Solvation Terms Research Articles

Reintroducing electrostatics into protein X-ray structure refinement: bulk solvent treated as a dielectric continuum.

Structural refinement of proteins involves the minimization of a target function that combines X-ray data with a set of restraints enforcing stereochemistry and packing. Electrostatic interactions are not ordinarily included in the target function, partly because they cannot be calculated reliably without a description of dielectric screening by solvent in the crystal. With the recent development of accurate implicit solvent models to describe this screening, the question arises as to whether a more detailed target function including electrostatic and solvation terms can yield more accurate structures or somewhat different structures of equivalent accuracy. The Generalized Born (GB) model is one such model that describes the solvent as a dielectric continuum, taking into account its heterogeneous distribution within the crystal. It is used here for X-ray refinements of three protein structures with experimental diffraction data to 2.4, 2.9 and 3.2 A, respectively. In each case, a higher resolution structure is available for comparison. The new target function includes stereochemical restraints, van der Waals, Coulomb and solvation interactions, along with the usual X-ray pseudo-energy term, which employs the likelihood estimator of Pannu and Read. Multiple simulated-annealing refinements were performed in torsion-angle space with a conventional target function and the new GB target function, yielding ensembles of refined structures. The new target function yields structures of similar accuracy, as measured by the free R factor, map/model correlations and deviations from the high-resolution structures. About 10% of side-chain conformations differ between the two sets of refinements, in the sense that the two ensembles of conformations do not completely overlap. Over 75% of the differences correspond to surface side chains. For one of the proteins, the GB set has a greater dispersion, indicating that for this case the conventional target function overestimates the true precision. As GB parameterization continues to improve, we expect that this approach will become increasingly useful.

The influence of molecular variation on protein interactions

We investigated the influence of solvation forces on protein-protein interactions for two forms of lysozyme: hen egg white (HEWL) and turkey egg white (TEWL). Turkey egg white has more surface exposed hydrophobic residues than HEWL and the protein-protein interactions of TEWL are shown to be more attractive than those of HEWL, for the conditions studied. The importance of including a solvation term in the potential of mean force model, to account for molecular variation in protein surface characteristics, is highlighted. We also show that the magnitude of this solvation term can be estimated using readily available data.

Algorithms for computational solvent mapping of proteins.

Computational mapping methods place molecular probes (small molecules or functional groups) on a protein surface to identify the most favorable binding positions by calculating an interaction potential. We have developed a novel computational mapping program called CS-Map (computational solvent mapping of proteins), which differs from earlier mapping methods in three respects: (i) it initially moves the ligands on the protein surface toward regions with favorable electrostatics and desolvation, (ii) the final scoring potential accounts for desolvation, and (iii) the docked ligand positions are clustered, and the clusters are ranked on the basis of their average free energies. To understand the relative importance of these factors, we developed alternative algorithms that use the DOCK and GRAMM programs for the initial search. Because of the availability of experimental solvent mapping data, lysozyme and thermolysin are considered as test proteins. Both DOCK and GRAMM speed up the initial search, and the combined algorithms yield acceptable mapping results. However, the DOCK-based approaches place the consensus site farther from its experimentally determined position than CS-Map, primarily because of the lack of a solvation term in the initial search. The GRAMM-based program also finds the correct consensus site for thermolysin. We conclude that good sampling is the most important requirement for successful mapping, but accounting for desolvation and clustering of ligand positions also help to reduce the number of false positives.

A computational study of lithium enolate mixed aggregates.

Ab initio calculations were performed to examine the formation of mixed dimer and trimer aggregates between the lithium enolate of acetaldehyde (lithium vinyloxide, LiOV) and lithium chloride, lithium bromide, and lithium amides. Gas-phase calculations showed that in the absence of solvation effects, the mixed trimer 2LiOV.LiX is the most favored species. Solvation in ethereal solvents was modeled by a combination of specific coordination of dimethyl ether ligands on each lithium and "dielectric solvation" (DSE, dielectric solvation energies), immersion of each molecule in a cavity within a continuous dielectric having the dielectric constant of THF at room temperature. DSE is less important for aggregates (reduced dipoles or quadrupoles) than monomers (dipoles) and is also reduced for the coordinatively solvated species. Both solvation terms reduce the exothermicity of aggregation. In many cases, lithium salts that are three- rather than four-coordinate have significant populations at room temperature. The strongly basic lithium amides prefer mixed aggregates with weaker bases than homoaggregates. The computational results are consistent with the limited experimental data available.

