Implicit Solvent Methods Research Articles

Hydration Thermodynamics of Non-Polar Aromatic Hydrocarbons: Comparison of Implicit and Explicit Solvation Models.

The precise description of solute-water interactions is essential to understand the chemo-physical nature in hydration processes. Such a hydration thermodynamics for various solutes has been explored by means of explicit or implicit solvation methods. Using the Poisson-Boltzmann solvation model, the implicit models are well designed to reasonably predict the hydration free energies of polar solutes. The implicit model, however, is known to have shortcomings in estimating those for non-polar aromatic compounds. To investigate a cause of error, we employed a novel systematic framework of quantum-mechanical/molecular-mechanical (QM/MM) coupling protocol in explicit solvation manner, termed DFT-CES, based on the grid-based mean-field treatment. With the aid of DFT-CES, we delved into multiple energy parts, thereby comparing DFT-CES and PB models component-by-component. By applying the modified PB model to estimate the hydration free energies of non-polar solutes, we find a possibility to improve the predictability of PB models. We expect that this study could shed light on providing an accurate route to study the hydration thermodynamics for various solute compounds.

Assessing the Performance of MM/PBSA, MM/GBSA, and QM-MM/GBSA Approaches on Protein/Carbohydrate Complexes: Effect of Implicit Solvent Models, QM Methods, and Entropic Contributions.

Rapid and accurate binding affinity prediction of protein-carbohydrate complexes is a major challenge in glycomimetics design. Among the existing computational techniques, end-point methods have received considerable interest because of their low computational cost. However, significant obstacles remain when such methods are applied to protein-glycan complexes. This article reports the performance of end-point free-energy calculation methods: molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA), MM/generalized Born surface area (MM/GBSA), and quantum mechanics-MM/GBSA (QM-MM/GBSA) on monosaccharides bound to RSL lectin from Ralstonia solanacearum. A careful investigation of the molecular dynamics simulation length, van der Waals radii sets, GB models, QM Hamiltonians, and entropic compensation has been made, and the results are compared with the experimental binding free energies from isothermal titration calorimetry/surface plasmon resonance measurements. The binding free energies using implicit solvent methods are found to be sensitive to the simulation length, radii set, GB model, and QM Hamiltonian. A simulation length of 10 ns using the radii set mbondi provides the best agreement with the experimental values ( r2 = 0.96) by MM/PBSA. The GBHCT model is in accord with the experimental values in MM/GBSA ( r2 = 0.91) or in combination with parameterized model number 6 (PM6) ( r2 = 0.98) in QM-MM/GBSA. Out of 12 QM Hamiltonians tested, PM6, density functional theory-based tight binding (DFTB), and their variants proved to be more efficient than other semiempirical methods. These methods perform equally well in predicting both absolute and relative binding free energies.

Electrostatic Polarization Energies of Charge Carriers in Organic Molecular Crystals: A Comparative Study with Explicit State-Specific Atomic Polarizability Based AMOEBA Force Field and Implicit Solvent Method.

The electrostatic polarization plays an important role in determining the energy levels of charge carriers in organic solids, which is controlled by the atomic polarizability in AMOEBA polarizable force field. QTAIM-based space partitioning of molecular polarizability is utilized to uniformly parametrize the state-specific atomic polarizability (SSAP) of π-conjugated organic small molecules to avoid fitting molecular polarizability of some artificial training set. Herein, the SSAPs are applied to explicitly extrapolate the electrostatic polarization energy ( E pol) of the charge carriers of nine π-conjugated organic crystals including six p-type transfer materials, oligoacenes and TIPS-substituted oligoacenes, and three n-type transfer materials, F-substituted oligoacenes and TCNQ. Our results demonstrate that the electrostatic polarization energies of the hole carrier ( E+pol) are smaller than that of the electron carrier ( E-pol) for p-type molecules while E+pol are larger than E-pol for n-type molecules. SSAP-based E pol values of oligoacenes behave as a nearly unvaried feature with the increase of conjugation length which is similar to implicit polarizable continuum model (PCM) results, while E pol obtained from the default atomic polarizability behaves with a notable decrease. Implicit PCM can correctly capture most of electrostatic polarization of ions in bulk system although it slightly underestimates the gap between the electrostatic polarization of hole and electron carriers in oligoacene crystals. Our results demonstrate that this unified parametrized SSAP provides a reliable and cheap tool to estimate the energy landscape of charge carriers in condensed-phase organic solids.

Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly.

Predicting solvation free energies and describing the complex water behavior that plays an important role in essentially all biological processes is a major challenge from the computational standpoint. While an atomistic, explicit description of the solvent can turn out to be too expensive in large biomolecular systems, most implicit solvent methods fail to capture “dewetting” effects and heterogeneous hydration by relying on a pre-established (i.e., guessed) solvation interface. Here we focus on the Variational Implicit Solvent Method, an implicit solvent method that adds water “plasticity” back to the picture by formulating the solvation free energy as a functional of all possible solvation interfaces. We survey VISM's applications to the problem of molecular recognition and report some of the most recent efforts to tailor VISM for more challenging scenarios, with the ultimate goal of including thermal fluctuations into the framework. The advances reported herein pave the way to make VISM a uniquely successful approach to characterize complex solvation properties in the recognition and binding of large-scale biomolecular complexes.

‘Martinizing’ the Variational Implicit Solvent Method (VISM): Solvation Free Energy for Coarse-Grained Proteins

Solvation is a fundamental driving force in many biological processes including biomolecular recognition and self-assembly, not to mention protein folding, dynamics, and function. Many computational methods attempt to provide an accurate description of the solvation effects underlying such processes. The Variational Implicit Solvent Method (VISM) is currently developed to estimate solvation free energies for systems of very complex topology, such as biomolecules. VISM's theoretical framework makes it unique because it couples hydrophobic, van der Waals and electrostatic interactions as a functional of the solvation interface. By minimizing this functional, VISM produces the solvation interface as an output of the theory, and is able to capture subtle though important behavior deriving from heterogeneous solvation patterns - such as polymodal hydration and dewetting. In this work, we adapted VISM to work with MARTINI, a well-established coarse-grained force field for proteins and other biomolecules, whose application is particularly interesting to study the interaction between very large biomolecular systems. We applied the MARTINI-VISM method to investigate the nature of dry-wet transitions in the encounter of two binding systems which differ greatly in terms of electrostatic/hydrophobic character: barstar-barnase and p53-MDM2. Our results demonstrate the suitability of the MARTINI-VISM method to study important solvation effects mediating protein-protein binding, which cannot be captured by more traditional implicit solvent methods.

"Martinizing" the Variational Implicit Solvent Method (VISM): Solvation Free Energy for Coarse-Grained Proteins.

Solvation is a fundamental driving force in many biological processes including biomolecular recognition and self-assembly, not to mention protein folding, dynamics, and function. The variational implicit solvent method (VISM) is a theoretical tool currently developed and optimized to estimate solvation free energies for systems of very complex topology, such as biomolecules. VISM’s theoretical framework makes it unique because it couples hydrophobic, van der Waals, and electrostatic interactions as a functional of the solvation interface. By minimizing this functional, VISM produces the solvation interface as an output of the theory. In this work, we push VISM to larger scale applications by combining it with coarse-grained solute Hamiltonians adapted from the MARTINI framework, a well-established mesoscale force field for modeling large-scale biomolecule assemblies. We show how MARTINI-VISM (MVISM) compares with atomistic VISM (AVISM) for a small set of proteins differing in size, shape, and charge distribution. We also demonstrate MVISM’s suitability to study the solvation properties of an interesting encounter complex, barnase–barstar. The promising results suggest that coarse-graining the protein with the MARTINI force field is indeed a valuable step to broaden VISM’s and MARTINI’s applications in the near future.

Solvation Effects on Methanol Decomposition on Pd(111), Pt(111), and Ru(0001)

Solvation is crucial in many chemical and electrochemical processes related to alcohol conversion on metal surfaces. Particularly, understanding the dehydrogenation mechanism of methanol on solvated Pd, Pt, and Ru surfaces could allow the design of efficient methanol fuel cells. The large computational cost related to adopting an explicit solvation approach into density functional theory can be reduced drastically by using implicit solvation methods. In this study, we use our recently developed continuum solvation model (MGCM) to elucidate the minimum number of explicit water molecules to add to the solvated methanol/metal surface systems to reproduce experimental data with an optimized balance between time and reliability. Our results stress the importance of adding two explicit water molecules, especially for the case of Ru surfaces. For this later system, we provide a first insight into the decomposition mechanism of methanol using first-principles calculations. Our predictions can be then a useful ref...

