Implicit solvent simulations of DNA and DNA-protein complexes: agreement with explicit solvent vs experiment

Molecular dynamics simulations of biomolecules with implicit solvent reduce the computational cost and complexity of such simulations so that longer time scales and larger system sizes can be reached. While implicit solvent simulations of proteins have become well established, the success of implicit solvent in the simulation of nucleic acids has not been fully established to date. Results obtained in this study demonstrate that stable and efficient simulations of DNA and a protein-DNA complex can be achieved with an implicit solvent model based on continuum dielectric electrostatics. Differences in conformational sampling of DNA with two sets of atomic radii that are used to define the dielectric interface between the solute and the continuum dielectric model of the solvent are investigated. Results suggest that depending on the choice of atomic radii agreement is either closer to experimental data or to explicit solvent simulations. Furthermore, partial conformational transitions toward A-DNA conformations when salt is added within the implicit solvent framework are observed.     

Treating entropy and conformational changes in implicit solvent simulations of small molecules

Implicit solvent models are increasingly popular for estimating aqueous solvation (hydration) free energies in molecular simulations and other applications. In many cases, parameters for these models are derived to reproduce experimental values for small molecule hydration free energies. Often, these hydration free energies are computed for a single solute conformation, neglecting solute conformational changes upon solvation. Here, we incorporate these effects using alchemical free energy methods. We find significant errors when hydration free energies are estimated using only a single solute conformation, even for relatively small, simple, rigid solutes. For example, we find conformational entropy (TDeltaS) changes of up to 2.3 kcal/mol upon hydration. Interestingly, these changes in conformational entropy correlate poorly (R2 = 0.03) with the number of rotatable bonds. The present study illustrates that implicit solvent modeling can be improved by eliminating the approximation that solutes are rigid.     

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.     

Solvent reaction field potential inside an uncharged globular protein: a bridge between implicit and explicit solvent models?

The solvent reaction field potential of an uncharged protein immersed in simple point charge/extended explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560 ns of simulation time. A finite, positive potential of 13-24 kbTec(-1) (where T=300 K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0 A from the solute surface, on average 0.008 ec/A3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99.     

ABSINTH: a new continuum solvation model for simulations of polypeptides in aqueous solutions

A new implicit solvation model for use in Monte Carlo simulations of polypeptides is introduced. The model is termed ABSINTH for self-Assembly of Biomolecules Studied by an Implicit, Novel, and Tunable Hamiltonian. It is designed primarily for simulating conformational equilibria and oligomerization reactions of intrinsically disordered proteins in aqueous solutions. The paradigm for ABSINTH is conceptually similar to the EEF1 model of Lazaridis and Karplus (Proteins 1999, 35, 133). In ABSINTH, the transfer of a polypeptide solute from the gas phase into a continuum solvent is the sum of a direct mean field interaction (DMFI), and a term to model the screening of polar interactions. Polypeptide solutes are decomposed into a set of distinct solvation groups. The DMFI is a sum of contributions from each of the solvation groups, which are analogs of model compounds. Continuum-mediated screening of electrostatic interactions is achieved using a framework similar to the one used for the DMFI. Promising results are shown for a set of test cases. These include the calculation of NMR coupling constants for short peptides, the assessment of the thermal stability of two small proteins, reversible folding of both an alpha-helix and a beta-hairpin forming peptide, and the polymeric properties of intrinsically disordered polyglutamine peptides of varying lengths. The tests reveal that the computational expense for simulations with the ABSINTH implicit solvation model increase by a factor that is in the range of 2.5-5.0 with respect to gas-phase calculations.     

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.     

Insight into the role of hydration on protein dynamics

The potential energy surface of a protein is rough. This intrinsic energetic roughness affects diffusion, and hence the kinetics. The dynamics of a system undergoing Brownian motion on this surface in an implicit continuum solvent simulation can be tuned via the frictional drag or collision frequency to be comparable to that of experiments or explicit solvent simulations. We show that the kinetic rate constant for a local rotational isomerization in stochastic simulations with continuum solvent and a collision frequency of 2 ps(-1) is about 10(4) times faster than that in explicit water and experiments. A further increase in the collision frequency to 60 ps(-1) slows down the dynamics, but does not fully compensate for the lack of explicit water. We also show that the addition of explicit water does not only slow down the dynamics by increasing the frictional drag, but also increases the local energetic roughness of the energy landscape by as much as 1.0 kcal/mol.     

