Statistical efficiency of methods for computing free energy of hydration

Dealing with Induced Fit, Conformational Selection, and Secondary Poses in Molecular Dynamics Simulations for Reliable Free Energy Predictions

In this study, we have tested the performance of standard molecular dynamics (MD) simulations, replicates of shorter standard MD simulations, and Hamiltonian Replica Exchange (HREM) simulations for the sampling of two macrocyclic hosts for guest delivery, characterized by induced fit (phenyl-based host) and conformation selection (naphthyl-based host) and of the ODR-BRD4(I) drug-receptor system where the ligand can assume two main poses. For the optimization of the HREM simulation, we have proposed and tested an on-the-fly iterative scheme for equalizing the acceptance ratio along the replica progression at a constant replica number resulting in a moderate impact of the sampling efficiency. Concerning standard MD, we have found that, while splitting the total allocated simulation time in short MD replicates can reproduce the sampling efficiency of HREM in the phenyl-based host and in the ODR-BRD4(I) complex, in the naphthyl-based macrocycle, characterized by long-lived metastable states, enhanced sampling techniques are the only viable alternative for a reliable canonical sampling of the rugged conformational landscape.

Toward a structural identification of metastable molecular conformations

Interpreting high-dimensional data from molecular dynamics simulations is a persistent challenge. In this paper, we show that for a small peptide, deca-alanine, metastable states can be identified through a neural net based on structural information alone. While processing molecular dynamics data, dimensionality reduction is a necessary step that projects high-dimensional data onto a low-dimensional representation that, ideally, captures the conformational changes in the underlying data. Conventional methods make use of the temporal information contained in trajectories generated through integrating the equations of motion, which forgoes more efficient sampling schemes. We demonstrate that EncoderMap, an autoencoder architecture with an additional distance metric, can find a suitable low-dimensional representation to identify long-lived molecular conformations using exclusively structural information. For deca-alanine, which exhibits several helix-forming pathways, we show that this approach allows us to combine simulations with different biasing forces and yields representations comparable in quality to other established methods. Our results contribute to computational strategies for the rapid automatic exploration of the configuration space of peptides and proteins.

Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches

The accurate calculation of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein-ligand binding affinity.

SAMPL7 blind predictions using nonequilibrium alchemical approaches

In the context of the SAMPL7 challenge, we computed, employing a non-equilibrium (NE) alchemical technique, the standard binding free energy of two series of host-guest systems, involving as a host the Isaac's TrimerTrip, a Cucurbituril-like open cavitand, and the Gilson's Cyclodextrin derivatives. The adopted NE alchemy combines enhanced sampling molecular dynamics simulations with driven fast out-of-equilibrium alchemical trajectories to recover the free energy via the Jarzynski and Crooks NE theorems. The GAFF2 non-polarizable force field was used for the parametrization. Performances were acceptable and similar in accuracy to those we submitted for Gibb's Deep Cavity Cavitands in the previous SAMPL6 host-guest challenge, confirming the reliability of the computational approach and exposing, in some cases, some important deficiencies of the GAFF2 non-polarizable force field.

From adaptive resolution to molecular dynamics of open systems

ABSTRACT

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method's advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments.

Methodological uncertainties in drug-receptor binding free energy predictions based on classical molecular dynamics

Computational approaches are becoming an essential tool in modern drug design and discovery, with fast compound triaging using a combination of machine learning and docking techniques followed by molecular dynamics binding free energies assessment using alchemical techniques. The traditional MD-based alchemical free energy perturbation (FEP) method faces severe sampling issues that may limits its reliability in automated workflows. Here we review the major sources of uncertainty in FEP protocols for drug discovery, showing how the sampling problem can be effectively tackled by switching to nonequilibrium alchemical techniques.

A remark on the efficiency of the double-system/single-box nonequilibrium approach in the SAMPL6 SAMPLing challenge

The alchemical nonequilibrium switching technique was one of several methods in the top tier of performance in the recent SAMPL6 SAMPLing challenge in both accuracy and efficiency. In this paper, in the context of nonequilibrium alchemical switching, we compare the efficiency of the double-system/single-box (DSSB) approach (used in the SAMPL6 challenges) to the standard single-system/double-box method (SSDB). Exploiting the Crooks theorem in a simple but effective test case, we analytically show that the DSSB approach is almost twice as efficient as SSDB for slow near-equilibrium switching but it gives basically no gain over the conventional SSDB approach when the variance of the work distribution exceeds few [Formula: see text], with the potential of producing artifacts and entanglements if not judiciously implemented.

