Free energy calculation using molecular dynamics simulation combined with the three dimensional reference interaction site model theory. I. Free energy perturbation and thermodynamic integration along a coupling parameter

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl^-, [ClO]^- (a two-site anion), and [NO₂]^- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl^-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

Remdesivir Strongly Binds to Both RNA-Dependent RNA Polymerase and Main Protease of SARS-CoV-2: Evidence from Molecular Simulations

The outbreak of a new coronavirus SARS-CoV-2 (severe acute respiratory syndrome-coronavirus 2) has caused a global COVID-19 (coronavirus disease 2019) pandemic, resulting in millions of infections and thousands of deaths around the world. There is currently no drug or vaccine for COVID-19, but it has been revealed that some commercially available drugs are promising, at least for treating symptoms. Among them, remdesivir, which can block the activity of RNA-dependent RNA polymerase (RdRp) in old SARS-CoV and MERS-CoV viruses, has been prescribed to COVID-19 patients in many countries. A recent experiment showed that remdesivir binds to SARS-CoV-2 with an inhibition constant of μM, but the exact target has not been reported. In this work, combining molecular docking, steered molecular dynamics, and umbrella sampling, we examined its binding affinity to two targets including the main protease (Mpro), also known as 3C-like protease, and RdRp. We showed that remdesivir binds to Mpro slightly weaker than to RdRp, and the corresponding inhibition constants, consistent with the experiment, fall to the μM range. The binding mechanisms of remdesivir to two targets differ in that the electrostatic interaction is the main force in stabilizing the RdRp-remdesivir complex, while the van der Waals interaction dominates in the Mpro-remdesivir case. Our result indicates that remdesivir can target not only RdRp but also Mpro, which can be invoked to explain why this drug is effective in treating COVID-19. We have identified residues of the target protein that make the most important contribution to binding affinity, and this information is useful for drug development for this disease.

Does SARS-CoV-2 Bind to Human ACE2 More Strongly Than Does SARS-CoV?

The 2019 novel coronavirus (SARS-CoV-2) epidemic, which was first reported in December 2019 in Wuhan, China, was declared a pandemic by the World Health Organization in March 2020. Genetically, SARS-CoV-2 is closely related to SARS-CoV, which caused a global epidemic with 8096 confirmed cases in more than 25 countries from 2002 to 2003. Given the significant morbidity and mortality rate, the current pandemic poses a danger to all of humanity, prompting us to understand the activity of SARS-CoV-2 at the atomic level. Experimental studies have revealed that spike proteins of both SARS-CoV-2 and SARS-CoV bind to angiotensin-converting enzyme 2 (ACE2) before entering the cell for replication. However, the binding affinities reported by different groups seem to contradict each other. Wrapp et al. (Science2020, 367, 1260–1263) showed that the spike protein of SARS-CoV-2 binds to the ACE2 peptidase domain (ACE2-PD) more strongly than does SARS-CoV, and this fact may be associated with a greater severity of the new virus. However, Walls et al. (Cell2020, 181, 281–292) reported that SARS-CoV-2 exhibits a higher binding affinity, but the difference between the two variants is relatively small. To understand the binding mechnism and experimental results, we investigated how the receptor binding domain (RBD) of SARS-CoV (SARS-CoV-RBD) and SARS-CoV-2 (SARS-CoV-2-RBD) interacts with a human ACE2-PD using molecular modeling. We applied a coarse-grained model to calculate the dissociation constant and found that SARS-CoV-2 displays a 2-fold higher binding affinity. Using steered all-atom molecular dynamics simulations, we demonstrate that, like a coarse-grained simulation, SARS-CoV-2-RBD was associated with ACE2-PD more strongly than was SARS-CoV-RBD, as evidenced by a higher rupture force and larger pulling work. We show that the binding affinity of both viruses to ACE2 is driven by electrostatic interactions.

How Good is Jarzynski's Equality for Computer-Aided Drug Design?

Accurate determination of the binding affinity of the ligand to the receptor remains a difficult problem in computer-aided drug design. Here, we study and compare the efficiency of Jarzynski’s equality (JE) combined with steered molecular dynamics and the linear interaction energy (LIE) method by assessing the binding affinity of 23 small compounds to six receptors, including β-lactamase, thrombin, factor Xa, HIV-1 protease (HIV), myeloid cell leukemia-1, and cyclin-dependent kinase 2 proteins. It was shown that Jarzynski’s nonequilibrium binding free energy ΔG_neq^Jar correlates with the available experimental data with the correlation levels R = 0.89, 0.86, 0.83, 0.80, 0.83, and 0.81 for six data sets, while for the binding free energy ΔG_LIE obtained by the LIE method, we have R = 0.73, 0.80, 0.42, 0.23, 0.85, and 0.01. Therefore, JE is recommended to be used for ranking binding affinities as it provides accurate and robust results. In contrast, LIE is not as reliable as JE, and it should be used with caution, especially when it comes to new systems.

