Hysteresis and nonequilibrium work theorem for DNA unzipping

We study by using Monte Carlo simulations the hysteresis in unzipping and rezipping of a double stranded DNA (dsDNA) by pulling its strands in opposite directions in the fixed force ensemble. The force is increased, at a constant rate from an initial value $g_0$ to some maximum value $g_m$ that lies above the phase boundary and then decreased back again to $g_{0}$. We observed hysteresis during a complete cycle of unzipping and rezipping. We obtained probability distributions of work performed over a cycle of unzipping and rezipping for various pulling rates. The mean of the distribution is found to be close (the difference being within 10%, except for very fast pulling) to the area of the hysteresis loop. We extract the equilibrium force versus separation isotherm by using the work theorem on repeated non-equilibrium force measurements. Our method is capable of reproducing the equilibrium and the non-equilibrium force-separation isotherms for the spontaneous rezipping of dsDNA.