Endpoint-restricted adiabatic free energy dynamics approach for the exploration of biomolecular conformational equilibria

Temperature Accelerated Sliced Sampling to Probe Ligand Dissociation from Protein

Modeling ligand unbinding in proteins to estimate the free energy of binding and probing the mechanism presents several challenges. They primarily pertain to the entropic bottlenecks resulting from protein and solvent conformations. While exploring the unbinding processes using enhanced sampling techniques, very long simulations are required to sample all of the conformational states as the system gets trapped in local free energy minima along transverse coordinates. Here, we demonstrate that temperature accelerated sliced sampling (TASS) is an ideal approach to overcome some of the difficulties faced by conventional sampling methods in studying ligand unbinding. Using TASS, we study the unbinding of avibactam inhibitor molecules from the Class C β-lactamase (CBL) active site. Extracting CBL-avibactam unbinding free energetics, unbinding pathways, and identifying critical interactions from the TASS simulations are demonstrated.

Finite temperature string method with umbrella sampling using path collective variables: application to secondary structure change in a protein

The transition of an α-helix to a β-sheet in proteins is among the most complex conformational changes seen in biomolecular systems. Due to long time scales involved in the transition, it is challenging to study such protein conformational changes using direct molecular dynamics simulations. This limitation is typically overcome using an indirect approach wherein one computes the free energy landscape associated with the transition. Computation of free energy landscapes, however, requires a suitable set of collective variables that describe the transition. In this work, we demonstrate the use of path collective variables [D. Branduardi, F. L. Gervasio and M. Parrinello, J. Chem. Phys., 2007, 126, 054103] and combine it with the finite temperature string (FTS) method [E. Weinan, W. Ren and E. Vanden-Eijnden, J. Phys. Chem. B, 2005, 109, 6688-6693] to determine the molecular mechanisms involved during the structural transition of the mini G-protein from an α-helix to a β-hairpin. The transition from the α-helix proceeds via unfolding of the terminal residues, giving rise to a β-turn unfolded intermediate to eventually form the β-hairpin. Our proposed algorithm uses umbrella sampling simulations to simulate images along the string and the weighted histogram analysis to compute the free energy along the computed transition path. This work demonstrates that the string method in combination with path collective variables can be exploited to study complex protein conformational changes such as a complete change in the secondary structure.

Exploration of high dimensional free energy landscapes by a combination of temperature-accelerated sliced sampling and parallel biasing

Temperature-accelerated sliced sampling (TASS) is an enhanced sampling method for achieving accelerated and controlled exploration of high-dimensional free energy landscapes in molecular dynamics simulations. With the aid of umbrella bias potentials, the TASS method realizes a controlled exploration and divide-and-conquer strategy for computing high-dimensional free energy surfaces. In TASS, diffusion of the system in the collective variable (CV) space is enhanced with the help of metadynamics bias and elevated-temperature of the auxiliary degrees of freedom (DOF) that are coupled to the CVs. Usually, a low-dimensional metadynamics bias is applied in TASS. In order to further improve the performance of TASS, we propose here to use a highdimensional metadynamics bias, in the same form as in a parallel bias metadynamics scheme. Here, a modified reweighting scheme, in combination with artificial neural network is used for computing unbiased probability distribution of CVs and projections of high-dimensional free energy surfaces. We first validate the accuracy and efficiency of our method in computing the four-dimensional free energy landscape for alanine tripeptide in vacuo. Subsequently, we employ the approach to calculate the eight-dimensional free energy landscape of alanine pentapeptide in vacuo. Finally, the method is applied to a more realistic problem wherein we compute the broad four-dimensional free energy surface corresponding to the deacylation of a drug molecule which is covalently complexed with a β-lactamase enzyme. We demonstrate that using parallel bias in TASS improves the efficiency of exploration of high-dimensional free energy landscapes.

Neural-Network-Based Path Collective Variables for Enhanced Sampling of Phase Transformations

The investigation of the microscopic processes underlying structural phase transformations in solids is extremely challenging for both simulation and experiment. Atomistic simulations of solid-solid phase transitions require extensive sampling of the corresponding high-dimensional and often rugged energy landscape. Here, we propose a rigorous construction of a 1D path collective variable that is used in combination with enhanced sampling techniques for efficient exploration of the transformation mechanisms. The path collective variable is defined in a space spanned by global classifiers that are derived from local structural units. A reliable identification of the local structural environments is achieved by employing a neural-network-based classification scheme. The proposed path collective variable is generally applicable and enables the investigation of both transformation mechanisms and kinetics.