Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies and in modeling electrostatic effects

Effects of geometry and chemistry on hydrophobic solvation

Inserting an uncharged van der Waals (vdw) cavity into water disrupts the distribution of water and creates attractive dispersion interactions between the solvent and solute. This free-energy change is the hydrophobic solvation energy (ΔG(vdw)). Frequently, it is assumed to be linear in the solvent-accessible surface area, with a positive surface tension (γ) that is independent of the properties of the molecule. However, we found that γ for a set of alkanes differed from that for four configurations of decaalanine, and γ = -5 was negative for the decaalanines. These findings conflict with the notion that ΔG(vdw) favors smaller A. We broke ΔG(vdw) into the free energy required to exclude water from the vdw cavity (ΔG(rep)) and the free energy of forming the attractive interactions between the solute and solvent (ΔG(att)) and found that γ < 0 for the decaalanines because -γ(att) > γ(rep) and γ(att) < 0. Additionally, γ(att) and γ(rep) for the alkanes differed from those for the decaalanines, implying that none of ΔG(att), ΔG(rep), and ΔG(vdw) can be computed with a constant surface tension. We also showed that ΔG(att) could not be computed from either the initial or final water distributions, implying that this quantity is more difficult to compute than is sometimes assumed. Finally, we showed that each atom's contribution to γ(rep) depended on multibody interactions with its surrounding atoms, implying that these contributions are not additive. These findings call into question some hydrophobic models.

Bridging Calorimetry and Simulation through Precise Calculations of Cucurbituril-Guest Binding Enthalpies

We used microsecond time scale molecular dynamics simulations to compute, at high precision, binding enthalpies for cucurbit[7]uril (CB7) with eight guests in aqueous solution. The results correlate well with experimental data from previously published isothermal titration calorimetry studies, and decomposition of the computed binding enthalpies by interaction type provides plausible mechanistic insights. Thus, dispersion interactions appear to play a key role in stabilizing these complexes, due at least in part to the fact that their packing density is greater than that of water. On the other hand, strongly favorable Coulombic interactions between the host and guests are compensated by unfavorable solvent contributions, leaving relatively modest electrostatic contributions to the binding enthalpies. The better steric fit of the aliphatic guests into the circular host appears to explain why their binding enthalpies tend to be more favorable than those of the more planar aromatic guests. The present calculations also bear on the validity of the simulation force field. Somewhat unexpectedly, the TIP3P water yields better agreement with experiment than the TIP4P-Ew water model, although the latter is known to replicate the properties of pure water more accurately. More broadly, the present results demonstrate the potential for computational calorimetry to provide atomistic explanations for thermodynamic observations.

Relative Binding Enthalpies from Molecular Dynamics Simulations Using a Direct Method

The potential for reliably predicting relative binding enthalpies, ΔΔE, from a direct method utilizing molecular dynamics is examined for a system of three phosphotyrosyl peptides binding to a protein receptor, the Src SH2 domain. The binding enthalpies were calculated from the potential energy differences between the bound and the unbound end-states of each peptide from equilibrium simulations in explicit water. The statistical uncertainties in the ensemble-mean energy values from multiple, independent simulations were obtained using a bootstrap method. Simulations were initiated with different starting coordinates as well as different velocities. Statistical uncertainties in ΔΔE are 2 to 3 kcal/mol based on calculations from 40, 10 ns trajectories for each system (three SH2–peptide complexes or unbound peptides). Uncertainties in relative component energies, comprising solute–solute, solute–solvent and solvent–solvent interactions, are considerably larger. Energy values were estimated from an unweighted ensemble averaging of multiple trajectories with the a priori assumption that all trajectories are equally likely. Distributions in energy–rmsd space indicate that the trajectories sample the same basin and the difference in mean energy values between trajectories is due to sampling of alternative local regions of this superbasin. The direct estimate of relative binding enthalpies is concluded to be a reasonable approach for well-ordered systems with ΔΔE values greater than ∼3 kcal/mol, although the approach would benefit from future work to determine properly distributed starting points that would enable efficient sampling of conformational space using multiple trajectories.

