Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

An evaluation of Poisson-Boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

For systems involving highly and oppositely charged proteins, electrostatic forces dominate association and contribute to biomolecular complex stability. Using experimental or theoretical alanine-scanning mutagenesis, it is possible to elucidate the contribution of individual ionizable amino acids to protein association. We evaluated our electrostatic free energy calculations by comparing calculated and experimental data for alanine mutants of five protein complexes. We calculated Poisson-Boltzmann electrostatic free energies based on a thermodynamic cycle, which incorporates association in a reference (Coulombic) and solvated (solution) state, as well as solvation effects. We observe that Coulombic and solvation free energy values correlate with experimental data in highly and oppositely charged systems, but not in systems comprised of similarly charged proteins. We also observe that correlation between solution and experimental free energies is dependent on dielectric coefficient selection for the protein interior. Free energy correlations improve as protein dielectric coefficient increases, suggesting that the protein interior experiences moderate dielectric screening, despite being shielded from solvent. We propose that higher dielectric coefficients may be necessary to more accurately predict protein-protein association. Additionally, our data suggest that Coulombic potential calculations alone may be sufficient to predict relative binding of protein mutants.     

Coupled molecular dynamics and continuum electrostatic method to compute the ionization pKa’s of proteins as a function of pH. Test on a large set of proteins

A computational method, to predict the pKa values of the ionizable residues Asp, Glu, His, Tyr, and Lys of proteins, is presented here. Calculation of the electrostatic free-energy of the proteins is based on an efficient version of a continuum dielectric electrostatic model. The conformational flexibility of the protein is taken into account by carrying out molecular dynamics simulations of 10 ns in implicit water. The accuracy of the proposed method of calculation of pKa values is estimated from a test set of experimental pKa data for 297 ionizable residues from 34 proteins. The pKa-prediction test shows that, on average, 57, 86, and 95% of all predictions have an error lower than 0.5, 1.0, and 1.5 pKa units, respectively. This work contributes to our general understanding of the importance of protein flexibility for an accurate computation of pKa, providing critical insight about the significance of the multiple neutral states of acid and histidine residues for pKa-prediction, and may spur significant progress in our effort to develop a fast and accurate electrostatic-based method for pKa-predictions of proteins as a function of pH.     

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.     

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.     

Study of the insulin dimerization: binding free energy calculations and per-residue free energy decomposition

A calculation of the binding free energy for the dimerization of insulin has been performed using the molecular mechanics-generalized Born surface area approach. The calculated absolute binding free energy is -11.9 kcal/mol, in approximate agreement with the experimental value of -7.2 kcal/mol. The results show that the dimerization is mainly due to nonpolar interactions. The role of the hydrogen bonds between the 2 monomers appears to give the direction of the interactions. A per-atom decomposition of the binding free energy has been performed to identify the residues contributing most to the self association free energy. Residues B24-B26 are found to make the largest favorable contributions to the dimerization. Other residues situated at the interface between the 2 monomers were found to make favorable but smaller contributions to the dimerization: Tyr B16, Val B12, and Pro B28, and to an even lesser extent, Gly B23. The energy decomposition on a per-residue basis is in agreement with experimental alanine scanning data. The results obtained from a single trajectory (i.e., the dimer trajectory is also used for the monomer analysis) and 2 trajectories (i.e., separate trajectories are used for the monomer and dimer) are similar.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.     

Atomic contacts in protein structures. A detailed analysis of atomic radii, packing, and overlaps

A rigorous quantitative assessment of atomic contacts and packing in native protein structures is presented. The analysis is based on optimized atomic radii derived from a set of high-resolution protein structures and reveals that the distribution of atomic contacts and overlaps is a structural constraint in proteins, irrespective of structural or functional classification and size. Furthermore, a newly developed method for calculating packing properties is introduced and applied to sets of protein structures at different levels of resolution. The results show that limited resolution yields decreasing packing quality, which underscores the relevance of packing considerations for structure prediction, design, dynamics, and docking.     

Use of restrained molecular dynamics in water to determine three-dimensional protein structure: prediction of the three-dimensional structure of Ecballium elaterium trypsin inhibitor II

Refinement of distance geometry (DG) structures of EETI-II (Heitz et al.: Biochemistry 28:2392-2398, 1989), a member of the squash family trypsin inhibitor, have been carried out by restrained molecular dynamics (RMD) in water. The resulting models show better side chain apolar/polar surface ratio and estimated solvation free energy than structures refined "in vacuo." The consistent lower values of residual NMR constraint violations, apolar/polar surface ratio, and solvation free energy for one of these refined structures allowed prediction of the 3D folding and disulfide connectivity of EETI-II. Except for the few first residues for which no NMR constraints were available, this computer model fully agreed with X-ray structures of CMTI-I (Bode et al.: FEBS Lett. 242:285-292, 1989) and EETI-II complexed with trypsin that appeared after the RMD simulation was completed. Restrained molecular dynamics in water is thus proved to be highly valuable for refinement of DG structures. Also, the successful use of apolar/polar surface ratio and of solvation free energy reinforce the analysis of Novotny et al. (Proteins 4:19-30, 1988) and shows that these criteria are useful indicators of correct versus misfolded models.     

