Stretching a heteropolymer

We study the elastic properties of single heteropolymers. By means of exact enumeration of conformations, Monte Carlo (MC) simulation, and variational principles, we calculate equilibrium force-extension curves of heterocopolymers for specific arrangements of the monomer types along the sequence. At a given extension $z$⁠, the time averaged measured force is the weighted sum of restoring forces for various configurations. Using variational principles, we calculate force-extension $(f-z)$ curves of heteropolymers with fixed extensions $z$⁠. These results are compared with $f-z$ curves obtained from MC simulations and exact enumeration of all conformations. Typical random sequences manifest several piecewise unfoldings of blocks of various size, which are overlapping due to thermal fluctuations. The shape of the elastic response of a heteropolymer reflects the disorder in the primary block structure and the binding energies of these blocks.