Net charge changes in the calculation of relative ligand-binding free energies via classical atomistic molecular dynamics simulation

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio-)chemical thermodynamics. Many important endogenous receptor-binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice-summation scheme or a cutoff-truncation scheme with Barker-Watts reaction-field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest-host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free-energy calculation studies if changes in the net charge are involved.

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins-a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein-protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models' differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes.

Solvation free energies of alanine peptides: the effect of flexibility

The electrostatic (ΔGel), van der Waals cavity-formation (ΔGvdw), and total (ΔG) solvation free energies for 10 alanine peptides ranging in length (n) from 1 to 10 monomers were calculated. The free energies were computed both with fixed, extended conformations of the peptides and again for some of the peptides without constraints. The solvation free energies, ΔGel, and components ΔGvdw, and ΔG, were found to be linear in n, with the slopes of the best-fit lines being γel, γvdw, and γ, respectively. Both γel and γ were negative for fixed and flexible peptides, and γvdw was negative for fixed peptides. That γvdw was negative was surprising, as experimental data on alkanes, theoretical models, and MD computations on small molecules and model systems generally suggest that γvdw should be positive. A negative γvdw seemingly contradicts the notion that ΔGvdw drives the initial collapse of the protein when it folds by favoring conformations with small surface areas. When we computed ΔGvdw for the flexible peptides, thereby allowing the peptides to assume natural ensembles of more compact conformations, γvdw was positive. Because most proteins do not assume extended conformations, a ΔGvdw that increases with increasing surface area may be typical for globular proteins. An alternative hypothesis is that the collapse is driven by intramolecular interactions. We find few intramolecular H-bonds but show that the intramolecular van der Waals interaction energy is more favorable for the flexible than for the extended peptides, seemingly favoring this hypothesis. The large fluctuations in the vdw energy may make attributing the collapse of the peptide to this intramolecular energy difficult.

Relative free enthalpies for point mutations in two proteins with highly similar sequences but different folds

Enveloping distribution sampling was used to calculate free-enthalpy changes associated with single amino acid mutations for a pair of proteins, GA95 and GB95, that show 95% sequence identity yet fold into topologically different structures. Of the L → A, I → F, and L → Y mutations at positions 20, 30, and 45, respectively, of the 56-residue sequence, the first and the last contribute the most to the free-enthalpy difference between the native and non-native sequence-structure combinations, in agreement with the experimental findings for this protein pair. The individual free-enthalpy changes are almost sequence-independent in the four-strand/one-helix structure, the stable form of GB95, while in the three-helix bundle structure, the stable form of GA95, an interplay between residues 20 and 45 is observed.

Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions

This paper extends the image charge solvation model (ICSM) [J. Chem. Phys. 131, 154103 (2009)], a hybrid explicit/implicit method to treat electrostatic interactions in computer simulations of biomolecules formulated for spherical cavities, to prolate spheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-spherical solutes in molecular dynamics (MD) simulations. In addition to the utilization of a general truncated octahedron as the MD simulation box, central to the proposed extension is an image approximation method to compute the reaction field for a point charge placed inside such a non-spherical cavity by using a single image charge located outside the cavity. The resulting generalized image charge solvation model (GICSM) is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulations as a reference. We find that, for improved computational efficiency due to smaller simulation cells and consequently a less number of explicit solvent molecules, the generalized model can still faithfully reproduce known static and dynamic properties of liquid water at least for systems considered in the present paper, indicating its great potential to become an accurate but more efficient alternative to the ICSM when bio-macromolecules of irregular shapes are to be simulated.

The electrostatic response of water to neutral polar solutes: implications for continuum solvent modeling

Continuum solvation models are widely used to estimate the hydration free energies of small molecules and proteins, in applications ranging from drug design to protein engineering, and most such models are based on the approximation of a linear dielectric response by the solvent. We used explicit-water molecular dynamics simulations with the TIP3P water model to probe this linear response approximation in the case of neutral polar molecules, using miniature cucurbituril and cyclodextrin receptors and protein side-chain analogs as model systems. We observe supralinear electrostatic solvent responses, and this nonlinearity is found to result primarily from waters' being drawn closer and closer to the solutes with increased solute-solvent electrostatic interactions; i.e., from solute electrostriction. Dielectric saturation and changes in the water-water hydrogen bonding network, on the other hand, play little role. Thus, accounting for solute electrostriction may be a productive approach to improving the accuracy of continuum solvation models.

