Efficient free-energy-profile reconstruction using adaptive stochastic perturbation protocols

Recognition of Potential COVID-19 Drug Treatments through the Study of Existing Protein-Drug and Protein-Protein Structures: An Analysis of Kinetically Active Residues

We report the results of our in silico study of approved drugs as potential treatments for COVID-19. The study is based on the analysis of normal modes of proteins. The drugs studied include chloroquine, ivermectin, remdesivir, sofosbuvir, boceprevir, and α-difluoromethylornithine (DMFO). We applied the tools we developed and standard tools used in the structural biology community. Our results indicate that small molecules selectively bind to stable, kinetically active residues and residues adjoining them on the surface of proteins and inside protein pockets, and that some prefer hydrophobic sites over other active sites. Our approach is not restricted to viruses and can facilitate rational drug design, as well as improve our understanding of molecular interactions, in general.

On the improvement of free-energy calculation from steered molecular dynamics simulations using adaptive stochastic perturbation protocols

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.

Pulling-spring modulation as a method for improving the potential-of-mean-force reconstruction in single-molecule manipulation experiments

The free-energy calculation is usually limited to close to equilibrium perturbation regimes because faster perturbations introduce a bias into the estimate. The Jarzynski equality offers a solution to this problem by directly connecting the free-energy difference and the external work, regardless how far from equilibrium that work may be. However, a limited sampling coupled to the fast perturbation introduces a slowly converging bias into the Jarzynski free-energy estimate also. In this paper we present two perturbation protocols devised with the intention to overcome the convergence issues of the Jarzynski-based potential of mean force estimation in the single-molecule, constant velocity manipulation experiments. The protocols are designed to improve the convergence issues by increasing the variation of the external work through the modulation of the spring used to pull a molecule. Of the two methods, the one which continuously changes the amplitude of the spring stiffness offers an excellent reconstruction and requires less than one tenth of the samples required by the normal, constant spring pulling to produce the same quality of the reconstruction.

Polymer-mediated entropic forces between scale-free objects

The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines, or planes) the only relevant length scales are the polymer size R(0) and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h << R(0), separation is the only remaining relevant scale and the entropic force must take the form F = Ak(B)T/h. The amplitude A is universal and can be related to exponents η governing the anomalous scaling of polymer correlations in the presence of obstacles. We use analytical, numerical, and ε-expansion techniques to compute the exponent η for a polymer attached to the tip of the cone (with or without an additional plate or cone) for ideal and self-avoiding polymers. The entropic force is of the order of 0.1 pN at 0.1 μm for a single polymer and can be increased for a star polymer.