Theoretical studies of the mechanical unfolding of the muscle protein titin: Bridging the time-scale gap between simulation and experiment

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Abstract
Brute-force, fully atomistic simulations of single molecule mechanical unfolding experiments are not feasible because current simulation time scales are about six orders of magnitude shorter than the time scales explored by experiments. To circumvent this difficulty, we have constructed a model, in which the unfolding dynamics of the I27 domain of the muscle protein titin is described as diffusive motion along a single unfolding coordinate R (equal to the domain extension) in the presence of an external driving potential and the potential of mean force G(R). The effect of the remaining degrees of freedom is described in terms of a viscous force with a friction coefficient η. The potential of mean force G(R) is computed from a series of equilibrium molecular dynamics trajectories performed with constrained values of R and η is extracted from a series of steered molecular dynamics simulations, in which R is increased at a constant rate and the mechanical response of the molecule is monitored as a function of time. The estimated G(R) allows us to calculate the force-dependent unfolding rate via transition-state theory and—by performing kinetic Monte Carlo simulations—to predict unfolding force distributions in experimentally relevant regimes. We compare the computed unfolding free energy profile with that deduced from atomic force microscopy studies of titin and find that, while the unfolding free energy barrier at zero force is nearly identical to the experimental value, the force dependence of the barrier is nonlinear, in contrast to most phenomenological models of titin unfolding. Because of this, the value ku(0) of the unfolding rate extrapolated to zero unfolding force, as well as the location of the unfolding transition state, differ from those previously estimated from experimental data. In particular, our estimate of ku(0) is several orders of magnitude lower than the unfolding rate measured in chemical denaturation experiments, suggesting that the two experimental techniques may probe different unfolding pathways. At the same time, the distribution of the unfolding force as well as its dependence on the pulling rate predicted by our simulations are found to be in agreement with atomic force microscopy experiments.