Dispersibility of carbon nanotubes in organic solvents: do we really have predictive models?

Predicting the physico-chemical properties of carbon nanotubes (CNTs) is highly demanding owing to tedious experimental efforts involved in their determination. Dispersibility of CNTs in organic solvents is one such property; however, studies involving its quantitative prediction are quite scarce and highly questionable, particularly, when the real external predictivity is desired. This work examines the real external predictivity of the existing models as well as those developed in the present work (using quantum-chemical descriptors) for the dispersibility of single-walled CNTs (SWCNTs). The real external predictivity is assessed on the basis of state-of-the-art external validation parameters obtained by employing an external prediction set which is not exposed to the model used for the prediction. Notably, most of the present and existing models pass through the internal validation, but unfortunately, barring some exception of poly-parameter models, most of the models fail when it comes to the external validation. Their failure was attributed to the descriptors employed which are in fact based on the gas-phase single molecular structure of organic solvents as well as based on the implicit solvent methods. A future approach towards the predictive models for the dispersibility of CNTs is suggested based on the explicit solvent methods.

Targeting HIV-1 Envelope Proteins Using a Fragment Discovery All-Atom Computational Algorithm.

Introduction: HIV viral envelope proteins are targets for small inhibitor molecules aimed at disrupting the cellular entry process. Potential peptide-class inhibitor molecules (rDNA drugs) have been previously identified, with mixed results, through biomimicry and phage display experimental methods. Here we describe a new approach based on computational fragment discovery. The method has the potential to not only optimize peptide binding affinity but also to rapidly produce alternative inhibitors against mutated strains.Methods: A comprehensive, all-atom implicit solvent method is used to bombard the C-heptad repeat unit of HIV-1 target envelope protein GP41 with single D-amino acid residues as they exist in their native state. A nascent peptide computational search process then identifies potential favorable sequences of attached ligands based on four peptide bond criteria. Finally, dynamic simulations of nascent peptides attached to host targets help refine potential peptide inhibitors for experimental HIV-1 challenge assays and testing.Results and Discussion: Initial testing of the method was done using 64,000 total ligands of D-amino acid residues at a total computational time of 0.05 microseconds per ligand, which resulted in several thousand attached ligands. Peptide bond criteria search employing three of the four bond constraints with a tolerance of 20 percent, resulted in four potential peptide inhibitors of 5 to 6 residues in length. Only one of the four peptides demonstrated IC50 values and partial viral inhibition based on cell challenge assays using CEM-SS host cells. That peptide inhibitor also computationally demonstrated long-time attachment and stability to a helical groove in its C-heptad target. This initial testing of peptide fragment discovery against HIV-1 has helped us refine the protocols and identify key areas of improvement.Conclusion: Our methods demonstrate the potential to design efficient peptide inhibitors to viral target proteins based on an all-atom dynamic simulation and using a ligand library as fragments of potential nascent peptides. Our methods can be greatly improved through the use of higher numbers of ligands, increased time of bombardment, and tighter constraints on the peptide bond search step. Our method may be important in the need to rapidly respond to target mutations and to advance multiple targeting methods based multiple peptide inhibitors.

A Seamless Grid-Based Interface for Mean-Field QM/MM Coupled with Efficient Solvation Free Energy Calculations.

Among various models that incorporate solvation effects into first-principles-based electronic structure theory such as density functional theory (DFT), the average solvent electrostatic potential/molecular dynamics (ASEP/MD) method is particularly advantageous. This method explicitly includes the nature of complicated solvent structures that is absent in implicit solvation methods. Because the ASEP/MD method treats only solvent molecule dynamics, it requires less computational cost than the conventional quantum mechanics/molecular mechanics (QM/MM) approaches. Herein, we present a real-space rectangular grid-based method to implement the mean-field QM/MM idea of ASEP/MD to plane-wave DFT, which is termed "DFT in classical explicit solvents", or DFT-CES. By employing a three-dimensional real-space grid as a communication medium, we can treat the electrostatic interactions between the DFT solute and the ASEP sampled from MD simulations in a seamless and straightforward manner. Moreover, we couple a fast and efficient free energy calculation method based on the two-phase thermodynamic (2PT) model with our DFT-CES method, which enables direct and simultaneous computation of the solvation free energies as well as the geometric and electronic responses of a solute of interest under the solvation effect. With the aid of DFT-CES/2PT, we investigate the solvation free energies and detailed solvation thermodynamics for 17 types of organic molecules, which show good agreement with the experimental data. We further compare our simulation results with previous theoretical models and assumptions made for the development of implicit solvation models. We anticipate that our proposed method, DFT-CES/2PT, will enable vast utilization of the ASEP/MD method for investigating solvation properties of materials by using periodic DFT calculations in the future.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling.

