Generalized born models of macromolecular solvation effects

The role of aspartic acid 143 in E. coli tRNA-guanine transglycosylase: insights from mutagenesis studies and computational modeling

tRNA guanine transglycosylase (TGT) is a tRNA-modifying enzyme which catalyzes the posttranscriptional exchange of guanine in position 34 of tRNA(Y,H,N,D) with the modified base queuine in eukaryotes or its precursor, preQ(1) base, in eubacteria. Thus, TGT must recognize the guanine in tRNA and the free base queuine or preQ(1) to catalyze this exchange. The crystal structure of Zymomonas mobilis TGT with preQ(1) bound suggests that a key aspartate is critically involved in substrate recognition. To explore this, a series of site-directed mutants of D143 in Escherichia coli TGT were made and characterized to investigate heterocyclic substrate recognition. Our data confirm that D143 has significant impact on K(M) of guanine; however, the trend in the K(M) data (D143A < D143N < D143S < D143T) is unexpected. Computational studies were used to further elucidate the interactions between guanine and the D143 mutants. A homology model of E. coli TGT was created, and the role of D143 was investigated by molecular dynamic simulations of guanine bound to the wild-type and D143-mutant TGTs. To validate the model systems against our kinetic data, free energies of binding were fit using the linear interaction energy (LIE) method. This is a unique application of the LIE method because the same ligand is bound to several mutant proteins rather than one protein binding several ligands. The atomic detail gained from the simulations provided a better understanding of the binding affinities of guanine with the mutant TGTs, revealing that water molecules enter the active site and hydrogen bond to the ligand and compensate for lost protein-ligand interactions. The trend of binding affinity for wild-type > D143A > D143N > D143S > D143T appears to be directly related to the degree of hydrogen bonding available to guanine in the binding site.

Dynamic behavior of the telomerase RNA hairpin structure and its relationship to dyskeratosis congenita

In this paper, we present the results from a comprehensive study of nanosecond-scale implicit and explicit solvent molecular dynamics simulations of the wild-type telomerase RNA hairpin. The effects of various mutations on telomerase RNA dynamics are also investigated. Overall, we found that the human telomerase hairpin is a very flexible molecule. In particular, periodically the molecule exhibits dramatic structural fluctuations represented by the opening and closing of a non-canonical base-pair region. These structural deviations correspond to significant disruptions of the direct hydrogen bonding network in the helix, widening of the major groove of the hairpin structure, and causing several U and C nucleotides to protrude into the major groove from the helix permitting them to hydrogen bond with, for example, the P3 domain of the telomerase RNA. We suggest that these structural fluctuations expose a nucleation point for pseudoknot formation. We also found that mutations in the pentaloop and non-canonical region stabilize the hairpin. Moreover, our results show that the hairpin with dyskeratosis congenita mutations is more stable and less flexible than the wild-type hairpin due to base stacking in the pentaloop. The results from our molecular dynamics simulations are in agreement with experimental observations. In addition, they suggest a possible mechanism for pseudoknot formation based on the dynamics of the hairpin structure and also may explain the mutational aspects of dyskeratosis congenita.

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.

Mutational and structural analyses of the hinge region of membrane type 1-matrix metalloproteinase and enzyme processing

Membrane type 1 (MT1)-matrix metalloproteinase (MMP) is a major mediator of collagen degradation in the pericellular space in both physiological and pathological conditions. Previous evidence has shown that on the cell surface, active MT1-MMP undergoes autocatalytic processing to a major membrane-tethered 44-kDa product lacking the catalytic domain and displaying Gly285 at its N terminus, which is at the beginning of the hinge domain. However, the importance of this site and the hinge region in MT1-MMP processing is unknown. In the current study, we generated mutations and deletions in the hinge of MT1-MMP and followed their effect on processing. These studies established Gly284-Gly285 as the main cleavage site involved in the formation of the 44-kDa species. However, alterations at this site did not prevent processing. Instead, they forced downstream cleavages within the stretch of residues flanked by Gln296 and Ser304 in the hinge region, as determined by the processing profile of various hinge deletion mutants. Also, replacement of the hinge of MT1-MMP with the longer MT3-MMP hinge did not prevent processing of MT1-MMP. Molecular dynamic studies using a computational model of MT1-MMP revealed that the hinge region is a highly motile element that undergoes significant motion in the highly exposed loop formed by Pro295-Arg302 consistent with being a prime target for proteolysis, in agreement with the mutational data. These studies suggest that the hinge of MT1-MMP evolved to facilitate processing, a promiscuous but compulsory event in the destiny of MT1-MMP, which may play a key role in the control of pericellular proteolysis.