Effective prediction model and determination of binding residues influential for inhibitors targeting HIV-1 integrase-LEDGF/p75 interface by employing solvent accessible surface area energy as key determinant

Development of a highly accurate prediction model for protein-ligand inhibition has been a major challenge in drug discovery. Herein, we describe a novel predictive model for the inhibition of HIV-1 integrase (IN)-LEDGF/p75 protein-protein interaction. The model was constructed using energy parameters approximated from molecular dynamics (MD) simulations and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) calculations. Chemometric analysis using partial least squares (PLS) regression revealed that solvent accessible surface area energy (ΔG_SASA) is the major determinant parameter contributing greatly to the prediction accuracy. PLS prediction model on the ΔG_SASA values collected from 41 complexes yielded a strong correlation between the predicted and the actual inhibitory activities (R² = 0.9666, RMSEC of pIC₅₀ values = 0.0890). Additionally, for the test set of 14 complexes, the model performed satisfactorily with very low pIC₅₀ errors (Q² = 0.5168, RMSEP = 0.3325). A strong correlation between the buried surface areas on the IN protein, when bound with IN-LEDGF/p75 inhibitors, and the respective ΔG_SASA values was also obtained. Furthermore, the current method could identify 'hot spots'of amino acid residues highly influential to the inhibitory activity prediction. This could present fruitful implications in binding site determination and future inhibitor developments targeting protein-protein interactions.Communicated by Ramaswamy H. Sarma.

Integral equation study of soft-repulsive dimeric fluids

We study fluid structure and water-like anomalies of a system constituted by dimeric particles interacting via a purely repulsive core-softened potential by means of integral equation theories. In our model, dimers interact through a repulsive pair potential of inverse-power form with a softened repulsion strength. By employing the Ornstein-Zernike approach and the reference interaction site model (RISM) theory, we study the behavior of water-like anomalies upon progressively increasing the elongation λ of the dimers from the monomeric case ([Formula: see text]) to the tangent configuration ([Formula: see text]). For each value of the elongation we consider two different values of the interaction potential, corresponding to one and two length scales, with the aim to provide a comprehensive description of the possible fluid scenarios of this model. Our theoretical results are systematically compared with already existing or newly generated Monte Carlo data: we find that theories and simulations agree in providing the picture of a fluid exhibiting density and structural anomalies for low values of λ and for both the two values of the interaction potential. Integral equation theories give accurate predictions for pressure and radial distribution functions, whereas the temperatures where anomalies occur are underestimated. Upon increasing the elongation, the RISM theory still predicts the existence of anomalies; the latter are no longer observed in simulations, since their development is likely precluded by the onset of crystallization. We discuss our results in terms of the reliability of integral equation theories in predicting the existence of water-like anomalies in core-softened fluids.

Large scale affinity calculations of cyclodextrin host-guest complexes: Understanding the role of reorganization in the molecular recognition process

Host-guest inclusion complexes are useful models for understanding the structural and energetic aspects of molecular recognition. Due to their small size relative to much larger protein-ligand complexes, converged results can be obtained rapidly for these systems thus offering the opportunity to more reliably study fundamental aspects of the thermodynamics of binding. In this work, we have performed a large scale binding affinity survey of 57 β-cyclodextrin (CD) host guest systems using the binding energy distribution analysis method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged estimates of the standard binding free energies are obtained for these systems by employing techniques such as parallel Hamitionian replica exchange molecular dynamics, conformational reservoirs and multistate free energy estimators. Good agreement with experimental measurements is obtained in terms of both numerical accuracy and affinity rankings. Overall, average effective binding energies reproduce affinity rank ordering better than the calculated binding affinities, even though calculated binding free energies, which account for effects such as conformational strain and entropy loss upon binding, provide lower root mean square errors when compared to measurements. Interestingly, we find that binding free energies are superior rank order predictors for a large subset containing the most flexible guests. The results indicate that, while challenging, accurate modeling of reorganization effects can lead to ligand design models of superior predictive power for rank ordering relative to models based only on ligand-receptor interaction energies.

Modified Anderson Method for Accelerating 3D-RISM Calculations Using Graphics Processing Unit

A fast algorithm is proposed to solve the three-dimensional reference interaction site model (3D-RISM) theory on a graphics processing unit (GPU). 3D-RISM theory is a powerful tool for investigating biomolecular processes in solution; however, such calculations are often both memory-intensive and time-consuming. We sought to accelerate these calculations using GPUs, but to work around the problem of limited memory size in GPUs, we modified the less memory-intensive "Anderson method" to give faster convergence to 3D-RISM calculations. Using this method on a Tesla C2070 GPU, we reduced the total computational time by a factor of 8, 1.4 times by the modified Andersen method and 5.7 times by GPU, compared to calculations on an Intel Xeon machine (eight cores, 3.33 GHz) with the conventional method.

Integral Equation Theory of Biomolecules and Electrolytes

The so-called three-dimensional version (3D-RISM) can be used to describe the interactions of solvent components (here we treat water and ions) with a chemical or biomolecular solute of arbitrary size and shape. Here we give an overview of the current status of such models, describing some aspects of “pure” electrolytes (water plus simple ions) and of ionophores, proteins and nucleic acids in the presence of water and salts. Here we focus primarily on interactions with water and dissolved salts; as a practical matter, the discussion is mostly limited to monovalent ions, since studies of divalent ions present many difficult problems that have not yet been addressed. This is not a comprehensive review, but covers a few recent examples that illustrate current issues.

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations.