Implicit Solvation Parameters Derived from Explicit Water Forces in Large-Scale Molecular Dynamics Simulations

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Tuning gold-based surface functionalization for streptavidin detection: A combined simulative and experimental study

A rationally designed gold-functionalized surface capable of capturing a target protein is presented using the biotin–streptavidin pair as a proof-of-concept. We carried out multiscale simulations to shed light on the binding mechanism of streptavidin on four differently biotinylated surfaces. Brownian Dynamics simulations were used to reveal the preferred initial orientation of streptavidin over the surfaces, whereas classical molecular dynamics was used to refine the binding poses and to investigate the fundamental forces involved in binding, and the binding kinetics. We assessed the binding events and the stability of the streptavidin attachment through a quartz crystal microbalance with dissipation monitoring (QCM-D). The sensing element comprises of biotinylated polyethylene glycol chains grafted on the sensor’s gold surface via thiol-Au chemistry. Finally, we compared the results from experiments and simulations. We found that the confined biotin moieties can specifically capture streptavidin from the liquid phase and provide guidelines on how to exploit the microscopic parameters obtained from simulations to guide the design of further biosensors with enhanced sensitivity.

Molecular dynamics simulation or structure refinement of proteins: are solvent molecules required? A case study using hen lysozyme

In protein simulation or structure refinement based on values of observable quantities measured in (aqueous) solution, solvent (water) molecules may be explicitly treated, omitted, or represented by a potential of mean-solvation-force term, depending on protein coordinates only, in the force field used. These three approaches are compared for hen egg white lysozyme (HEWL). This 129-residue non-spherical protein contains a variety of secondary-structure elements, and ample experimental data are available: 1630 atom–atom Nuclear Overhauser Enhancement (NOE) upper distance bounds, 213 ³ J-couplings and 200 S² order parameters. These data are used to compare the performance of the three approaches. It is found that a molecular dynamics (MD) simulation in explicit water approximates the experimental data much better than stochastic dynamics (SD) simulation in vacuo without or with a solvent-accessible-surface-area (SASA) implicit-solvation term added to the force field. This is due to the missing energetic and entropic contributions and hydrogen-bonding capacities of the water molecules and the missing dielectric screening effect of this high-permittivity solvent. Omission of explicit water molecules leads to compaction of the protein, an increased internal strain, distortion of exposed loop and turn regions and excessive intra-protein hydrogen bonding. As a consequence, the conformation and dynamics of groups on the surface of the protein, which may play a key role in protein–protein interactions or ligand or substrate binding, may be incorrectly modelled. It is thus recommended to include water molecules explicitly in structure refinement of proteins in aqueous solution based on nuclear magnetic resonance (NMR) or other experimentally measured data.

Molecular Simulations Guidelines for Biological Nanomaterials: From Peptides to Membranes

In studying biological processes and focusing on the molecular mechanisms at the basis of these, molecular dynamics (MD) simulations have demonstrated to be a very useful tool for the past 50 years. This suite of computational methods calculates the time-dependent evolution of a molecular system using physics-based first principles. In this chapter, we give a brief introduction to the theory and practical use of molecular dynamics simulations, highlighting the different models and algorithms that have been developed to tackle specific problems, with a special focus on classical force fields. Some examples of how simulations have been used in the past will help the reader in discerning their power, limitations, and significance.

On the Effect of the Various Assumptions and Approximations used in Molecular Simulations on the Properties of Bio-Molecular Systems: Overview and Perspective on Issues

Computer simulations of molecular systems enable structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic or supra-molecular level and plays an increasingly important role in chemistry, biology and physics. To interpret the results of such simulations appropriately, the degree of uncertainty and potential errors affecting the calculated properties must be considered. Uncertainty and errors arise from (1) assumptions underlying the molecular model, force field and simulation algorithms, (2) approximations implicit in the interatomic interaction function (force field), or when integrating the equations of motion, (3) the chosen values of the parameters that determine the accuracy of the approximations used, and (4) the nature of the system and the property of interest. In this overview, advantages and shortcomings of assumptions and approximations commonly used when simulating bio-molecular systems are considered. What the developers of bio-molecular force fields and simulation software can do to facilitate and broaden research involving bio-molecular simulations is also discussed.

Combining the polarizable Drude force field with a continuum electrostatic Poisson-Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson-Boltzmann/solvent-accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self-consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well-experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas-phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute-solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non-polar solvation effects. © 2018 Wiley Periodicals, Inc.