PowerBorn: A Barnes-Hut Tree Implementation for Accurate and Efficient Born Radii Computation

Implicit solvent models are one of the standard tools in computational biophysics. While Poisson-Boltzmann methods offer highly accurate results within this framework, generalized Born models have been used due to their higher computational efficiency in many (bio)molecular simulations, where computational power is a limiting factor. In recent years, there have been remarkable advances to reduce some deficiencies in the generalized Born models. On the other hand, these advances come at an increased computational cost that contrasts the reasons for choosing generalized Born models over Poisson-Boltzmann methods. To address this performance issue, we present a new algorithm for Born radii computation, one performance critical part in the evaluation of generalized Born models, which is based on a Barnes-Hut tree code scheme. We show that an implementation of this algorithm provides accurate Born radii and polar solvation free energies in comparison to Poisson-Boltzmann computations, while delivering up to an order of magnitude better performance over existing, similarly accurate methods. The C++ implementation of this algorithm will be available at http://www.int.kit.edu/nanosim/ .

Electrostatics interactions in classical simulations

Electrostatic interactions are crucial for both the accuracy and performance of atomistic biomolecular simulations. In this chapter we review well-established methods and current developments aiming at efficiency and accuracy. Specifically, we review the classical Ewald summations, particle-particle particle-method particle-method Ewald algorithms, multigrid, fast multipole, and local methods. We also highlight some recent developments targeting more accurate, yet classical, representation of the molecular charge distribution.

Prediction of protein relative enthalpic stability from molecular dynamics simulations of the folded and unfolded states

For proteins of known structure, the relative enthalpic stability with respect to wild-type, ΔΔH(U), can be estimated by direct computation of the folded and unfolded state energies. We propose a model by which the change in stability upon mutation can be predicted from all-atom molecular dynamics simulations for the folded state and a peptide-based model for the unfolded state. The unfolding enthalpies are expressed in terms of environmental and hydration-solvent reorganization contributions that readily allow a residue-specific analysis of ΔΔH(U). The method is applied to estimate the relative enthalpic stability of variants with buried charged groups in T4 lysozyme. The predicted relative stabilities are in good agreement with experimental data. Environmental factors are observed to contribute more than hydration to the overall ΔΔH(U). The residue-specific analysis finds that the effects of burying charge are both localized and long-range. The enthalpy for hydration-solvent reorganization varies considerably among different amino-acid types, but because the variant folded state structures are similar to those of the wild-type, the hydration-solvent reorganization contribution to ΔΔH(U) is localized at the mutation site, in contrast to environmental contributions. Overall, mutation of apolar and polar amino acids to charged amino acids are destabilizing, but the reasons are complex and differ from site to site.

Enthalpic barriers dominate the folding and unfolding of the human Cu, Zn superoxide dismutase monomer

The rate-limiting step in the formation of the native dimeric state of human Cu, Zn superoxide dismutase (SOD1) is a very slow monomer folding reaction that governs the lifetime of its unfolded state. Mutations at dozens of sites in SOD1 are known to cause a fatal motor neuron disease, amyotrophic lateral sclerosis, and recent experiments implicate the unfolded state as a source of soluble oligomers and histologically observable aggregates thought to be responsible for toxicity. To determine the thermodynamic properties of the transition state ensemble (TSE) limiting the folding of this high-contact-order β-sandwich motif, we performed a combined thermal/urea denaturation thermodynamic/kinetic analysis. The barriers to folding and unfolding are dominated by the activation enthalpy at 298 K and neutral pH; the activation entropy is favorable and reduces the barrier height for both reactions. The absence of secondary structure formation or large-scale chain collapse prior to crossing the barrier for folding led to the conclusion that dehydration of nonpolar surfaces in the TSE is responsible for the large and positive activation enthalpy. Although the activation entropy favors the folding reaction, the transition from the unfolded state to the native state is entropically disfavored at 298 K. The opposing entropic contributions to the free energies of the TSE and the native state during folding provide insights into structural properties of the TSE. The results also imply a crucial role for water in governing the productive folding reaction and enhancing the propensity for the aggregation of SOD1.