Solution effects and the order of the helix–coil transition in polyalanine

We study helix–coil transitions in an all-atom model of polyalanine. Molecules of up to length 30 residues are investigated by multicanonical simulations. Results from two implicit solvent models are compared with each other and with that from simulations in gas phase. While the helix–coil transition is in all three models a true thermodynamic phase transition, we find that its strength is reduced by the protein–solvent interaction term. The order of the helix–coil transition depends on the details of the solvation term.

MOPED: method for optimizing physical energy parameters using decoys.

We present a method called MOPED for optimizing energetic and structural parameters in computational models, including all-atom energy functions, when native structures and decoys are given. The present method goes beyond previous approaches in treating energy functions that are nonlinear in the parameters and continuous in the degrees of freedom. We illustrate the method by improving solvation parameters in the energy function EEF1, which consists of the CHARMM19 polar hydrogen force field augmented by a Gaussian solvation term. Although the published parameters for EEF1 correctly discriminate the native from decoys in the decoy sets of Levitt et al., they fail on several of the more difficult decoy sets of Baker et al. MOPED successfully finds improved parameters that allow EEF1 to discriminate native from decoy structures on all protein structures that do not have metals or prosthetic groups.

Implicit solvent models for flexible protein-protein docking by molecular dynamics simulation.

The suitability of three implicit solvent models for flexible protein-protein docking by procedures using molecular dynamics simulation is investigated. The three models are (i) the generalized Born (GB) model implemented in the program AMBER6.0; (ii) a distance-dependent dielectric (DDD) model; and (iii) a surface area-dependent model that we have parameterized and call the NPSA model. This is a distance-dependent dielectric model modified by neutralizing the ionizable side-chains and adding a surface area-dependent solvation term. These solvent models were first tested in molecular dynamics simulations at 300 K of the native structures of barnase, barstar, segment B1 of protein G, and three WW domains. These protein structures display a range of secondary structure contents and stabilities. Then, to investigate the performance of the implicit solvent models in protein docking, molecular dynamics simulations of barnase/barstar complexation, as well as PIN1 WW domain/peptide complexation, were conducted, starting from separated unbound structures. The simulations show that the NPSA model has significant advantages over the DDD and GB models in maintaining the native structures of the proteins and providing more accurate docked complexes.

Lattice models of protein folding permitting disordered native states

Self-avoiding lattice walks are often used as minimalist models of proteins. Typically, the polypeptide chain is represented as a lattice walk with each amino acid residue lying on a lattice point, and the Hamiltonian being a sum of interactions between pairs of sequentially nonadjacent residues on adjacent points. Interactions depend on the types of the two residues, and there are usually two or more types. A sequence is said to fold to a particular “native” conformation if the ground state is nondegenerate, i.e., that native conformation is the unique global energy minimum conformation. However, real proteins have some flexibility in the folded state. If this is permitted in a lattice model, the most stably and cooperatively folding sequences have very disordered native states unless the Hamiltonian either favors only a few specific interactions or includes a solvation term. The result points the way toward qualitatively more realistic lattice models for protein folding.

Artificial protein cavities as specific ligand-binding templates: characterization of an engineered heterocyclic cation-binding site that preserves the evolved specificity of the parent protein

Cavity complementation has been observed in many proteins, where an appropriate small molecule binds to a cavity-forming mutant. Here, the binding of compounds to the W191G cavity mutant of cytochrome c peroxidase is characterized by X-ray crystallography and binding thermodynamics. Unlike cavities created by removal of hydrophobic side-chains, the W191G cavity does not bind neutral or hydrophobic compounds, but displays a strong specificity for heterocyclic cations, consistent with the role of the protein to stabilize a tryptophan radical at this site. Ligand dissociation constants for the protonated cationic state ranged from 6 μM for 2-amino-5-methylthiazole to 1 mM for neutral ligands, and binding was associated with a large enthalpy-entropy compensation. X-ray structures show that each of 18 compounds with binding behavior bind specifically within the artificial cavity and not elsewhere in the protein. The compounds make multiple hydrogen bonds to the cavity walls using a subset of the interactions seen between the protein and solvent in the absence of ligand. For all ligands, every atom that is capable of making a hydrogen bond does so with either protein or solvent. The most often seen interaction is to Asp235, and most compounds bind with a specific orientation that is defined by their ability to interact with this residue. Four of the ligands do not have conventional hydrogen bonding atoms, but were nevertheless observed to orient their most polar CH bond towards Asp235. Two of the larger ligands induce disorder in a surface loop between Pro190 and Asn195 that has been identified as a mobile gate to cavity access. Despite the predominance of hydrogen bonding and electrostatic interactions, the small variation in observed binding free energies were not correlated readily with the strength, type or number of hydrogen bonds or with calculated electrostatic energies alone. Thus, as with naturally occurring binding sites, affinities to W191G are likely to be due to a subtle balance of polar, non-polar, and solvation terms. These studies demonstrate how cavity complementation and judicious choice of site can be used to produce a protein template with an unusual ligand-binding specificity.