A novel RNA pentaloop fold involved in targeting ADAR2

Adenosine deaminases that act on RNA (ADARs) catalyze the site-specific conversion of adenosine to inosine in primary mRNA transcripts, thereby affecting coding potential of mature mRNAs. Structural determinants that define the adenosine moieties for specific ADARs-mediated deaminations are currently unknown. We report the solution structure of the central region of the human R/G stem-loop pre-mRNA, a natural ADAR2 substrate encoding the subunit B of the glutamate receptor (R/G site). The structure reveals that the GCU(A/C)A pentaloop that is conserved in mammals and birds adopts a novel fold. The fold is stabilized by a complex interplay of hydrogen bonds and stacking interactions. We propose that this new pentaloop structure is an important determinant of the R/G site recognition by ADAR2.

Computational Study of the Structure, Dynamics, and Photophysical Properties of Conjugated Polymers and Oligomers under Nanoscale Confinement

Computational simulations were used to investigate the dynamics and resulting structures of several para-phenylenevinylene (PPV) based polymers and oligomers (PPV, 2-methoxy-5-(2'-ethyl-hexyloxy)-p-phenylenevinylene --> MEH-PPV and 2,5,2',5'-tetrahexyloxy-7,8'-dicyano-p-phenylenevinylene --> CN-PPV). The results show how the morphology and structure are controlled to a large extent by the nature of the solute-solvent interactions in the initial solution-phase preparation. Secondary structural organization is induced by using the solution-phase structures to generate solvent-free single molecule nanoparticles. Isolation of these single molecule nanostructures from microdroplets of dilute solution results in the formation of electrostatically oriented nanostructures at a glass surface. Our structural modeling suggests that these oriented nanostructures consist of folded PPV conjugated segments with folds occurring at tetrahedral defects (sp3 C-C bonds) within the polymer chain. This picture is supported by detailed experimental fluorescence and scanning probe microscopy studies. We also present results from a fully quantum theoretical treatment of these systems which support the general conclusion of structure-mediated photophysical properties.

Incorporating variable dielectric environments into the generalized Born model

A generalized Born (GB) model is proposed that approximates the electrostatic part of macromolecular solvation free energy over the entire range of the solvent and solute dielectric constants. The model contains no fitting parameters, and is derived by matching a general form of the GB Green function with the exact Green's function of the Poisson equation for a random charge distribution inside a perfect sphere. The sphere is assumed to be filled uniformly with dielectric medium epsilon(in), and is surrounded by infinite solvent of constant dielectric epsilon(out). This model is as computationally efficient as the conventional GB model based on the widely used functional form due to Still et al. [J. Am. Chem. Soc. 112, 6127 (1990)], but captures the essential physics of the dielectric response for all values of epsilon(in) and epsilon(out). This model is tested against the exact solution on a perfect sphere, and against the numerical Poisson-Boltzmann (PB) treatment on a set of macromolecules representing various structural classes. It shows reasonable agreement with both the exact and the numerical solutions of the PB equation (where available) considered as reference, and is more accurate than the conventional GB model over the entire range of dielectric values.