Large scale relative protein ligand binding affinities using non-equilibrium alchemy

Ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design. However, their broad uptake and impact is held back by the notoriously complex setup of the calculations. Only a few tools other than the free energy perturbation approach by Schrödinger Inc. (referred to as FEP+) currently enable end-to-end application. Here, we present for the first time an approach based on the open-source software pmx that allows to easily set up and run alchemical calculations for diverse sets of small molecules using the GROMACS MD engine. The method relies on theoretically rigorous non-equilibrium thermodynamic integration (TI) foundations, and its flexibility allows calculations with multiple force fields. In this study, results from the Amber and Charmm force fields were combined to yield a consensus outcome performing on par with the commercial FEP+ approach. A large dataset of 482 perturbations from 13 different protein-ligand datasets led to an average unsigned error (AUE) of 3.64 ± 0.14 kJ mol-1, equivalent to Schrödinger's FEP+ AUE of 3.66 ± 0.14 kJ mol-1. For the first time, a setup is presented for overall high precision and high accuracy relative protein-ligand alchemical free energy calculations based on open-source software.

Applicability of a thermodynamic cycle approach for a force field parametrization targeting non-aqueous solvation free energies

Accurate solvation free energy ΔG_solv predictions require well parametrized force fields. In order to refit Lennard-Jones (LJ) parameters for improved ΔG_solv predictions for a variety of compound classes and chemical environments, a large number of ΔG_solv calculations is required. As the calculation of ΔG_solv is computational expensive, there is need for efficient but precise calculation methods. In this work, we focus on the computation of non-aqueous solvation free energies. We compare ΔG_solv results from highly precise reference simulations for transferring a solute from the vacuum into a condensed phase and results obtained from a thermodynamic cycle implementation. As test systems, we alter LJ parameters ε and σ of widely used GAFF atom types ca, cl, n1, oh and os in various solute/solvent combinations. We examine the degree of configurational space overlap and find an impact by hydrogen bonds and the solvent accessible surface area. We conclude that the application of a thermodynamic cycle for the parametrization of force fields targeting ΔG_solv is useful if the adaptation of LJ parameters is limited to atom types in the solute or if only ε is changed.

SAMPL6 blind predictions of water-octanol partition coefficients using nonequilibrium alchemical approaches

In this paper, we compute, by means of a non equilibrium alchemical technique, the water-octanol partition coefficients (LogP) for a series of drug-like compounds in the context of the SAMPL6 challenge initiative. Our blind predictions are based on three of the most popular non-polarizable force fields, CGenFF, GAFF2, and OPLS-AA and are critically compared to other MD-based predictions produced using free energy perturbation or thermodynamic integration approaches with stratification. The proposed non-equilibrium method emerges has a reliable tool for LogP prediction, systematically being among the top performing submissions in all force field classes for at least two among the various indicators such as the Pearson or the Kendall correlation coefficients or the mean unsigned error. Contrarily to the widespread equilibrium approaches, that yielded apparently very disparate results in the SAMPL6 challenge, all our independent prediction sets, irrespective of the adopted force field and of the adopted estimate (unidirectional or bidirectional) are, mutually, from moderately to strongly correlated.

Steering a solute between coexisting solvation states: Revisiting nonequilibrium work relations and the calculation of free energy differences

By analogy with single-molecule pulling experiments, we present a computational framework to obtain free energy differences between complex solvation states. To illustrate our approach, we focus on the calculation of solvation free energies (SFEs). However, the method can be readily extended to cases involving more complex solutes and solvation conditions as well as to the calculation of binding free energies. The main idea is to drag the solute across the simulation box where atomistic and ideal gas representations of the solvent coexist at constant temperature and chemical potential. At finite pulling speeds, the resulting work allows one to extract SFEs via nonequilibrium relations, whereas at infinitely slow pulling speeds, this process becomes equivalent to the thermodynamic integration method. Results for small molecules well agree with literature data and pave the way to systematic studies of arbitrarily large and complex molecules.

Solvation free energies via alchemical simulations: let's get honest about sampling, once more

Free energy perturbation (FEP) approaches with stratification have seen widespread and increasing use in computational studies of biologically relevant molecules. However, when the molecular systems are characterized by a complex conformational free energy landscape, the assessment of convergence remains a concern for many practitioners. The sampling problem in FEP has been authoritatively addressed in a recent perspective paper [D. Mobley, J. Comput.-Aided Mol. Des., 2012, 26, 93], incisively entitled "Let's get honest about sampling". Here, I return to the issue of sampling in the determination of the octanol-water partition coefficient for a synthetic precursor of kinase inhibitors that has been included in the recent extension of the SAMPL6 blind challenge of log P coefficients. I will show that even for this simple compound, whose conformational space is essentially dictated by two sp₃ rotable bonds connecting rigid planar units, canonical sampling using standard techniques can be surprisingly hard to achieve. I will also show how the conformational sampling problem can be effectively bypassed using unidirectional and bidirectional nonequilibrium work methods, reliably recovering the solvation energy with minimal methodological uncertainty.