An Effective Solvation Term Based on Atomic Occupancies for Use in Protein Simulations

Abstract

Several approaches to the treatment of solvent effects based on continuum models are reviewed and a new method based on occupied atomic volumes (occupancies) is proposed and tested. The new method describes protein-water interactions in terms of atomic solvation parameters, which represent the solvation free energy per unit of volume. These parameters were determined for six different atoms types, using experimental free energies of solvation. The method was implemented in the GROMOS and PRESTO molecular simulation program suites. Simulations with the solvation term require 20-50% more CPU time than the corresponding vacuum simulations and are approximately 20 times faster than explicit water simulations. The method and parameters were tested by carrying out 200 ps simulations of BPTI in water, in vacuo, and with the solvation term. The performance of the solvation term was assessed by comparing the structures and energies from the solvation simulations with the equivalent quantities derived from several BPTI crystal structures and from the explicit water and vacuum simulations. The model structures were evaluated in terms of exposed total surface, buried and exposed polar surfaces, secondary structure preservation, number of hydrogen bonds, energy contributions, and positional deviations from BPTI crystal structures. Vacuum simulations produced unrealistic structures with respect to all criteria applied. The structures resulting from the simulations with explicit water were closer to the 5PTI crystal structure, although part of the secondary structure dissolved. The simulations with the effective solvation term produce structures that are normal according to all evaluations and in most respects are remarkably similar to the 5PTI crystal structure despite considerable positional fluctuations during the simulations. The segments where the model and crystal structures differ are known to be flexible and the observed difference may be physically realistic. The effective solvation term based on occupancies is not only very efficient in terms of computer time but also results in meaningful structural properties for BPTI. It may therefore be generally useful in molecular dynamics of macromolecules.     

Modeling the Hydration Layer around Proteins: HyPred

Protein hydration plays an integral role in determining protein function and stability. We develop a simple method with atomic level precision for predicting the solvent density near the surface of a protein. A set of proximal radial distribution functions are defined and calculated for a series of different atom types in proteins using all-atom, explicit solvent molecular dynamic simulations for three globular proteins. A major improvement in predicting the hydration layer is found when the protein is held immobile during the simulations. The distribution functions are used to develop a model for predicting the hydration layer with sub-1-Ångstrom resolution without the need for additional simulations. The model and the distribution functions for a given protein are tested in their ability to reproduce the hydration layer from the simulations for that protein, as well as those for other proteins and for simulations in which the protein atoms are mobile. Predictions for the density of water in the hydration shells are then compared with high occupancy sites observed in crystal structures. The accuracy of both tests demonstrates that the solvation model provides a basis for quantitatively understanding protein solvation and thereby predicting the hydration layer without additional simulations.     

Parametric sensitivity analysis of avian pancreatic polypeptide (APP)

Computer simulations utilizing a classical force field have been widely used to study biomolecular properties. It is important to identify the key force field parameters or structural groups controlling the molecular properties. In the present paper the sensitivity analysis method is applied to study how various partial charges and solvation parameters affect the equilibrium structure and free energy of avian pancreatic polypeptide (APP). The general shape of APP is characterized by its three principal moments of inertia. A molecular dynamics simulation of APP was carried out with the OPLS/Amber force field and a continuum model of solvation energy. The analysis pinpoints the parameters which have the largest (or smallest) impact on the protein equilibrium structure (i.e., the moments of inertia) or free energy. A display of the protein with its atoms colored according to their sensitivities illustrates the patterns of the interactions responsible for the protein stability. The results suggest that the electrostatic interactions play a more dominant role in protein stability than the part of the solvation effect modeled by the atomic solvation parameters. © 1995 Wiley-Liss, Inc.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Atomic force microscopy studies of functional and dysfunctional pulmonary surfactant films. I. Micro- and nanostructures of functional pulmonary surfactant films and the effect of SP-A

