavior of fibrin networks.