"Solvent hydrogen-bond occlusion": A new model of polar desolvation for biomolecular energetics

Water engages in two important types of interactions near biomolecules: it forms ordered "cages" around exposed hydrophobic regions, and it participates in hydrogen bonds with surface polar groups. Both types of interaction are critical to biomolecular structure and function, but explicitly including an appropriate number of solvent molecules makes many applications computationally intractable. A number of implicit solvent models have been developed to address this problem, many of which treat these two solvation effects separately. Here, we describe a new model to capture polar solvation effects, called SHO ("solvent hydrogen-bond occlusion"); our model aims to directly evaluate the energetic penalty associated with displacing discrete first-shell water molecules near each solute polar group. We have incorporated SHO into the Rosetta energy function, and find that scoring protein structures with SHO provides superior performance in loop modeling, virtual screening, and protein structure prediction benchmarks. These improvements stem from the fact that SHO accurately identifies and penalizes polar groups that do not participate in hydrogen bonds, either with solvent or with other solute atoms ("unsatisfied" polar groups). We expect that in future, SHO will enable higher-resolution predictions for a variety of molecular modeling applications. © 2017 Wiley Periodicals, Inc.

Calculation of distribution coefficients in the SAMPL5 challenge from atomic solvation parameters and surface areas

In the context of SAMPL5, we submitted blind predictions of the cyclohexane/water distribution coefficient (D) for a series of 53 drug-like molecules. Our method is purely empirical and based on the additive contribution of each solute atom to the free energy of solvation in water and in cyclohexane. The contribution of each atom depends on the atom type and on the exposed surface area. Comparatively to similar methods in the literature, we used a very small set of atomic parameters: only 10 for solvation in water and 1 for solvation in cyclohexane. As a result, the method is protected from overfitting and the error in the blind predictions could be reasonably estimated. Moreover, this approach is fast: it takes only 0.5 s to predict the distribution coefficient for all 53 SAMPL5 compounds, allowing its application in virtual screening campaigns. The performance of our approach (submission 49) is modest but satisfactory in view of its efficiency: the root mean square error (RMSE) was 3.3 log D units for the 53 compounds, while the RMSE of the best performing method (using COSMO-RS) was 2.1 (submission 16). Our method is implemented as a Python script available at https://github.com/diogomart/SAMPL5-DC-surface-empirical .

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

Design and application of implicit solvent models in biomolecular simulations

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Implicit solvent replaces explicit water by a potential of mean force.

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Popular models are SASA, VOL and Generalized Born.

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Implicit solvent is used in MD, protein modelling, folding, design, prediction and drug screening.

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Large-scale simulations allow for parametrisation via force matching.

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Application to nucleic acids and membranes is challenging.

We review implicit solvent models and their parametrisation by introducing the concepts and recent devlopments of the most popular models with a focus on parametrisation via force matching. An overview of recent applications of the solvation energy term in protein dynamics, modelling, design and prediction is given to illustrate the usability and versatility of implicit solvation in reproducing the physical behaviour of biomolecular systems. Limitations of implicit modes are discussed through the example of more challenging systems like nucleic acids and membranes.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Variational Optimization of an All-Atom Implicit Solvent Force Field to Match Explicit Solvent Simulation Data

The development of accurate implicit solvation models with low computational cost is essential for addressing many large-scale biophysical problems. Here, we present an efficient solvation term based on a Gaussian solvent-exclusion model (EEF1) for simulations of proteins in aqueous environment, with the primary aim of having a good overlap with explicit solvent simulations, particularly for unfolded and disordered states - as would be needed for multiscale applications. In order to achieve this, we have used a recently proposed coarse-graining procedure based on minimization of an entropy-related objective function to train the model to reproduce the equilibrium distribution obtained from explicit water simulations. Via this methodology, we have optimized both a charge screening parameter and a backbone torsion term against explicit solvent simulations of an α-helical and a β-stranded peptide. The performance of the resulting effective energy function, termed EEF1-SB, is tested with respect to the properties of folded proteins, the folding of small peptides or fast-folding proteins, and NMR data for intrinsically disordered proteins. The results show that EEF1-SB provides a reasonable description of a wide range of systems, but its key advantage over other methods tested is that it captures very well the structure and dimension of disordered or weakly structured peptides. EEF1-SB is thus a computationally inexpensive (~ 10 times faster than Generalized-Born methods) and transferable approximation for treating solvent effects.

GSATools: analysis of allosteric communication and functional local motions using a structural alphabet

Motivation: GSATools is a free software package to analyze conformational ensembles and to detect functional motions in proteins by means of a structural alphabet. The software integrates with the widely used GROMACS simulation package and can generate a range of graphical outputs. Three applications can be supported: (i) investigation of the conformational variability of local structures; (ii) detection of allosteric communication; and (iii) identification of local regions that are critical for global functional motions. These analyses provide insights into the dynamics of proteins and allow for targeted design of functional mutants in theoretical and experimental studies.

Availability: The C source code of the GSATools, along with a set of pre-compiled binaries, is freely available under GNU General Public License from http://mathbio.nimr.mrc.ac.uk/wiki/GSATools.

Contact:alessandro.pandini@kcl.ac.uk or jkleinj@nimr.mrc.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.