Monolayers of a functional pulmonary surfactant (PS) can reach very low surface tensions well below their equilibrium value. The mechanism by which PS monolayers reach such low surface tensions and maintain film stability remains unknown. As shown previously by fluorescence microscopy, phospholipid phase transition and separation seem to be important for the normal biophysical properties of PS. This work studied phospholipid phase transitions and separations in monolayers of bovine lipid extract surfactant using atomic force microscopy. Atomic force microscopy showed phospholipid phase separation on film compression and a monolayer-to-multilayer transition at surface pressure 40-50 mN/m. The tilted-condensed phase consisted of domains not only on the micrometer scale, as detected previously by fluorescence microscopy, but also on the nanometer scale, which is below the resolution limits of conventional optical methods. The nanodomains were embedded uniformly within the liquid-expanded phase. On compression, the microdomains broke up into nanodomains, thereby appearing to contribute to tilted-condensed and liquid-expanded phase remixing. Addition of surfactant protein A altered primarily the nanodomains and promoted the formation of multilayers. We conclude that the nanodomains play a predominant role in affecting the biophysical properties of PS monolayers and the monolayer-to-multilayer transition.     

Ion disturbance and clustering in the NaCl water solutions

Ion clustering and the solvation properties in the NaCl solutions are explored by molecular dynamics simulations with several popular force fields. The existence of ions has a negligible disturbance to the hydrogen bond structures and rotational mobility of water beyond the first ion solvation shells, which is suggested by the local hydrogen bond structures and the rotation times of water. The potential of mean force (PMF) of ion pair in the dilute solution presents a consistent view with the populations of ion clusters in the electrolyte solutions. The aggregation level of ions is sensitive to the force field used in the simulations. The ion-ion interaction potential plays an important role in the forming of the contact ion pair. The entropy of water increases as the ion pair approaches each other and the association of ion pair is driven by the increment of water entropy according to the results from the selected force fields. The kinetic transition from the single solvent separated state to the contact ion pair is controlled by the enthalpy loss of solution.

Effective water model for Monte Carlo simulations of proteins

We present an effective theory for water. Our goal is to formulate on accurate model for the effects of solvation on protein dynamics, without incurring the huge computational cost and the slow temporal evolution typical of molecular dynamics simulations of liquids. We replace the individual water molecules in an all-atom potential with a local dielectric density field, with self interactions given by the Landau-Ginzburg free energy and external interactions by Lennard-Jones forces at the surface of the protein atoms. We explore conformational space with finite temperature Monte Carlo dynamics, using parallel Langevin and Fourier acceleration algorithms well suited to data-parallel computer architectures such as the Connection Machine. To establish the validity of our approximations, we compare our electrostatic contribution to the solvalion energy with the results of Lim, Bashford, and Karplus using a conventional static continuum dielectric cavity model, and the non electrostatic contributions with estimates of hydrophohic surface free energy. Our model can also accommodate ionic charges and temperature fluctuations, We propose future investigations extending our effective theory of solvation to include explicit orientational entropy and hydroxen-bonding terms. © 1995 John Wiley & Sons, Inc.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Excluded volume approximation to protein-solvent interaction. The solvent contact model.

Important properties of globular proteins, such as the stability of its folded state, depend sensitively on interactions with solvent molecules. Existing methods for estimating these interactions, such as the geometrical surface model, are either physically misleading or too time consuming to be applied routinely in energy calculations. As an alternative, we derive here a simple model for the interactions between protein atoms and solvent atoms in the first hydration layer, the solvent contact model, based on the conservation of the total number of atomic contacts, a consequence of the excluded-volume effect. The model has the conceptual advantage that protein-protein contacts and protein-solvent contacts are treated in the same language and the technical advantage that the solvent term becomes a particularly simple function of interatomic distances. The model allows rapid calculation of any physical property that depends only on the number and type of protein-solvent nearest-neighbor contacts. We propose use of the method in the calculation of protein solvation energies, conformational energy calculations, and molecular dynamics simulations.     