An Extended Charge Equilibration Method

We present a method for estimating partial atomic charges that uses all of the measured ionization energies (first, second, third, etc.) for every atom in the periodic table. We build on the charge equilibration (Qeq) method of Rappé and Goddard (which used only the first ionization energies) but reduce the number of ad hoc parameters from at least one for every type of atom to just two global parameters: a dielectric strength and a modified parameter for hydrogen atoms. Periodic electrostatic interactions are calculated via Ewald sums, and the partial charges are determined by simultaneously solving a system of linear equations; no iteration is required. We compare the predicted partial atomic charges of this extended charge equilibration (EQeq) scheme against plane-wave density-functional theory derived charges determined via the REPEAT method for 12 diverse metal-organic frameworks (MOFs). We also compare EQeq charges against ChelpG charges calculated using nonperiodic MOF fragments, as well as against Qeq charges as implemented in Accelrys Materials Studio. We demonstrate that for the purpose of ranking MOFs from best to worst for carbon capture applications, EQeq charges perform as well as charges derived from electrostatic potentials, but EQeq requires only a tiny fraction of the computational cost (seconds vs days for the MOFs studied). The source code for the EQeq algorithm is provided.

Molecular dynamics simulation study of the water-mediated interaction between zwitterionic and charged surfaces

We calculated the potential of mean force (PMF) for the interaction between a model zwitterionic bilayer and a model charged bilayer. To understand the role of water, we separated the PMF into two components: one due to direct interaction and the other due to water-mediated interaction. In our calculations, we observed that water-mediated interaction is attractive at larger distances and repulsive at shorter. The calculation of the entropic and enthalpic contributions to the solvent-mediated components of the PMF showed that attraction is entropically dominant, while repulsion is dominated by the enthalpy.

Statistical mechanics and molecular dynamics in evaluating thermodynamic properties of biomolecular recognition

Molecular recognition plays a central role in biochemical processes. Although well studied, understanding the mechanisms of recognition is inherently difficult due to the range of potential interactions, the molecular rearrangement associated with binding, and the time and length scales involved. Computational methods have the potential for not only complementing experiments that have been performed, but also in guiding future ones through their predictive abilities. In this review, we discuss how molecular dynamics (MD) simulations may be used in advancing our understanding of the thermodynamics that drive biomolecular recognition. We begin with a brief review of the statistical mechanics that form a basis for these methods. This is followed by a description of some of the most commonly used methods: thermodynamic pathways employing alchemical transformations and potential of mean force calculations, along with end-point calculations for free energy differences, and harmonic and quasi-harmonic analysis for entropic calculations. Finally, a few of the fundamental findings that have resulted from these methods are discussed, such as the role of configurational entropy and solvent in intermolecular interactions, along with selected results of the model system T4 lysozyme to illustrate potential and current limitations of these methods.

Computation of methodology-independent single-ion solvation properties from molecular simulations. III. Correction terms for the solvation free energies, enthalpies, entropies, heat capacities, volumes, compressibilities, and expansivities of solvated ions

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system or box size) and treatment of electrostatic interactions (Coulombic, lattice-sum, or cutoff-based) used during these simulations. However, as shown by Kastenholz and Hünenberger [J. Chem. Phys. 124, 224501 (2006)], correction terms can be derived for the effects of: (A) an incorrect solvent polarization around the ion and an incomplete or/and inexact interaction of the ion with the polarized solvent due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite-size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site, and the possible presence of a polarized air-liquid interface or of a constraint of vanishing average electrostatic potential in the simulated system; and (D) an inaccurate dielectric permittivity of the employed solvent model. Comparison with standard experimental data also requires the inclusion of appropriate cavity-formation and standard-state correction terms. In the present study, this correction scheme is extended by: (i) providing simple approximate analytical expressions (empirically-fitted) for the correction terms that were evaluated numerically in the above scheme (continuum-electrostatics calculations); (ii) providing correction terms for derivative thermodynamic single-ion solvation properties (and corresponding partial molar variables in solution), namely, the enthalpy, entropy, isobaric heat capacity, volume, isothermal compressibility, and isobaric expansivity (including appropriate standard-state correction terms). The ability of the correction scheme to produce methodology-independent single-ion solvation free energies based on atomistic simulations is tested in the case of Na(+) hydration, and the nature and magnitude of the correction terms for derivative thermodynamic properties is assessed numerically.