Transient cavities and the excess chemical potentials of hard-spheroid solutes in dipolar hard-sphere solvents

Monte Carlo computer simulations are used to study transient cavities and the solvation of hard-spheroid solutes in dipolar hard-sphere solvents. The probability distribution of spheroidal cavities in the solvent is shown to be well described by a Gaussian function, and the variations of fit parameters with cavity elongation and solvent properties are analyzed. The excess chemical potentials of hard-spheroid solutes with aspect ratios x in the range of 15< or =x< or =5, and with volumes between 1 and 20 times that of a solvent molecule, are presented. It is shown that for a given molecular volume and solvent dipole moment (or temperature) a spherical solute has the lowest excess chemical potential and hence the highest solubility, while a prolate solute with aspect ratio x should be more soluble than an oblate solute with aspect ratio 1x. For a given solute molecule, the excess chemical potential increases with increasing temperature; this same trend can be observed in hydrophobic solvation. A scaled-particle theory based on the solvent equation of state and a fitted solute-solvent interfacial tension shows excellent agreement with the simulation results over the whole range of solute elongations and volumes considered. An information-theoretic model based on the solvent density and radial distribution function is less successful, being accurate only for small solute volumes and low solvent densities.     

Solvent models for protein–ligand binding: Comparison of implicit solvent poisson and surface generalized born models with explicit solvent simulations

Solvent effects play a crucial role in mediating the interactions between proteins and their ligands. Implicit solvent models offer some advantages for modeling these interactions, but they have not been parameterized on such complex problems, and therefore, it is not clear how reliable they are. We have studied the binding of an octapeptide ligand to the murine MHC class I protein using both explicit solvent and implicit solvent models. The solvation free energy calculations are more than 10³ faster using the Surface Generalized Born implicit solvent model compared to FEP simulations with explicit solvent. For some of the electrostatic calculations needed to estimate the binding free energy, there is near quantitative agreement between the explicit and implicit solvent model results; overall, the qualitative trends in the binding predicted by the explicit solvent FEP simulations are reproduced by the implicit solvent model. With an appropriate choice of reference system based on the binding of the discharged ligand, electrostatic interactions are found to enhance the binding affinity because the favorable Coulomb interaction energy between the ligand and protein more than compensates for the unfavorable free energy cost of partially desolvating the ligand upon binding. Some of the effects of protein flexibility and thermal motions on charging the peptide in the solvated complex are also considered. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 591–607, 2001     

Extending the horizon: towards the efficient modeling of large biomolecular complexes in atomic detail

The application of evaluation of implicit solvent methods for the simulation of biomolecules is described. Detailed comparisons with explicit solvent are described for the modeling of peptide and proteins in continuum aqueous solvent. In addition, we are presenting new data on the simulation of DNA with implicit solvent and describe the development of a heterogeneous dielectric model for the simulation of integral membranes. The performance of implicit solvent simulations based on the GBMV generalized Born method is compared with explicit solvent simulations, and implications for the simulation of very large biomolecular complexes is discussed. We are anticipating that the work described herein will lead to new, efficient modeling tools that will allow the simulation of longer timescales and larger system sizes in order to meet current and future challenges by the experimental community.     

Acceleration of convergence in Monte Carlo simulations of aqueous solutions using the metropolis algorithm. Hydrophobic hydration of methane

Convergence problems encountered in the computer simulations of aqueous solutions are discussed. Solute–solvent radial distribution functions are shown to converge very poorly when the standard Metropolis Monte Carlo procedure is applied. To overcome this difficulty, several modifications are made in the Metropolis method. Optimum maximum step sizes are determined for simulations of liquid water. A scheme is employed for preferential sampling of both the solvent and the solute molecules. To test these modifications, a simulation is carried out for pure liquid water, treating a single water molecule as a “solute.” The convergence of the radial distribution functions is found to be accelerated significantly. A further test is made by simulating an aqueous solution of methane, consisting of one methane molecule (using the EPEN /2 potential for methane–water interactions) and 124 water molecules (using the MCY potential for water–water interactions). Again, the convergence of solute–solvent radial distribution functions is found to be accelerated. The computation of partial molar thermodynamic quantities, however, still suffers from convergence difficulties. This problem is discussed in detail. The EPEN /2 potential is found to yield structural and thermodynamic features of hydrophobic hydration that are consistent with available experimental and theoretical results for aqueous solutions of methane.     