Molecular Dynamics Simulation of Model Lipid Membranes: Structural Effects of Impurities

Abstract

The gel to fluid phase transition or ordered to disordered phase transition observed in biological membranes are simulated by using constant energy Molecular Dynamics. The surface part of the membrane is modelled as a two-dimensional matrix formed by the head groups of the phospholipid molecules. Head molecules which are modelled as three spheres fused with three force centers, interact with each other via van der Waals and Coulomb type interactions. The -so called- impurity or foreign molecule embedded in the surface represents the protein type molecule which is present in biological membranes and control its activity. It is modelled as a pentagon having one force centers in each corner. It also interacts with the surface molecules again via van der Waals and Coulomb type interactions. The surface density is kept constant in the simulations of the systems with or without impurity. Structural and orientational changes due to impurity were observed and proved by monitoring two-dimensional order parameter. It has been shown that melting of the surface or breakage of the ordering of the surface molecules becomes easier and ordered to disordered phase transition temperature was lowered by 100 K if the impurity is present.     

Solvation Energy and Thermal Stability of Hydrophilization-Modified α-Chymotrypsin

As reported in the literature [Mozhaev et al. (1988), Eur. J. Biochem. 173, 147–154], when a series of modifiers, especially the cyclic anhydrides of pyromellitic and mellitic acids, are introduced into each lysine located in the -chymotrypsin (CT) surface, a substantial hydrophilization of the enzyme surface can occur and remarkable stabilization effects of modified enzymes can be obtained. In this paper, four models are applied to calculate the solvation energy of native and the modified CT based on their tertiary structures, which can be built by the CVFF force field. Analyzing the relationship between the solvation energy and the thermal stability in detail, we find that the results of three solvation energy models (Ooi model, WE-1 model, and WE-2 model) can be used to illustrate the relative stability among these enzymes qualitatively. The present study should be of practical value as well as of some theoretical interest.     

Solvation model dependency of helix-coil transition in polyalanine

Helix-coil transitions in polyalanine molecules of length 10 are studied by multi-canonical Monte Carlo simulations. The solvation effects are included by either a distance-dependent dielectric permittivity or by a term that is proportional to the solvent-accessible surface area of the peptide. We found a strong dependence of the characteristics of the helix-coil transition from the details of the solvation model.     

A modified squeeze-out mechanism for generating high surface pressures with pulmonary surfactant

The exact mechanism by which pulmonary surfactant films reach the very low surface tensions required to stabilize the alveoli at end expiration remains uncertain. We utilized the nanoscale sensitivity of atomic force microscopy (AFM) to examine phospholipid (PL) phase transition and multilayer formation for two Langmuir-Blodgett (LB) systems: a simple 3 PL surfactant-like mixture and the more complex bovine lipid extract surfactant (BLES). AFM height images demonstrated that both systems develop two types of liquid condensed (LC) domains (micro- and nano-sized) within a liquid expanded phase (LE). The 3 PL mixture failed to form significant multilayers at high surface pressure (π while BLES forms an extensive network of multilayer structures containing up to three bilayers. A close examination of the progression of multilayer formation reveals that multilayers start to form at the edge of the solid-like LC domains and also in the fluid-like LE phase. We used the elemental analysis capability of time-of-flight secondary ion mass spectrometry (ToF-SIMS) to show that multilayer structures are enriched in unsaturated PLs while the saturated PLs are concentrated in the remaining interfacial monolayer. This supports a modified squeeze-out model where film compression results in the hydrophobic surfactant protein-dependent formation of unsaturated PL-rich multilayers which remain functionally associated with a monolayer enriched in disaturated PL species. This allows the surface film to attain low surface tensions during compression and maintain values near equilibrium during expansion.     

