Abstract
The potential of mean force (PMF) calculation in single molecule manipulation experiments performed via the steered molecular dynamics (SMD) technique is a computationally very demanding task because the analyzed system has to be perturbed very slowly to be kept close to equilibrium. Faster perturbations, far from equilibrium, increase dissipation and move the average work away from the underlying free energy profile, and thus introduce a bias into the PMF estimate. The Jarzynski equality offers a way to overcome the bias problem by being able to produce an exact estimate of the free energy difference, regardless of the perturbation regime. However, with a limited number of samples and high dissipation the Jarzynski equality also introduces a bias. In our previous work, based on the Brownian motion formalism, we introduced three stochastic perturbation protocols aimed at improving the PMF calculation with the Jarzynski equality in single molecule manipulation experiments and analogous computer simulations. This paper describes the PMF reconstruction results based on full-atom molecular dynamics simulations, obtained with those three protocols. We also want to show that the protocols are applicable with the second-order cumulant expansion formula. Our protocols offer a very noticeable improvement over the simple constant velocity pulling. They are able to produce an acceptable estimate of PMF with a significantly reduced bias, even with very fast perturbation regimes. Therefore, the protocols can be adopted as practical and efficient tools for the analysis of mechanical properties of biological molecules.
Highlights
Proteins with mechanical functions can be roughly divided into two large groups
The aim of this paper is to present three stochastic perturbation protocols we developed in attempt to improve the potential of mean force (PMF) calculation with the Jarzynski equality
We describe a standard steered molecular dynamics (SMD) constant velocity perturbation protocol, analogous to the protocols applied with real-life protein manipulation tools, such as the atomic force microscopy (AFM), or the optical tweezers
Summary
Proteins with mechanical functions can be roughly divided into two large groups. Members of the first group are mechanically active which means that they perform biological tasks by generating a mechanical force through their own conformational changes. The aim of this paper is to present three stochastic perturbation protocols we developed in attempt to improve the PMF calculation with the Jarzynski equality. Numerical and perturbation methods were developed in attempt to improve the calculation of free energy Those methods move a given molecular system between two terminal states by means of an external potential. A fast SMD perturbation, at least three orders of magnitude faster than real-word AFM experiments, generates a significant dissipation which may raise the Jarzynski bias to a level which can hardly be reduced through the increase in the number of samples [10,16]. The results based on the constant velocity pulling showed that the Jarzynski equality can give a relatively accurate PMF estimate, with a limited number of samples, only in a close to equilibrium regime. A ten times faster pulling (10 m/s) introduces a bias which even 10,000 puling trajectories cannot reduce [16]
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