Bin W. Zhang

Large‐scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high‐performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta‐cyclodextrin‐heptanoate host‐guest system in the context of one‐ and two‐dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.

Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies.

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.

The Role of Interfacial Water in Protein–Ligand Binding: Insights from the Indirect Solvent Mediated Potential of Mean Force

Classical density functional theory (DFT) can be used to relate the thermodynamic properties of solutions to the indirect solvent mediated part of the solute-solvent potential of mean force (PMF). Standard, but powerful numerical methods can be used to estimate the solute-solvent PMF from which the indirect part can be extracted. In this work we show how knowledge of the direct and indirect parts of the solute-solvent PMF for water at the interface of a protein receptor can be used to gain insights about how to design tighter binding ligands. As we show, the indirect part of the solute-solvent PMF is equal to the sum of the 1-body (energy + entropy) terms in the inhomogeneous solvation theory (IST) expansion of the solvation free energy. To illustrate the effect of displacing interfacial water molecules with particular direct/indirect PMF signatures on the binding of ligands, we carry out simulations of protein binding with several pairs of congeneric ligands. We show that interfacial water locations that contribute favorably or unfavorably at the 1-body level (energy + entropy) to the solvation free energy of the solute can be targeted as part of the ligand design process. Water locations where the indirect PMF is larger in magnitude provide better targets for displacement when adding a functional group to a ligand core.

Conformational Free Energy Changes via an Alchemical Path without Reaction Coordinates

We introduce a novel method called restrain-free energy perturbation-release (R-FEP-R) to estimate conformational free energy changes via an alchemical path, which for some conformational landscapes like those associated with cellular signaling proteins in the kinase family is more direct and readily converged than the corresponding free energy changes along the physical path. The R-FEP-R method was developed from the dual topology free energy perturbation method that is widely applied to estimate the binding free energy difference between two ligands. In R-FEP-R, the free energy change between two conformational basins is calculated by free energy perturbations that remove those atoms involved in the conformational change from their initial conformational basin while simultaneously growing them back according to the final conformational basin. Both the initial and final dual topology states are unphysical, but they are designed in a way such that the unphysical contributions to the initial and final partition functions cancel. Compared with other advanced sampling algorithms such as umbrella sampling and metadynamics, the R-FEP-R method does not require predetermined transition pathways or reaction coordinates that connect the two conformational states. As a first illustration, the R-FEP-R method was applied to calculate the free energy change between conformational basins for alanine dipeptide in solution and for a side chain in the binding pocket of T4 lysozyme. The results obtained by R-FEP-R agree with the benchmarks very well.

Stratified UWHAM and Its Stochastic Approximation for Multicanonical Simulations Which are Far from Equilibrium

We describe a new analysis tool called Stratified unbinned Weighted Histogram Analysis Method (Stratified-UWHAM), which can be used to compute free energies and expectations from a multicanonical ensemble when a subset of the parallel simulations is far from being equilibrated because of barriers between free energy basins which are only rarely (or never) crossed at some states. The Stratified-UWHAM equations can be obtained in the form of UWHAM equations but with an expanded set of states. We also provide a stochastic solver, Stratified RE-SWHAM, for Stratified-UWHAM to remove its computational bottleneck. Stratified-UWHAM and Stratified RE-SWHAM are applied to study three test topics: the free energy landscape of alanine dipeptide, the binding affinity of a host-guest binding complex, and path sampling for a two-dimensional double well potential. The examples show that when some of the parallel simulations are only locally equilibrated, the estimates of free energies and equilibrium distributions provided by the conventional UWHAM (or MBAR) solutions exhibit considerable biases, but the estimates provided by Stratified-UWHAM and Stratified RE-SWHAM agree with the benchmark very well. Lastly, we discuss features of the Stratified-UWHAM approach which is based on coarse-graining in relation to two other maximum likelihood-based methods which were proposed recently, that also coarse-grain the multicanonical data.