Density Functional Theory of Solvation and Its Relation to Implicit Solvent Models

We describe a density functional theory approach to solvation in molecular solvents. The solvation free energy of a complex solute can be obtained by direct minimization of a density functional, instead of the thermodynamic integration scheme necessary when using atomistic simulations. In the homogeneous reference fluid approximation, the expression of the free-energy functional relies on the knowledge of the direct correlation function of the pure solvent. After discussing general molecular solvents, we present a generic density functional describing a dipolar solvent and we show how it can be reduced to the conventional implicit solvent models when the solvent microscopic structure is neglected. With respect to those models, the functional includes additional effects such as the microscopic structure of the solvent, the dipolar saturation effect, and the nonlocal character of the dielectric constant. We also show how this functional can be minimized numerically on a three-dimensional grid around a solute of complex shape to provide, in a single shot, both the average solvent structure and the absolute solvation free energy.

Peptide Mapping Identifies Hotspot Site of Modification in Human Serum Albumin by Methylglyoxal Involved in Ligand Binding and Esterase Activity

Methylglyoxal is a potent glycating agent under physiological conditions. Human serum albumin is modified by methylglyoxal in vivo. The glycation adducts formed and structural and functional changes induced by methylglyoxal modification have not been fully disclosed. Methylglyoxal reacted with human serum albumin under physiological conditions to form mainly the hydroimidazolone N(delta)-(5-hydro-5-methyl-4-imidazolon-2-yl)-ornithine (92% of total modification) with a minor formation of argpyrimidine, N(epsilon)-(1-carboxyethyl)lysine, and methylglyoxal lysine dimer. When human serum albumin was modified minimally with methylglyoxal, tryptic peptide mapping indicated a hotspot of modification at Arg-410 located in drug-binding site II and the active site of albumin-associated esterase activity. Modification of Arg-410 by methylglyoxal was found in albumin glycated in vivo. Other sites of minor modification were: Arg-114, Arg-186, Arg-218, and Arg-428. Hydroimidazolone formation at Arg-410 inhibited ketoprofen binding and esterase activity; correspondingly, glycation in the presence of ketoprofen inhibited Arg-410 modification and loss of esterase activity. The pH dependence of esterase activity indicated a catalytic group with pK(a) = 7.9 +/- 0.1, assigned to the catalytic base Tyr-411 with the conjugate base stabilized by interaction with the guanidinium group of Arg-410. Modification by methylglyoxal destabilized Tyr-411 and increased the pK(a) to 8.8 +/- 0.1. Molecular dynamics and modeling studies indicated that hydroimidazolone formation caused structural distortion leading to disruption of arginine-directed hydrogen bonding and loss of electrostatic interactions. Methylglyoxal modification of critical arginine residues, therefore, whether experimental or physiological, is expected to disrupt protein-ligand interactions and inactivate enzyme activity by hydroimidazolone formation.

Interplay of charge distribution and conformation in peptides: Comparison of theory and experiment

We assessed the correlation between charge distribution and conformation of flexible peptides by comparing the theoretically calculated potentiometric-titration curves of two model peptides, Ac-Lys5-NHMe (a model of poly-L-lysine) and Ac-Lys-Ala11-Lys-Gly2-Tyr-NH2 (P1) in water and methanol, with the experimental curves. The calculation procedure consisted of three steps: (i) global conformational search of the peptide under study using the electrostatically driven Monte Carlo (EDMC) method with the empirical conformational energy program for peptides (ECEPP)/3 force field plus the surface-hydration (SRFOPT) or the generalized Born surface area (GBSA) solvation model as well as a molecular dynamics method with the assisted model building and energy refinement (AMBER)99/GBSA force field; (ii) reevaluation of the energy in the pH range considered by using the modified Poisson-Boltzmann approach and taking into account all possible protonation microstates of each conformation, and (iii) calculation of the average degree of protonation of the peptide at a given pH value by Boltzmann averaging over conformations. For Ac-Lys5-NHMe, the computed titration curve agrees qualitatively with the experimental curve of poly-L-lysine in 95% methanol. The experimental titration curves of peptide P1 in water and methanol indicate a remarkable downshift of the first pK(a) value compared to the values for reference compounds (n-butylamine and phenol, respectively), suggesting the presence of a hydrogen bond between the tyrosine hydroxyl oxygen and the H(epsilon) proton of a protonated lysine side chain. The theoretical titration curves agree well with the experimental curves, if conformations with such hydrogen bonds constitute a significant part of the ensemble; otherwise, the theory predicts too small a downward pH shift.

