Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics

Abstract

Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, in order to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories.

Cosolvent Effects on the Growth of Protein Aggregates Formed by a Single Domain Globular Protein and an Intrinsically Disordered Protein

“…obtained from different umbrella windows using the weighted histogram analysis method (WHAM) 91,92 (details are in the SI). The free energy F (Q inter , Q intra,dim ) is computed using the equation…”

“…The effect of cosolvents on protein conformations is taken into account using MTM and perturbation theory. 74,87 The probability of observing protein conformations generated using metadynamics simulations 86,91 in the absence of a cosolvent ([C] = 0) are reweighed 90 to construct the FES for fibril growth in the presence of a cosolvent with concentration [C] (see SI for a detailed description of the simulation method and data analysis).…”

“…Metadynamics simulations 86,90,91 are performed to compute the free energy for fibril growth in the absence of cosolvents ([C] = 0) (see SI for details). To compute the effect of cosolvent on the fibril growth, the term ∆G tr ({r}, [C]), which describes the effect of cosolvent on a protein conformation is treated as a perturbation in eq.…”

“…The free energy of fibril growth in the presence of cosolvents is computed by reweighing the probabilities of protein conformations obtained in the absence of cosolvents. [90][91][92] Detailed description of the simulation method and data analysis is described in the SI. Table 3: GdmCl effect on the relative difference between the energy minima of different basins, and barrier height separating the basins in the free energy landscape of cSrc-SH3 dimerization (Fig.…”

Transient states and barriers from molecular simulations and milestoning theory: kinetics in ligand-protein recognition and compound design

“…Various methods such as aMD, metadynamics, weighted ensemble, scale-MD, and PaCS-MD have been used to accelerate sampling the ligand binding/unbinding processes [16][17][18][19][20][21][22][23][24][25][26][27] . In terms of the binding paths found, various algorithms such as umbrella sampling 28,29 and milestoning [30][31][32][33] have been used to estimate kinetic rates and free energy profile. Multiple states may be identified from the trajectories, and the Markov state model (MSM) can be applied to estimate the transition rates 34,35 .…”