Elucidating the energetics of entropically driven protein-ligand association: calculations of absolute binding free energy and entropy

The binding of proteins and ligands is generally associated with the loss of translational, rotational, and conformational entropy. In many cases, however, the net entropy change due to binding is positive. To develop a deeper understanding of the energetics of entropically driven protein-ligand binding, we calculated the absolute binding free energies and binding entropies for two HIV-1 protease inhibitors Nelfinavir and Amprenavir using the double-decoupling method with molecular dynamics simulations in explicit solvent. For both ligands, the calculated absolute binding free energies are in general agreement with experiments. The statistical error in the computed ΔG(bind) due to convergence problem is estimated to be ≥2 kcal/mol. The decomposition of free energies indicates that, although the binding of Nelfinavir is driven by nonpolar interaction, Amprenavir binding benefits from both nonpolar and electrostatic interactions. The calculated absolute binding entropies show that (1) Nelfinavir binding is driven by large entropy change and (2) the entropy of Amprenavir binding is much less favorable compared with that of Nelfinavir. Both results are consistent with experiments. To obtain qualitative insights into the entropic effects, we decomposed the absolute binding entropy into different contributions based on the temperature dependence of free energies along different legs of the thermodynamic pathway. The results suggest that the favorable entropic contribution to binding is dominated by the ligand desolvation entropy. The entropy gain due to solvent release from binding site appears to be more than offset by the reduction of rotational and vibrational entropies upon binding.

Computational design principles for bioactive dendrimer based constructs as antagonists of the TLR4-MD-2-LPS complex

The cell surface interaction between bacterial lipopolysaccharide (LPS), Toll-like receptor 4 (TLR4) and MD-2 is central to bacterial sepsis syndromes and wound healing. We have shown that a generation (G) 3.5 polyamidoamine (PAMAM) dendrimer that was partially glycosylated with glucosamine inhibits TLR4-MD-2-LPS induced inflammation in a rabbit model of tissue scaring. However, it was a mixture of closely related chemical species because of the polydispersity of the starting PAMAM dendrimer. Generation 2 triazine dendrimers with single chemical entity material status are available at low cost and at the kilogram scale. PAMAM dendrimer can be synthetically grafted onto this triazine core dendrimer to make new triazine-PAMAM hybrid dendrimers. This led us to examine whether molecular modelling methods could be used to identify the key structural design principles for a bioactive lead molecule that could be synthesized and biologically evaluated. We describe our computer aided molecular studies of several dendrimer based constructs and the key design principles identified. Our approach should be more broadly applicable to the biologically focused, rational and accelerated design of molecules for other TLR receptors. They could be useful for treating infectious, inflammatory and malignant diseases.

Glycan Reader: automated sugar identification and simulation preparation for carbohydrates and glycoproteins

Understanding how glycosylation affects protein structure, dynamics, and function is an emerging and challenging problem in biology. As a first step toward glycan modeling in the context of structural glycobiology, we have developed Glycan Reader and integrated it into the CHARMM-GUI, http://www.charmm-gui.org/input/glycan. Glycan Reader greatly simplifies the reading of PDB structure files containing glycans through (i) detection of carbohydrate molecules, (ii) automatic annotation of carbohydrates based on their three-dimensional structures, (iii) recognition of glycosidic linkages between carbohydrates as well as N-/O-glycosidic linkages to proteins, and (iv) generation of inputs for the biomolecular simulation program CHARMM with the proper glycosidic linkage setup. In addition, Glycan Reader is linked to other functional modules in CHARMM-GUI, allowing users to easily generate carbohydrate or glycoprotein molecular simulation systems in solution or membrane environments and visualize the electrostatic potential on glycoprotein surfaces. These tools are useful for studying the impact of glycosylation on protein structure and dynamics.

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ∼91% by tunneling in the case of protium and ∼80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.