Generation of native-like protein structures from limited NMR data, modern force fields and advanced conformational sampling

Determining an accurate initial native-like protein fold is one of the most important and time-consuming steps of de novo NMR structure determination. Here we demonstrate that high-quality native-like models can be rapidly generated from initial structures obtained using limited NOE assignments, through replica exchange molecular dynamics refinement with a generalized Born implicit solvent (REX/GB). Conventional structure calculations using an initial sparse NOE set were unable to identify a unique topology for the zinc-bound C-terminal domain of E. coli chaperone Hsp33, due to a lack of unambiguous long range NOEs. An accurate overall topology was eventually obtained through laborious hand identification of long range NOEs. However we were able to obtain high-quality models with backbone RMSD values of about 2 angstroms with respect to the final structures, using REX/GB refinement with the original limited set of initial NOE restraints. These models could then be used to make further assignments of ambiguous NOEs and thereby speed up the structure determination process. The ability to calculate accurate starting structures from the limited unambiguous NOE set available at the beginning of a structure calculation offers the potential of a much more rapid and automated process for NMR structure determination.

Peptide and protein folding and conformational equilibria: theoretical treatment of electrostatics and hydrogen bonding with implicit solvent models

Since biomolecules exist in aqueous and membrane environments, the accurate modeling of solvation, and hydrogen bonding interactions in particular, is essential for the exploration of structure and function in theoretical and computational studies. In this chapter, we focus on alternatives to explicit solvent models and discuss recent advances in generalized Born (GB) implicit solvent theories. We present a brief review of the successes and shortcomings of the application of these theories to biomolecular problems that are strongly linked to backbone H-bonding and electrostatics. This discussion naturally leads us to explore existing areas for improvement in current GB theories and our approach towards addressing a number of the key issues that remain in the refinement of these models. Specifically, the critical importance of balancing solvation forces and intramolecular forces in GB models is illustrated by examining the influence of backbone hydrogen bond strength and backbone dihedral energetics on conformational equilibria of small peptids.

Nonuniform charge scaling (NUCS): A practical approximation of solvent electrostatic screening in proteins

In molecular mechanics calculations, electrostatic interactions between chemical groups are usually represented by a Coulomb potential between the partial atomic charges of the groups. In aqueous solution these interactions are modified by the polarizable solvent. Although the electrostatic effects of the polarized solvent on the protein are well described by the Poisson--Boltzmann equation, its numerical solution is computationally expensive for large molecules such as proteins. The procedure of nonuniform charge scaling (NUCS) is a pragmatic approach to implicit solvation that approximates the solvent screening effect by individually scaling the partial charges on the explicit atoms of the macromolecule so as to reproduce electrostatic interaction energies obtained from an initial Poisson--Boltzmann analysis. Once the screening factors have been determined for a protein the scaled charges can be easily used in any molecular mechanics program that implements a Coulomb term. The approach is particularly suitable for minimization-based simulations, such as normal mode analysis, certain conformational reaction path or ligand binding techniques for which bulk solvent cannot be included explicitly, and for combined quantum mechanical/molecular mechanical calculations when the interface to more elaborate continuum solvent models is lacking. The method is illustrated using reaction path calculations of the Tyr 35 ring flip in the bovine pancreatic trypsin inhibitor.