Role of the electrostatic energy between the photo-products and ionic groups on the photoinduced electron transfer rates from aromatic amino acids to the excited flavin in five single-point substitution isoforms of the charged amino acid residue-13 in the FMN-binding protein

Effect of the charge (negative, positive or neutral) of amino acid residue-13 on the photoinduced electron transfer (ET) from Trp32, Tyr35 and Trp106 to the excited isoalloxazine was evaluated in the flavin mononucleotide-binding protein from Desulfovibrio vulgaris isolate Miyazaki F (DvFBP). The protein structures of the wild type and the four isoforms where glutamic acid-13 is replaced with lysine (E13K), arginine (E13R), threonine (E13T) and glutamine (E13Q) in aqueous solution were obtained by molecular dynamics simulation. The distances between the amino acid residue-13 and isoalloxazine (Iso), and between the amino acid residue-13 and the ET donors were longer than 1 nm. The ET rates were evaluated with the Kakitani and Mataga model (KM theory) from their ultrafast fluorescence dynamics by means of a non-linear least squares method. Electrostatic (ES) energies between the photo-products and other ionic groups in the proteins markedly varied among ET donors and among the DvFBP isoforms, while the other physical quantities related to the ET rates, the solvent reorganisation and ES energies between the Iso anion and the donor cations did not vary much between the proteins and donors. A plot of the logarithmic ET rates versus either the total free energy gaps or the net ES energies between the photo-products and the other ionic groups both displayed a parabolic function and so the net ES energies are an important influential factor upon the ET rate, in addition to the donor–acceptor distance.     

Modeling of peptides and proteins in a membrane environment: I. A solvation model mimicking a lipid bilayer

A theoretical solvation model of peptides and proteins that mimics the heterogeneous membrane-water system was proposed. Our approach is based on the combined use of atomic parameters of solvation for water and hydrocarbons, which approximates the hydrated polar groups and acyl chains of lipids, respectively. This model was tested in simulations of several peptides: a nonpolar 20-mer polyleucine, a hydrophobic peptide with terminal polar groups, and a strongly amphiphilic peptide. The conformational space of the peptides in the presence of the membrane was studied by the Monte Carlo method. Unlike a polar solvent and vacuum, the membrane-like environment was shown to stabilize the α-helical conformation: low-energy structures have a helicity index of 100% in all cases. At the same time, the energetically most favorable orientations of the peptides relative to the membrane depend on their hydrophobic properties: nonpolar polyleucine is entirely immersed in the bilayer and the hydrophobic peptide with polar groups at the termini adopts a transbilayer orientation, whereas the amphiphilic peptide lies at the interface parallel to the membrane plane. The results of the simulations agree well with the available experimental data for these systems. In the following communications of this series, we plan to describe applications of the solvation model to membrane-bound proteins and peptides with biologically important functional activities.     

Improved protein free energy calculation by more accurate treatment of nonbonded energy: Application to chymotrypsin inhibitor 2, V57A

We developed a software package for improved free energy calculation, in which spherical solvent boundary potential, cell multipole method, and Nosé-Hoover equation are employed. The performance of the developed software package is demonstrated in the case of valine to alanine mutation of the 57th residue in chymotrypsin inhibitor 2. By using this package, we obtained results quantitatively comparable to experimental results. By the free energy component analysis, it is shown that leucine 51, arginine 65, arginine 67, and phenylalanine 69 residues contribute significantly to the total free energy shift, ΔΔG. Among them, contribution from the hydrophilic arginine 67 residue, which is in close contact with the mutation site, is the largest. Structure around the mutation site is largely changed by the mutation. The structure change is caused mainly by two effects, hydrophobic interaction and short-range interaction along the sequence. Effects of Nosé-Hoover algorithm and Kirkwood reaction field are also discussed. Proteins 30:388–400, 1998. © 1998 Wiley-Liss, Inc.     