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Evaluation of Methods for the Calculation of the pKa of Cysteine Residues in Proteins.

Methods for the calculation of the pKa ionizable amino acids are valuable tools for understanding pH-dependent properties of proteins. Cysteine is unique among the amino acids because of the chemical reactivity of its thiol group (S-H), which plays an instrumental role in several biochemical and regulatory functions. The acidity of noncatalytic cysteine residues is a factor in their susceptibility to chemical modification. Despite the plethora of existing pKa computing methods, no definitive protocol exists for accurately calculating the pKa's of cysteine residues in proteins. A cysteine pKa test set was developed, which is comprised of 18 cysteine residues in 12 proteins where the pKa's have been determined experimentally and an experimental structure is available. The pKa's of these residues were calculated using three methods that use an implicit solvent model (H++, MCCE, and PROPKA) and an all-atom replica-exchange thermodynamic integration approach with the CHARMM36 and AMBER ff99SB-ILDNP force fields. The models that use implicit solvation methods were generally unreliable in predicting cysteine residue pKa's, with RMSDs between 3.41 and 4.72 pKa units. On average, the explicit solvent methods performed better than the implicit solvent methods. RMSD values of 2.40 and 3.20 were obtained for simulations with the CHARMM36 and AMBER ff99SB-ILDNP force fields, respectively. Further development of these methods is necessary because the performance of the best method is similar to that of the null-model (RMSD = 2.74) and these differences in RMSD are of limited statistical significance given the small size of our test set.

Albumin (BSA) Adsorption over Graphene in Aqueous Environment: Influence of Orientation, Adsorption Protocol, and Solvent Treatment.

We report 150 ns explicit solvent MD simulations of the adsorption on graphene of albumin (BSA) in two orientations and using two different adsorption protocols, i.e., free and forced adsorption. Our results show that free adsorption occurs with little structural rearrangements. Even taking adsorption to an extreme, by forcing it with a 5 nN downward force applied during the initial 20 ns, we show that along a particular orientation BSA is able to preserve the structural properties of the majority of its binding sites. Furthermore, in all the cases considered in this work, the ibuprofen binding site has shown a strong resilience to structural changes. Finally, we compare these results with implicit solvent simulations and find that the latter predicts an extreme protein unfolding upon adsorption. The origin of this discrepancy is attributed to a poor description of the water entropic forces at interfaces in the implicit solvent methods.

Molecular dynamics study of bio‐manipulation in aqueous media

Nano-manipulation is one of the most important aspects of nano-robotics and nano-assembly. The positioning process is considered by many researches to be one of the most important parts of nano-assembly, but has been poorly investigated, particularly for biologic samples. This Letter is devoted to modelling the process of positioning a biomolecule with atomic force microscopy (AFM) in an aqueous media using molecular dynamics simulations. Carbon nanotube (CNT) and graphite sheet are selected as AFM tip and substrate, respectively. To consider the effects of the medium on the manipulation, several models for decreasing the calculations including implicit, coarse grained, and all-atom methods have been investigated. They examined several parameters which may affect the quality of the manipulation process such as the CNT initial position with respect to the sample and substrate, its diameter and positioning strategies (pushing or pulling). The results demonstrate that despite of the implicit solvent methods, coarse-grained model can simulate the aqueous media accurately with lower computational cost. Furthermore, pulling method with a CNT which has a larger diameter and a smaller gap with respect to the substrate is the most appropriate setting for manipulation.