A critical role for Gly25 in the B chain of human thrombin

We have recently identified (Akhavan S et al., Thromb Haemost 2000; 84: 989-97) a patient with a mild bleeding diathesis associated to an homozygous mutation in the thrombin B chain (Gly25Ser, chymotrypsinogen numbering, i.e. position 330 in human prothrombin numbering). Transient transfection of wild-type prothrombin (FII-WT) and mutant prothrombin (designated FII-G25(330)S) cDNA in COS-7 cells showed a mild reduction (50%) in FII-G25(330)S production. Recombinant proteins, stably expressed in Chinese hamster ovary cells, were isolated and activated by Taipan snake or Echis carinatus venoms. We show that the G25(330)S mutation results in a decrease in the rate of prothrombin proteolytic activation. The mutation also significantly decreases (i) the catalytic activity of thrombin with a 9-fold reduction in catalytic efficiency of the mutant toward S-2238; (ii) the interaction with benzamidine; (iii) the rate of inhibition by TLCK and antithrombin; and (iv) the rate of hydrolysis of macromolecular substrates (fibrinogen, protein C). In contrast, exosite I does not appear to be affected by the molecular defect. These results, together with molecular modeling and dynamics, indicate that Gly25(330) is important for proper expression and probably proper folding of prothrombin, and also plays a critical role in both the alignment of the catalytic triad and the flexibility of one of the activation segments of prothrombin.

Computational protein design is a challenge for implicit solvation models

Increasingly complex schemes for representing solvent effects in an implicit fashion are being used in computational analyses of biological macromolecules. These schemes speed up the calculations by orders of magnitude and are assumed to compromise little on essential features of the solvation phenomenon. In this work we examine this assumption. Five implicit solvation models, a surface area-based empirical model, two models that approximate the generalized Born treatment and a finite difference Poisson-Boltzmann method are challenged in situations differing from those where these models were calibrated. These situations are encountered in automatic protein design procedures, whose job is to select sequences, which stabilize a given protein 3D structure, from a large number of alternatives. To this end we evaluate the energetic cost of burying amino acids in thousands of environments with different solvent exposures belonging, respectively, to decoys built with random sequences and to native protein crystal structures. In addition we perform actual sequence design calculations. Except for the crudest surface area-based procedure, all the tested models tend to favor the burial of polar amino acids in the protein interior over nonpolar ones, a behavior that leads to poor performance in protein design calculations. We show, on the other hand, that three of the examined models are nonetheless capable of discriminating between the native fold and many nonnative alternatives, a test commonly used to validate force fields. It is concluded that protein design is a particularly challenging test for implicit solvation models because it requires accurate estimates of the solvation contribution of individual residues. This contrasts with native recognition, which depends less on solvation and more on other nonbonded contributions.

Conformation of glycosaminoglycans by ion mobility mass spectrometry and molecular modelling

We have performed conformational analyses of heparin-derived oligosaccharide ions in the gas phase using a combination of ion-mobility mass spectrometry and molecular modelling. Negative mode electrospray ionisation was used to generate singly (disaccharide, [C12H15NO19S3Na3]-) and doubly charged (tetrasaccharides, [C24H30N2O38S6Na6]2- and [C24H31N2O35S5Na5]2-) ions containing three and six Na+ ions, respectively. Good agreement was obtained between the experimental and theoretical cross sections. The latter were obtained using modelled structures generated by the AMBER-based force field. Analysis of the conformations of the oligosaccharide ions shows that sodium cations play a major role in stabilizing these ions in the gas phase. This was seen in the formation of oligomers of the disaccharide ion and "compact" structures of tetrasaccharide ions. Interestingly, the gas phase conformations of the three tetrasaccharide ions with different primary structures were significantly different.

Constant pH molecular dynamics in generalized Born implicit solvent

A new method is proposed for constant pH molecular dynamics (MD), employing generalized Born (GB) electrostatics. Protonation states are modeled with different charge sets, and titrating residues sample a Boltzmann distribution of protonation states as the simulation progresses, using Monte Carlo sampling based on GB-derived energies. The method is applied to four different crystal structures of hen egg-white lysozyme (HEWL). pK(a) predictions derived from the simulations have root-mean-square (RMS) error of 0.82 relative to experimental values. Similarity of results between the four crystal structures shows the method to be independent of starting crystal structure; this is in contrast to most electrostatics-only models. A strong correlation between conformation and protonation state is noted and quantitatively analyzed, emphasizing the importance of sampling protonation states in conjunction with dynamics.

