Kinetic Monte Carlo simulation of titin unfolding

Abstract

Recently, it has become possible to unfold a single protein molecule titin, by pulling it with an atomic-force-microscope tip. In this paper, we propose and study a stochastic kinetic model of this unfolding process. Our model assumes that each immunoglobulin domain of titin is held together by six hydrogen bonds. The external force pulls on these bonds and lowers the energy barrier that prevents the hydrogen bond from breaking; this increases the rate of bond breaking and decreases the rate of bond healing. When all six bonds are broken, the domain unfolds. Since the experiment controls the pulling rate, not the force, the latter is calculated from a wormlike chain model for the protein. In the limit of high pulling rate, this kinetic model is solved by a novel simulation method. In the limit of low pulling rate, we develop a quasiequilibrium rate theory, which is tested by simulations. The results are in agreement with the experiments: the distribution of the unfolding force and the dependence of the mean unfolding force on the pulling rate are similar to those measured. The simulations also explain why the work of the force to break bonds is less than the bond energy and why the breaking-force distribution varies from sample to sample. We suggest that one can synthesize polymers that are well described by our model and that they may have unusual mechanical properties.