A Practical Implicit Membrane Potential for NMR Structure Calculations of Membrane Proteins

The highly anisotropic environment of the lipid bilayer membrane imposes significant constraints on the structures and functions of membrane proteins. However, NMR structure calculations typically use a simple repulsive potential that neglects the effects of solvation and electrostatics, because explicit atomic representation of the solvent and lipid molecules is computationally expensive and impractical for routine NMR-restrained calculations that start from completely extended polypeptide templates. Here, we describe the extension of a previously described implicit solvation potential, eefxPot, to include a membrane model for NMR-restrained calculations of membrane protein structures in XPLOR-NIH. The key components of eefxPot are an energy term for solvation free energy that works together with other nonbonded energy functions, a dedicated force field for conformational and nonbonded protein interaction parameters, and a membrane function that modulates the solvation free energy and dielectric screening as a function of the atomic distance from the membrane center, relative to the membrane thickness. Initial results obtained for membrane proteins with structures determined experimentally in lipid bilayer membranes show that eefxPot affords significant improvements in structural quality, accuracy, and precision. Calculations with eefxPot are straightforward to implement and can be used to both fold and refine structures, as well as to run unrestrained molecular-dynamics simulations. The potential is entirely compatible with the full range of experimental restraints measured by various techniques. Overall, it provides a useful and practical way to calculate membrane protein structures in a physically realistic environment.     

Using Molecular Dynamics Simulations on Crambin to Evaluate the Suitability of Different Continuum Dielectric and Hydrogen Atom Models for Protein Simulations

Abstract

Molecular dynamics simulations of enzymes with enough explicit waters of solvation to realistically account for solute-solvent interactions can burden the computational resources required to perform the simulation by more than two orders of magnitude. Since enzyme simulations even with an implicit solvation model can be imposing for a supercomputer, it is important to assess the suitability of different continuum dielectric models for protein simulations. A series of 100-picosecond molecular dynamics simulations were performed on the X-ray crystal structure of the protein crambin to examine how well computed structures, obtained using seven continuum dielectric and two hydrogen atom models, agreed with the X-ray structure. The best level of agreement between computed and experimental structures was obtained using a constant dielectric of 2 and the all-hydrogen model. Continuum dielectric models of 1,1^*r, and 2^*r also led to computed structures in reasonably good agreement with the X-ray structure. In all cases, the all-hydrogen model gave better agreement than the united atom model, although, in one case, the difference was not significant. Dielectric models of 4, 80, and 4^*r with either hydrogen model yielded significantly poorer fits. It is especially noteworthy that the observed trends did not semiquantitatively converge until about 50 picoseconds into the simulations, suggesting that validation studies for protein calculations based on energy minimizations or short simulations should be viewed with caution.     

The Implementation of the Iterative Diagonalization Scheme and ab initio Molecular Dynamics Simulation with the LAPW Method

Abstract

A new ab initio molecular dynamics method based on the full-potential linearized-augmented-plane-wave (LAPW) basis set has been implemented. The LAPW basis set has been successfully employed for systems containing localized electrons such as first row atoms and transition metals. In our implementation of the LAPW-MD scheme, iterative residual minimization algorithm is used to solve the electronic states problem. The atoms are moved according to forces derived from the Hellman–Feynman theorem and incomplete basis set correction terms. The performance of the program is further enhanced by parallelization. We will discuss technical details of the program implementation and present results obtained from this code to the equilibrium structures and vibrational properties of simple diatomic molecules.     

CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.     

An extended aqueous solvation model based on atom-weighted solvent accessible surface areas: SAWSA v2.0 model