Evaluating thermodynamic integration performance of the new amber molecular dynamics package and assess potential halogen bonds of enoyl-ACP reductase (FabI) benzimidazole inhibitors

Thermodynamic integration (TI) can provide accurate binding free energy insights in a lead optimization program, but its high computational expense has limited its usage. In the effort of developing an efficient and accurate TI protocol for FabI inhibitors lead optimization program, we carefully compared TI with different Amber molecular dynamics (MD) engines (sander and pmemd), MD simulation lengths, the number of intermediate states and transformation steps, and the Lennard-Jones and Coulomb Softcore potentials parameters in the one-step TI, using eleven benzimidazole inhibitors in complex with Francisella tularensis enoyl acyl reductase (FtFabI). To our knowledge, this is the first study to extensively test the new AMBER MD engine, pmemd, on TI and compare the parameters of the Softcore potentials in the one-step TI in a protein-ligand binding system. The best performing model, the one-step pmemd TI, using 6 intermediate states and 1 ns MD simulations, provides better agreement with experimental results (RMSD = 0.52 kcal/mol) than the best performing implicit solvent method, QM/MM-GBSA from our previous study (RMSD = 3.00 kcal/mol), while maintaining similar efficiency. Briefly, we show the optimized TI protocol to be highly accurate and affordable for the FtFabI system. This approach can be implemented in a larger scale benzimidazole scaffold lead optimization against FtFabI. Lastly, the TI results here also provide structure-activity relationship insights, and suggest the parahalogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well-known halogen bond favoring enzyme.

Proposal of Calculation Protocols for Implicit Solvation Methods in Conformational Analysis Involving the Gauche Effect

Proposal of Calculation Protocols for Implicit Solvation Methods in Conformational Analysis Involving the Gauche Effect

Density functional theory study of the electrochemical interface between a Pt electrode and an aqueous electrolyte using an implicit solvent method

We present a computational study of the interface of a Pt electrode and an aqueous electrolyte employing semi-empirical dispersion corrections and an implicit solvent model within first-principles calculations. The electrode potential is parametrized within the computational hydrogen electrode scheme. Using one explicit layer, we find that the most realistic interface configuration is a water bilayer in the H-up configuration. Furthermore, we focus on the contribution of the dispersion interaction and the presence of water on H, O, and OH adsorption energies. This study demonstrates that the implicit water scheme represents a computationally efficient method to take the presence of an aqueous electrolyte interface with a metal electrode into account.

Implicit solvent methods for free energy estimation.

Solvation is a fundamental contribution in many biological processes and especially in molecular binding. Its estimation can be performed by means of several computational approaches. The aim of this review is to give an overview of existing theories and methods to estimate solvent effects giving a specific focus on the category of implicit solvent models and their use in Molecular Dynamics. In many of these models, the solvent is considered as a continuum homogenous medium, while the solute can be represented at the atomic detail and at different levels of theory. Despite their degree of approximation, implicit methods are still widely employed due to their trade-off between accuracy and efficiency. Their derivation is rooted in the statistical mechanics and integral equations disciplines, some of the related details being provided here. Finally, methods that combine implicit solvent models and molecular dynamics simulation, are briefly described.

QM Computations on Complete Nucleic Acids Building Blocks: Analysis of the Sarcin-Ricin RNA Motif Using DFT-D3, HF-3c, PM6-D3H, and MM Approaches.

A set of conformations obtained from explicit solvent molecular dynamics (MD) simulations of the Sarcin-Ricin internal loop (SRL) RNA motif is investigated using quantum mechanical (QM, TPSS-D3/def2-TZVP DFT-D3) and molecular mechanics (MM, AMBER parm99bsc0+χol3 force field) methods. Solvent effects are approximated using implicit solvent methods (COSMO for DFT-D3; GB and PB for MM). Large-scale DFT-D3 optimizations of the full 11-nucleotide motif are compared to MM results and reveal a higher flexibility of DFT-D3 over the MM in the optimization procedure. Conformational energies of the SRL motif expose significant differences in the DFT-D3 and MM energy descriptions that explain difficulties in MD simulations of the SRL motif. The TPSS-D3 data are in excellent agreement with results obtained by the hybrid functionals PW6B95-D3 and M06-2X. Computationally more efficient methods such as PM6-D3H and HF-3c show promising but partly inconsistent results. It is demonstrated that large-scale DFT-D3 computations on complete nucleic acids building blocks are a viable tool to complement the picture obtained from MD simulations and can be used as benchmarks for faster computational methods. Methodological challenges of large-scale QM computations on nucleic acids such as missing solvent-solute interactions and the truncation of the studied systems are discussed.

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes.

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.