Modeling aqueous solvation with semi-explicit assembly

We describe a computational solvation model called semi-explicit assembly (SEA). SEA water captures much of the physics of explicit-solvent models but with computational speeds approaching those of implicit-solvent models. We use an explicit-water model to precompute properties of water solvation shells around simple spheres, then assemble a solute's solvation shell by combining the shells of these spheres. SEA improves upon implicit-solvent models of solvation free energies by accounting for local solute curvature, accounting for near-neighbor nonadditivities, and treating water's dipole as being asymmetrical with respect to positive or negative solute charges. SEA does not involve parameter fitting, because parameters come from the given underlying explicit-solvation model. SEA is about as accurate as explicit simulations as shown by comparisons against four different homologous alkyl series, a set of 504 varied solutes, solutes taken retrospectively from two solvation-prediction events, and a hypothetical polar-solute series, and SEA is about 100-fold faster than Poisson-Boltzmann calculations.

Recent theoretical and computational advances for modeling protein-ligand binding affinities

We review recent theoretical and algorithmic advances for the modeling of protein ligand binding free energies. We first describe a statistical mechanics theory of noncovalent association, with particular focus on deriving the fundamental formulas on which computational methods are based. The second part reviews the main computational models and algorithms in current use or development, pointing out the relations with each other and with the theory developed in the first part. Particular emphasis is given to the modeling of conformational reorganization and entropic effect. The methods reviewed are free energy perturbation, double decoupling, the Binding Energy Distribution Analysis Method, the potential of mean force method, mining minima and MM/PBSA. These models have different features and limitations, and their ranges of applicability vary correspondingly. Yet their origins can all be traced back to a single fundamental theory.

A comparative study on the ability of two implicit solvent lipid models to predict transmembrane helix tilt angles

Free-energy profiles describing the relative orientation of membrane proteins along predefined coordinates can be efficiently calculated by means of umbrella simulations. Such simulations generate reliable orientational distributions but are difficult to converge because of the very long equilibration times of the solvent and the lipid bilayer in explicit representation. Two implicit lipid membrane models are here applied in combination with the umbrella sampling strategy to the simulation of the transmembrane (TM) helical segment from virus protein U (Vpu). The models are used to study both orientation and energetics of this α-helical peptide as a function of hydrophobic mismatch. We observe that increasing the degree of positive hydrophobic mismatch increased the tilt angle of Vpu. These findings agree well with experimental data and as such validate the solvation models used in this study.

New estimators for calculating solvation entropy and enthalpy and comparative assessments of their accuracy and precision

We present two new methods for estimating the entropy and enthalpy decomposition of free energy calculations. These methods are based on temperature derivatives of the Bennett Acceptance Ratio and the Multistate Bennett Acceptance Ratio estimators, respectively. We test the accuracy of these new estimators using a simple one-dimensional model. A detailed assessment of their performance is reported by studying the solvation of N-methylacetamide. Finally, we quantify the free energies of solvation for 11 model compounds using the OPLS-AA force field and a variation of this force field. Thermodynamic decompositions of these calculated free energies are obtained to highlight the utility of these quantities for refining force field parameters by comparing computed free energies and their decompositions to their experimental counterparts.

Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach

Using a nonlocal electrostatic approach that incorporates the short-range structure of the contacting media, we evaluated the electrostatic contribution to the energy of the complex formation of two model proteins. In this study, we have demonstrated that the existence of an ordered interfacial water layer at the protein-solvent interface reduces the charging energy of the proteins in the aqueous solvent, and consequently increases the electrostatic contribution to the protein binding (change in free energy upon the complex formation of two proteins). This is in contrast with the finding of the continuum electrostatic model, which suggests that electrostatic interactions are not strong enough to compensate for the unfavorable desolvation effects.

Biomolecular Structure and Modeling: Historical Perspective

physics, chemistry, and biology have been connected by a web of causal explanation organized by induction-based theories that telescope into one another. … Thus, quantum theory underlies atomic physics, which is the foundation of reagent chemistry and its specialized offshoot biochemistry, which interlock with molecular biology — essentially, the chemistry of organic macromolecules — and hence, through successively higher levels of organization, cellular, organismic, and evolutionary biology. … Such is the unifying and highly productive understanding of the world that has evolved in the natural sciences.