A new method is proposed for calculating aqueous solvation free energy based on atom-weighted solvent accessible surface areas. The method, SAWSA v2.0, gives the aqueous solvation free energy by summing the contributions of component atoms and a correction factor. We applied two different sets of atom typing rules and fitting processes for small organic molecules and proteins, respectively. For small organic molecules, the model classified the atoms in organic molecules into 65 basic types and additionally. For small organic molecules we proposed a correction factor of hydrophobic carbon to account for the aggregation of hydrocarbons and compounds with long hydrophobic aliphatic chains. The contributions for each atom type and correction factor were derived by multivariate regression analysis of 379 neutral molecules and 39 ions with known experimental aqueous solvation free energies. Based on the new atom typing rules, the correlation coefficient (r) for fitting the whole neutral organic molecules is 0.984, and the absolute mean error is 0.40 kcal mol^–1, which is much better than those of the model proposed by Wang et al. and the SAWSA model previously proposed by us. Furthermore, the SAWSA v2.0 model was compared with the simple atom-additive model based on the number of atom types (NA). The calculated results show that for small organic molecules, the predictions from the SAWSA v2.0 model are slightly better than those from the atom-additive model based on NA. However, for macromolecules such as proteins, due to the connection between their molecular conformation and their molecular surface area, the atom-additive model based on the number of atom types has little predictive power. In order to investigate the predictive power of our model, a systematic comparison was performed on seven solvation models including SAWSA v2.0, GB/SA_1, GB/SA_2, PB/SA_1, PB/SA_2, AM1/SM5.2R and SM5.0R. The results showed that for organic molecules the SAWSA v2.0 model is better than the other six solvation models. For proteins, the model classified the atoms into 20 basic types and the predicted aqueous free energies of solvation by PB/SA were used for fitting. The solvation model based on the new parameters was employed to predict the solvation free energies of 38 proteins. The predicted values from our model were in good agreement with those from the PB/SA model and were much better than those given by the other four models developed for proteins.Figure The definition of hydrophobic carbons. Here CA, CB and CD are three carbon atoms; X represents a heteroatom. According to our definition, CB is a hydrophobic carbon, CA is not a hydrophobic carbon because a heteroatom is within four atoms and CD is not a hydrophobic carbon because CD is sp²- hydridized and in a six-member ring.Electronic Supplementary Material Supplementary material is available for this article at     

Structure of Mixed Solvent Electrolyte Solutions via Gibbs Ensemble Monte Carlo Simulation

Abstract

Previously reported Gibbs ensemble Monte Carlo simulations of vapor-liquid equilibrium in methanol-water and methanol-water-NaCl mixtures are extended to permit study of the microscopic structure of the liquid phases of these systems. The salt effect in a prototypical mixed solvent electrolyte solution (water-methanol-NaCl) is microscopically interpreted in terms of the structural changes undergone by the solvation shells of the ions in the liquid phase of water-methanol-NaCl systems in vapor-liquid equilibrium at constant pressure.     

A B3LYP and MP2(full) theoretical investigation into cooperativity effects,aromaticity and thermodynamic properties in the Na+⋯benzonitrile⋯H2O ternary complex

In this work the growth of a graphene monolayer on copper substrate, as typically achieved via chemical vapor deposition of propene (C₃H₆), was investigated by first-principles and kinetic Monte Carlo calculations. A comparison between calculated C1s core-level binding energies and electron spectroscopy measurements showed that graphene nucleates from isolated carbon atoms adsorbed on surface defects or sub-superficial layers upon hydrocarbon fragmentation. In this respect, ab initio nudged elastic band simulations yield the energetic barriers characterizing the diffusion of elemental carbon on the Cu(111) surface and atomic carbon uptake by the growing graphene film. Our calculations highlight a strong interaction between the growing film edges and the copper substrate, indicative of the importance of the grain boundaries in the epitaxy process. Furthermore, we used activation energies to compute the reaction rates for the different mechanisms occurring at the carbon–copper interface via harmonic transition state theory. Finally, we simulated the long-time system growth evolution through a kinetic Monte Carlo approach for different temperatures and coverage. Our ab initio and Monte Carlo simulations of the out-of-equilibrium system point towards a growth model strikingly different from that of standard film growth. Graphene growth on copper turns out to be a catalytic, thermally-activated process that nucleates from carbon monomers, proceeds by adsorption of carbon atoms, and is not self-limiting. Furthermore, graphene growth seems to be more effective at carbon supersaturation of the surface—a clear fingerprint of a large activation barrier for C attachment. Our growth model and computational results are in good agreement with recent X-ray photoelectron spectroscopy experimental measurements.