Solvation enthalpies of free radicals: O-O bond strength in di-tert-butylperoxide.

The photolysis reaction of di-tert-butylperoxide was studied in various solvents by photoacoustic calorimetry (PAC). This technique allows the determination of the enthalpy of this homolysis reaction, which by definition corresponds to the O-O bond dissociation enthalpy of the peroxide in solution, DHsin(degrees)(O-O). The derived value from these experiments in benzene, 156.7 +/- 9.9 kJ mol(-1), is very similar to a widely accepted value for the gas-phase bond dissociation enthalpy, DH(degrees)(O-O) = 159.0 +/- 2.1 kJ mol(-1). However, when the PAC-based value is used together with auxiliary experimental data and Drago's ECW model to estimate the required solvation terms, it leads to 172.3 +/- 10.2 kJ mol(-1) for the gas-phase bond dissociation enthalpy. This result, significantly higher than the early literature value, is however in excellent agreement with a recent gas-phase determination of 172.5 +/- 6.6 kJ mol(-1). The procedure to derive the gas-phase DH(degrees)(O-O) was tested by repeating the PAC experiments in carbon tetrachloride and acetonitrile. The average of the values thus obtained was DH(degrees)(O-O) = 179.6 +/- 4.5 kJ mol(-1), confirming that the early gas-phase result is a lower limit. More importantly, the present study questions the usual assumption that the solvation terms of homolysis reactions producing free radicals in solution should cancel, and suggests a methodology to estimate solvation enthalpies of free radicals.

Identifying native-like protein structures using physics-based potentials.

As the field of structural genomics matures, new methods will be required that can accurately and rapidly distinguish reliable structure predictions from those that are more dubious. We present a method based on the CHARMM gas phase implicit hydrogen force field in conjunction with a generalized Born implicit solvation term that allows one to make such discrimination. We begin by analyzing pairs of threaded structures from the EMBL database, and find that it is possible to identify the misfolded structures with over 90% accuracy. Further, we find that misfolded states are generally favored by the solvation term due to the mispairing of favorable intramolecular ionic contacts. We also examine 29 sets of 29 misfolded globin sequences from Levitt's "Decoys 'R' Us" database generated using a sequence homology-based method. Again, we find that discrimination is possible with approximately 90% accuracy. Also, even in these less distorted structures, mispairing of ionic contacts results in a more favorable solvation energy for misfolded states. This is also found to be the case for collapsed, partially folded conformations of CspA and protein G taken from folding free energy calculations. We also find that the inclusion of the generalized Born solvation term, in postprocess energy evaluation, improves the correlation between structural similarity and energy in the globin database. This significantly improves the reliability of the hypothesis that more energetically favorable structures are also more similar to the native conformation. Additionally, we examine seven extensive collections of misfolded structures created by Park and Levitt using a four-state reduced model also contained in the "Decoys 'R' Us" database. Results from these large databases confirm those obtained in the EMBL and misfolded globin databases concerning predictive accuracy, the energetic advantage of misfolded proteins regarding the solvation component, and the improved correlation between energy and structural similarity due to implicit solvation. Z-scores computed for these databases are improved by including the generalized Born implicit solvation term, and are found to be comparable to trained and knowledge-based scoring functions. Finally, we briefly explore the dynamic behavior of a misfolded protein relative to properly folded conformations. We demonstrate that the misfolded conformation diverges quickly from its initial structure while the properly folded states remain stable. Proteins in this study are shown to be more stable than their misfolded counterparts and readily identified based on energetic as well as dynamic criteria. In summary, we demonstrate the utility of physics-based force fields in identifying native-like conformations in a variety of preconstructed structural databases. The details of this discrimination are shown to be dependent on the construction of the structural database.

Theoretical studies of d(A:T)-based parallel-stranded DNA duplexes.