Exploring the role of the phospholipid ligand in endothelial protein C receptor: A molecular dynamics study

Endothelial protein C receptor (EPCR) is a CD1‐like transmembrane glycoprotein with important regulatory roles in protein C (PC) pathway, enhancing PC's anticoagulant, anti‐inflammatory, and antiapoptotic activities. Similarly to homologous CD1d, EPCR binds a phospholipid [phosphatidylethanolamine (PTY)] in a groove corresponding to the antigen‐presenting site, although it is not clear if lipid exchange can occur in EPCR as in CD1d. The presence of PTY seems essential for PC γ‐carboxyglutamic acid (Gla) domain binding. However, the lipid‐free form of the EPCR has not been characterized. We have investigated the structural role of PTY on EPCR, by multiple molecular dynamics (MD) simulations of ligand bound and unbound forms of the protein. Structural changes, subsequent to ligand removal, led to identification of two stable and folded ligand‐free conformations. Compared with the bound form, unbound structures showed a narrowing of the A′ pocket and a high flexibility of the helices around it, in agreement with CD1d simulation. Thus, a lipid exchange with a mechanism similar to CD1d is proposed. In addition, unbound conformations presented a reduced interaction surface for Gla domain, confirming the role of PTY in establishing the proper EPCR conformation for the interaction with its partner protein. Single MD simulations were also obtained for 29 mutant models with predicted structural stability and impaired binding ability. Ligand affinity calculations, based on linear interaction energy method, showed that substitution‐induced conformational changes affecting helices around the A′ pocket were associated to a reduced binding affinity. Mutants responsible for this effect may represent useful reagents for experimental tests. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Modeling of peptides and proteins in a membrane environment: II. Structural and energetic aspects of glycophorin A in a lipid bilayer

The conformational space of a hydrophobic peptide fragment of glycophorin A in a lipid membrane was studied with the Monte Carlo method using the solvation model described in the first communication of this series. The simulation was performed for various starting orientations of the peptide relative the membrane bilayer: outside, inside, partially immersed, and transbilayer. We showed that the membrane substantially stabilizes the α-helical conformation of the central hydrophobic part of the glycophorin A molecule, which for the most part is immersed in the apolar core of the bilayer. For various conformational states, energy values were calculated and the orientations of the peptide relative to the membrane were characterized. Depending on the thickness of the bilayer, either an entirely α-helical conformation in transbilayer orientation or a conformation with a kink in the central part of the helix with theN- andC-termini exposed on one side of the membrane corresponds to the minimal-energy structure. The transmembrane orientation of glycophorin A is energetically advantageous when the membrane thickness is close to the length of its hydrophobic helical portion, which is consistent with the effect ofhydrophobic match observed experimentally. The prospects for further refinement of the model are discussed. For communication I, see [1].     

Role of tyrosine hot‐spot residues at the interface of colicin E9 and immunity protein 9: A comparative free energy simulation study

The endonuclease activity of the bacterial colicin 9 enzyme is controlled by the specific and high‐affinity binding of immunity protein 9 (Im9). Molecular dynamics simulation studies in explicit solvent were used to investigate the free energy change associated with the mutation of two hot‐spot interface residues [tyrosine (Tyr): Tyr54 and Tyr55] of Im9 to Ala. In addition, the effect of several other mutations (Leu33Ala, Leu52Ala, Val34Ala, Val37Ala, Ser48Ala, and Ile53Ala) with smaller influence on binding affinity was also studied. Good qualitative agreement of calculated free energy changes and experimental data on binding affinity of the mutations was observed. The simulation studies can help to elucidate the molecular details on how the mutations influence protein–protein binding affinity. The role of solvent and conformational flexibility of the partner proteins was studied by comparing the results in the presence or absence of solvent and with or without positional restraints. Restriction of the conformational mobility of protein partners resulted in significant changes of the calculated free energies but of similar magnitude for isolated Im9 and for the complex and therefore in only modest changes of binding free energy differences. Although the overall binding free energy change was similar for the two Tyr–Ala mutations, the physical origin appeared to be different with solvation changes contributing significantly to the Tyr55Ala mutation and to a loss of direct protein–protein interactions dominating the free energy change due to the Tyr54Ala mutation. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Immunophysical properties and prediction of activities for vaccinia virus complement control protein and smallpox inhibitor of complement enzymes using molecular dynamics and electrostatics

We present immunophysical modeling for VCP, SPICE, and three mutants using MD simulations and Poisson-Boltzmann-type electrostatic calculations. VCP and SPICE are homologous viral proteins that control the complement system by imitating, structurally and functionally, natural regulators of complement activation. VCP and SPICE consist of four CCP modules connected with short flexible loops. MD simulations demonstrate that the rather complex modules of VCP/SPICE and their mutants exhibit a high degree of intermodular spatial mobility, which is affected by surface mutations. Electrostatic calculations using snapshots from the MD trajectories demonstrate variable spatial distribution of the electrostatic potentials, which suggests dynamic binding properties. We use covariance analysis to identify correlated modular oscillations. We also use electrostatic similarity indices to cluster proteins with common electrostatic properties. Our results are compared with experimental data to form correlations between the overall positive electrostatic potential of VCP/SPICE with binding and activity. We show how these correlations can be used to predict binding and activity properties. This work is expected to be useful for understanding the function of native CCP-containing regulators of complement activation and receptors and for the design of antiviral therapeutics and complement inhibitors.