Prediction of pKa shifts in proteins using a combination of molecular mechanical and continuum solvent calculations

The prediction of pKa shifts of ionizable groups in proteins is of great relevance for a number of important biological phenomena. We present an implementation of the MM-GBSA approach, which combines molecular mechanical (MM) and generalized Born (GB) continuum solvent energy terms, to the calculation of pKa values of a panel of nine proteins, including 69 individual comparisons with experiment. While applied so far mainly to the calculation of biomolecular binding free energies, we show that this method can also be used for the estimation of protein pKa shifts, with an accuracy around 1 pKa unit, even for strongly shifted residues. Our analysis reveals that the nonelectrostatic terms that are part of the MM-GBSA free energy expression are important contributors to improved prediction accuracy. This suggests that most of the previous approaches that focus only on electrostatic interactions could be improved by adding other nonpolar energy terms to their free energy expression. Interestingly, our method yields best accuracy at protein dielectric constants of epsilonint = 2-4, which is in contrast to previous approaches that peak at higher epsilonint > or = 8. An important component of our procedure is an intermediate minimization step of each protonation state involving different rotamers and tautomers as a way to explicitly model protein relaxation upon (de)protonation.

Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method

A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment).

Lysozyme FoldedIn SilicoAccording to the Limited Conformational Sub-space

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.

Stabilization of internal charges in a protein: water penetration or conformational change?

The ionizable amino acid side chains of proteins are usually located at the surface. However, in some proteins an ionizable group is embedded in an apolar internal region. Such buried ionizable groups destabilize the protein and may trigger conformational changes in response to pH variations. Because of the prohibitive energetic cost of transferring a charged group from water to an apolar medium, other stabilizing factors must be invoked, such as ionization-induced water penetration or structural changes. To examine the role of water penetration, we have measured the 17O and 2H magnetic relaxation dispersions (MRD) for the V66E and V66K mutants of staphylococcal nuclease, where glutamic acid and lysine residues are buried in predominantly apolar environments. At neutral pH, where these residues are uncharged, we find no evidence of buried water molecules near the mutation site. This contrasts with a previous cryogenic crystal structure of the V66E mutant, but is consistent with the room-temperature crystal structure reported here. MRD measurements at different pH values show that ionization of Glu-66 or Lys-66 is not accompanied by penetration of long-lived water molecules. On the other hand, the MRD data are consistent with a local conformational change in response to ionization of the internal residues.

Solvation forces on biomolecular structures: a comparison of explicit solvent and Poisson-Boltzmann models

Continuum electrostatics methods have become increasingly popular due to their ability to provide approximate descriptions of solvation energies and forces without expensive sampling required by explicit solvent models. In particular, the Poisson-Boltzmann equation (PBE) provides electrostatic potentials, solvation energies, and forces by modeling the solvent as a featureless, dielectric material, and the mobile ions as a continuous distribution of charge. Polar solvation forces and energies obtained from the PBE are often supplemented with simple solvent-accessible surface area (SASA) models of nonpolar solvation. Given the recent development of methods that enable the use of PBE and SASA forces in molecular dynamics simulations, it is important to determine the ability of these implicit solvent models to accurately reproduce the solvation forces of more detailed explicit solvent simulations. In this article, we compare PBE and SASA solvation forces with explicit solvent forces for several snapshots from eight trajectories of static conformations of intestinal fatty acid binding protein. The results from this comparison show that current implementations of the PBE are capable of generating polar solvation forces that correlate well with explicit solvent forces but systematically overestimate the magnitude of the interaction. However, SASA-based nonpolar forces are found to have no significant correlation with nonpolar explicit solvent forces. Nevertheless, due to the small magnitude of the nonpolar forces in the current system, a good correlation is still obtained for total solvation forces. The good correlation of implicit solvent forces with more detailed explicit solvent models is encouraging and implies that the systematic errors identified in these models could be corrected by appropriate parameterization of the force fields.