Poly d(A:T) parallel-stranded DNA duplexes based on the Hoogsteen and reverse Watson-Crick hydrogen bond pairing are studied by means of extensive molecular dynamics (MD) simulations and molecular mechanics coupled to Poisson-Boltzmann (MM-PB/SA) calculations. The structural, flexibility, and reactivity characteristics of Hoogsteen and reverse Watson-Crick parallel duplexes are described from the analysis of the trajectories. Theoretical calculations show that the two parallel duplexes are less stable than the antiparallel Watson-Crick duplex. The difference in stability between antiparallel and parallel duplexes increases steadily as the length of the duplex increases. The reverse Watson-Crick arrangement is slightly more stable than the Hoogsteen duplex, the difference being also increased linearly with the length of the duplex. A subtle balance of intramolecular and solvation terms is responsible for the preference of a given helical structure.

Contribution of Solvation Energy in Protein‐Peptide Recognition Systems

AbstractThe contribution of solvation energy to guiding molecular recognition for six rigid protein‐peptide systems bad been evaluated by the variation in the number of the identified native‐like configurations and in the driving force of specific interaction resulting from the addition of the explicit solvation term in the force field function. The AMBER force field energy and the total energy including the force field energy and the WZS solvation energy were calculated for sampled configurations. The results obtained by the calculations of both force field and total energies were compared with each other. It suggests that the contribution of solvation energy is important to guiding the specific recognition of the systems in which the ligands possess larger hydrophobic or aromatic residues while the protein receptors provide the active surfaces with hydrophobic property.

A gaussian statistical mechanical model for the equilibrium thermodynamics of barnase folding

Given an all non-hydrogen-atom potential function that implicitly includes solvation effects, it is possible to adjust its parameters to favor the correct native structure for several proteins over decoys produced by ungapped threading. It is also possible to further train it to reproduce the experimental free energy of unfolding in aqueous solution at 298 K for wild-type barnase and 66 mutants. For this, the native state is represented by the crystal structure at a single energy level with a calculated low degeneracy; the denatured state is represented by the extended conformation and a high calculated degeneracy. The same two-state model can be extended to account for the stability of all 67 sequences toward urea denaturation at 298 K by building in a solvation term that depends on urea concentration. With the addition of one more parameter set to give the correct heat capacity of unfolded barnase in solution, it is possible to approximate the experimental thermodynamics of barnase thermal denaturation: melting temperature, width of thermal transition, ΔG, ΔH, ΔS, and ΔCp. This requires a novel sort of statistical mechanical model where the two states each have a Gaussian density of microscopic state distribution as a function of energy.

Rapid boundary element solvation electrostatics calculations in folding simulations: Successful folding of a 23-residue peptide

Solvation effects play a profound role in the energetics of protein folding. While a continuum dielectric model of solvation may provide a sufficiently accurate estimate of the solvation effects, until now this model was too computationally expensive and unstable for folding simulations. Here we proposed a fast yet accurate and robust implementation of the boundary element solution of the Poisson equation, the REBEL algorithm. Using our earlier double-energy scheme, we included for the first time the mathematically rigorous continuous REBEL solvation term in our Biased Probability Monte Carlo (BPMC) simulations of the peptide folding. The free energy of a 23-residue beta beta alpha-peptide was then globally optimized with and without the solvation electrostatics contribution. An ensemble of beta beta alpha conformations was found at and near the global minimum of the energy function with the REBEL electrostatic solvation term. Much poorer correspondence to the native solution structure was found in the "control" simulations with a traditional method to account for solvation via a distance-dependent dielectric constant. Each simulation took less than 40 h (21 h without electrostatic solvation calculation) on a single Alpha 677 MHz CPU and involved more than 40,000 solvation energy evaluations. This work demonstrates for the first time that such a simulation can be performed in a realistic time frame. The proposed procedure may eliminate the energy evaluation accuracy bottleneck in folding simulations.