A high‐performance parallel‐generalized born implementation enabled by tabulated interaction rescaling

Implicit solvent representations, in general, and generalized Born models, in particular, provide an attractive way to reduce the number of interactions and degrees of freedom in a system. The instantaneous relaxation of the dielectric shielding provided by an implicit solvent model can be extremely efficient for high‐throughput and Monte Carlo studies, and a reduced system size can also remove a lot of statistical noise. Despite these advantages, it has been difficult for generalized Born implementations to significantly outperform optimized explicit‐water simulations due to more complex functional forms and the two extra interaction stages necessary to calculate Born radii and the derivative chain rule terms contributing to the force. Here, we present a method that uses a rescaling transformation to make the standard generalized Born expression a function of a single variable, which enables an efficient tabulated implementation on any modern CPU hardware. The total performance is within a factor 2 of simulations in vacuo. The algorithm has been implemented in Gromacs, including single‐instruction multiple‐data acceleration, for three different Born radius models and corresponding chain rule terms. We have also adapted the model to work with the virtual interaction sites commonly used for hydrogens to enable long‐time steps, which makes it possible to achieve a simulation performance of 0.86 μs/day for BBA5 with 1‐nm cutoff on a single quad‐core desktop processor. Finally, we have also implemented a set of streaming kernels without neighborlists to accelerate the non‐cutoff setup occasionally used for implicit solvent simulations of small systems. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Explicit ion, implicit water solvation for molecular dynamics of nucleic acids and highly charged molecules

An explicit ion, implicit water solvent model for molecular dynamics was developed and tested with DNA and RNA simulations. The implicit water model uses the finite difference Poisson (FDP) model with the smooth permittivity method implemented in the OpenEye ZAP libraries. Explicit counter-ions, co-ions, and nucleic acid were treated with a Langevin dynamics molecular dynamics algorithm. Ion electrostatics is treated within the FDP model when close to the solute, and by the Coulombic model when far from the solute. The two zone model reduces computation time, but retains an accurate treatment of the ion atmosphere electrostatics near the solute. Ion compositions can be set to reproduce specific ionic strengths. The entire ion/water treatment is interfaced with the molecular dynamics package CHARMM. Using the CHARMM-ZAPI software combination, the implicit solvent model was tested on A and B form duplex DNA, and tetraloop RNA, producing stable simulations with structures remaining close to experiment. The model also reproduced the A to B duplex DNA transition. The effect of ionic strength, and the structure of the counterion atmosphere around B form duplex DNA were also examined.     

Evaluation of DNA Force Fields in Implicit Solvation

DNA structural deformations and dynamics are crucial to its interactions in the cell. Theoretical simulations are essential tools to explore the structure, dynamics, and thermodynamics of biomolecules in a systematic way. Molecular mechanics force fields for DNA have benefited from constant improvements during the last decades. Several studies have evaluated and compared available force fields when the solvent is modeled by explicit molecules. On the other hand, few systematic studies have assessed the quality of duplex DNA models when implicit solvation is employed. The interest of an implicit modeling of the solvent consists in the important gain in the simulation performance and conformational sampling speed. In this study, respective influences of the force field and the implicit solvation model choice on DNA simulation quality are evaluated. To this end, extensive implicit solvent duplex DNA simulations are performed, attempting to reach both conformational and sequence diversity convergence. Structural parameters are extracted from simulations and statistically compared to available experimental and explicit solvation simulation data. Our results quantitatively expose the respective strengths and weaknesses of the different DNA force fields and implicit solvation models studied. This work can lead to the suggestion of improvements to current DNA theoretical models.     

The behavior of fluids near solutes: a density functional theory and computer simulation study

The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.