Three-dielectric-layer hybrid solvation model with spheroidal cavities in biomolecular simulations

This paper extends the three-dielectric-layer hybrid solvation model for treating electrostatic interactions in biomolecular simulations from the spherical geometry [Comm. Comp. Phys. 6, 955 (2009)] to the prolate/oblate spheroidal geometries. In the resulting model, the inner spheroidal cavity of a low dielectric constant epsilon(i) contains an irregular-shaped solute and some explicit solvent molecules, while the unbounded outer layer is used to implicitly model the bulk solvent as a dissimilar continuum medium of a high dielectric constant epsilon(o). The thin intermediate translation layer, which also consists of explicit solvent molecules, assumes a continuous variation of the dielectric permittivity epsilon(r) changing smoothly from epsilon(i) to epsilon(o). In particular, the so-called quasiharmonic dielectric permittivity profile is introduced based on a harmonic interpolation, thus allowing analytical series solutions of the generalized Coulomb potential and the self-polarization energy in terms of the associated Legendre functions. A key advantage of the proposed quasiharmonic dielectric model lies in the fact that it overcomes the inherent mathematical divergence in the self-polarization energy that exists in the simple and widely used steplike dielectric model. Numerical examples are included to show some simulated behaviors of the quasiharmonic dielectric model and the corresponding analytical solution.

Pairwise decomposition of residue interaction energies of single chain Fv with HIV-1 p17 epitope variants

Computational assisted modeling was carried out to investigate the importance of specific residues in the binding site of scFv. In this study, scFv against HIV-1 epitope at the C-terminal on p17 (scFv anti-p17) was used as a candidate molecule for evaluating the method. The wild-type p17 and its nine natural mutants were docked with scFv anti-p17. Potential mean force (PMF) scores predicted the most favorable binding interaction, and the correlation agreed well with the corresponding activity data from the peptide based ELISA. In the interaction with solvent molecules, the 3D structures of scFv anti-p17 and selected peptide epitopes were further investigated by molecular dynamics (MDs) simulation with the AMBER 9 program. Post-processing of the snapshot at equilibrium was performed to evaluate the binding free energy and pairwise decomposition or residue-based energy calculation of complexes in solution using the Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) protocol. Our results demonstrated that the specific residues located in the complementary determining regions (CDRs) of scFv anti-p17, MET100, LYS101, ASN169, HIS228, and LEU229, play a crucial role in the effective binding interaction with the absolute relative decomposed energy more than 2.00 kcal/mol in comparison to the original substrate.

A computational pathway for bracketing native-like structures fo small alpha helical globular proteins

Impressive advances in the applications of bioinformatics for protein structure prediction coupled with growing structural databases on one hand and the insurmountable time-scale problem with ab initio computational methods on the other continue to raise doubts whether a computational solution to the protein folding problem--categorized as an NP-hard problem--is within reach in the near future. Combining some specially designed biophysical filters and vector algebra tools with ab initio methods, we present here a promising computational pathway for bracketing native-like structures of small alpha helical globular proteins departing from secondary structural information. The automated protocol is initiated by generating multiple structures around the loops between secondary structural elements. A set of knowledge-based biophysical filters namely persistence length and radius of gyration, developed and calibrated on approximately 1000 globular proteins, is introduced to screen the trial structures to filter out improbable candidates for the native and reduce the size of the library of probable structures. The ensemble so generated encompasses a few structures with native-like topology. Monte Carlo optimizations of the loop dihedrals are then carried out to remove steric clashes. The resultant structures are energy minimized and ranked according to a scoring function tested previously on a series of decoy sets vis-a-vis their corresponding natives. We find that the 100 lowest energy structures culled from the ensemble of energy optimized trial structures comprise at least a few to within 3-5 angstroms of the native. Thus the formidable "needle in a haystack" problem is narrowed down to finding an optimal solution amongst a computationally tractable number of alternatives. Encouraging results obtained on twelve small alpha helical globular proteins with the above outlined pathway are presented and discussed.

Transport properties of water at functionalized molecular interfaces

Understanding transport properties of solvent such as diffusion and viscosity at interfaces with biomacromolecules and hard materials is of fundamental importance to both biology and biotechnology. Our study utilizes equilibrium molecular dynamics simulations to calculate solvent transport properties at a model peptide and microarray surface. Both diffusion and selected components of viscosity are considered. Solvent diffusion is found to be affected near the peptide and surface. The stress-stress correlation function of solvent near the hard surface exhibits long time memory. Both diffusion and viscosity are shown to be closely correlated with the density distribution function of water along the microarray surface.