Discrimination of near‐native protein structures from misfolded models by empirical free energy functions

Free energy potentials, combining molecular mechanics with empirical solvation and entropic terms, are used to discriminate native and near-native protein conformations from slightly misfolded decoys. Since the functional forms of these potentials vary within the field, it is of interest to determine the contributions of individual free energy terms and their combinations to the discriminative power of the potential. This is achieved in terms of quantitative measures of discrimination that include the correlation coefficient between RMSD and free energy, and a new measure labeled the minimum discriminatory slope (MDS). In terms of these criteria, the internal energy is shown to be a good discriminator on its own, which implies that even well-constructed decoys are substantially more strained than the native protein structure. The discrimination improves if, in addition to the internal energy, the free energy expression includes the electrostatic energy, calculated by assuming non-ionized side chains, and an empirical solvation term, with the classical atomic solvation parameter model providing slightly better discrimination than a structure-based atomic contact potential. Finally, the inclusion of a term representing the side chain entropy change, and calculated by an established empirical scale, is so inaccurate that it makes the discrimination worse. It is shown that both the correlation coefficient and the MDS value (or its dimensionless form) are needed for an objective assessment of a potential, and that together they provide much more information on the origins of discrimination than simple inspection of the RMSD-free energy plots. Proteins 2000;41:518–534. © 2000 Wiley-Liss, Inc.

Free energy determinants of tertiary structure and the evaluation of protein models.

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.

Discrimination of near-native protein structures from misfolded models by empirical free energy functions

Free energy potentials, combining molecular mechanics with empirical solvation and entropic terms, are used to discriminate native and near-native protein conformations from slightly misfolded decoys. Since the functional forms of these potentials vary within the field, it is of interest to determine the contributions of individual free energy terms and their combinations to the discriminative power of the potential. This is achieved in terms of quantitative measures of discrimination that include the correlation coefficient between RMSD and free energy, and a new measure labeled the minimum discriminatory slope (MDS). In terms of these criteria, the internal energy is shown to be a good discriminator on its own, which implies that even well-constructed decoys are substantially more strained than the native protein structure. The discrimination improves if, in addition to the internal energy, the free energy expression includes the electrostatic energy, calculated by assuming non-ionized side chains, and an empirical solvation term, with the classical atomic solvation parameter model providing slightly better discrimination than a structure-based atomic contact potential. Finally, the inclusion of a term representing the side chain entropy change, and calculated by an established empirical scale, is so inaccurate that it makes the discrimination worse. It is shown that both the correlation coefficient and the MDS value (or its dimensionless form) are needed for an objective assessment of a potential, and that together they provide much more information on the origins of discrimination than simple inspection of the RMSD-free energy plots.

Scoring docked conformations generated by rigid-body protein-protein docking.

Rigid-body methods, particularly Fourier correlation techniques, are very efficient for docking bound (co-crystallized) protein conformations using measures of surface complementarity as the target function. However, when docking unbound (separately crystallized) conformations, the method generally yields hundreds of false positive structures with good scores but high root mean square deviations (RMSDs). This paper describes a two-step scoring algorithm that can discriminate near-native conformations (with less than 5 A RMSD) from other structures. The first step includes two rigid-body filters that use the desolvation free energy and the electrostatic energy to select a manageable number of conformations for further processing, but are unable to eliminate all false positives. Complete discrimination is achieved in the second step that minimizes the molecular mechanics energy of the retained structures, and re-ranks them with a combined free-energy function which includes electrostatic, solvation, and van der Waals energy terms. After minimization, the improved fit in near-native complex conformations provides the free-energy gap required for discrimination. The algorithm has been developed and tested using docking decoys, i.e., docked conformations generated by Fourier correlation techniques. The decoy sets are available on the web for testing other discrimination procedures. Proteins 2000;40:525-537.

De novo protein design. I. in search of stability and specificity

We have developed a fully automated protein design strategy that works on the entire sequence of the protein and uses a full atom representation. At each step of the procedure, an all-atom model of the protein is built using the template protein structure and the current designed sequence. The energy of the model is used to drive a Monte Carlo optimization in sequence space: random moves are either accepted or rejected based on the Metropolis criterion. We rely on the physical forces that stabilize native protein structures to choose the optimum sequence. Our energy function includes van der Waals interactions, electrostatics and an environment free energy. Successful protein design should be specific and generate a sequence compatible with the template fold and incompatible with competing folds. We impose specificity by maintaining the amino acid composition constant, based on the random energy model. The specificity of the optimized sequence is tested by fold recognition techniques. Successful sequence designs for the B1 domain of protein G, for the lambda repressor and for sperm whale myoglobin are presented. We show that each additional term of the energy function improves the performance of our design procedure: the van der Waals term ensures correct packing, the electrostatics term increases the specificity for the correct native fold, and the environment solvation term ensures a correct pattern of buried hydrophobic and exposed hydrophilic residues. For the globin family, we show that we can design a protein sequence that is stable in the myoglobin fold, yet incompatible with the very similar hemoglobin fold.