Theoretical and experimental study of the D2194G mutation in the C2 domain of coagulation factor V

Coagulation factor V (FV) is a large plasma glycoprotein with functions in both the pro- and anticoagulant pathways. In carriers of the so-called R2-FV haplotype, the FV D2194G mutation, in the C2 membrane-binding domain, is associated with low expression levels, suggesting a potential folding/stability problem. To analyze the molecular mechanisms potentially responsible for this in vitro phenotype, we used molecular dynamics (MD) and continuum electrostatic calculations. Implicit solvent simulations were performed on the x-ray structure of the wild-type C2 domain and on a model of the D2194G mutant. Because D2194 is located next to a disulfide bond (S-S bond), MD calculations were also performed on S-S bond depleted structures. D2194 is part of a salt-bridge network and investigations of the stabilizing/destabilizing role of these ionic interactions were carried out. Five mutant FV molecules were created and the expression levels measured with the aim of assessing the tolerance to amino acid changes in this region of molecule. Analysis of the MD trajectories indicated increased flexibility in some areas and energetic comparisons suggested overall destabilization of the structure due to the D2194G mutation. This substitution causes electrostatic destabilization of the domain by approximately 3 kcal/mol. Together these effects likely explain the lowered expression levels in R2-FV carriers.

Exploring protein native states and large-scale conformational changes with a modified generalized born model

Implicit solvation models provide, for many applications, a reasonably accurate and computationally effective way to describe the electrostatics of aqueous solvation. Here, a popular analytical Generalized Born (GB) solvation model is modified to improve its accuracy in calculating the solvent polarization part of free energy changes in large-scale conformational transitions, such as protein folding. In contrast to an earlier GB model (implemented in the AMBER-6 program), the improved version does not overstabilize the native structures relative to the finite-difference Poisson-Boltzmann continuum treatment. In addition to improving the energy balance between folded and unfolded conformers, the algorithm (available in the AMBER-7 and NAB molecular modeling packages) is shown to perform well in more than 50 ns of native-state molecular dynamics (MD) simulations of thioredoxin, protein-A, and ubiquitin, as well as in a simulation of Barnase/Barstar complex formation. For thioredoxin, various combinations of input parameters have been explored, such as the underlying gas-phase force fields and the atomic radii. The best performance is achieved with a previously proposed modification to the torsional potential in the Amber ff99 force field, which yields stable native trajectories for all of the tested proteins, with backbone root-mean-square deviations from the native structures being approximately 1.5 A after 6 ns of simulation time. The structure of Barnase/Barstar complex is regenerated, starting from an unbound state, to within 1.9 A relative to the crystal structure of the complex.

Structure-based design of inhibitors of NS3 serine protease of hepatitis C virus

We have designed small focused combinatorial library of hexapeptide inhibitors of NS3 serine protease of the hepatitis C virus (HCV) by structure-based molecular design complemented by combinatorial optimisation of the individual residues. Rational residue substitutions were guided by the structure and properties of the binding pockets of the enzyme's active site. The inhibitors were derived from peptides known to inhibit the NS3 serine protease by using unusual amino acids and alpha-ketocysteine or difluoroaminobutyric acid, which are known to bind to the S1 pocket of the catalytic site. Inhibition constants (Ki) of the designed library of inhibitors were predicted from a QSAR model that correlated experimental Ki of known peptidic inhibitors of NS3 with the enthalpies of enzyme-inhibitor interaction computed via molecular mechanics and the solvent effect contribution to the binding affinity derived from the continuum model of solvation. The library of the optimised inhibitors contains promising drug candidates-water-soluble anionic hexapeptides with predicted Ki* in the picomolar range.

A semi-implicit solvent model for the simulation of peptides and proteins

We present a new model of biomolecules hydration based on macroscopic electrostatic theory, that can both describe the microscopic details of solvent-solute interactions and allow for an efficient evaluation of the electrostatic hydration free energy. This semi-implicit model considers the solvent as an ensemble of polarizable pseudoparticles whose induced dipole describe both the electronic and orientational solvent polarization. In the presented version of the model, there is no mutual dipolar interaction between the particles, and they only interact through short-ranged Lennard-Jones interactions. The model has been integrated into a molecular dynamics code, and offers the possibility to simulate efficiently the conformational evolution of biomolecules. It is able to provide estimations of the electrostatic solvation free energy within short time windows during the simulation. It has been applied to the study of two small peptides, the octaalanine and the N-terminal helix of ribonuclease A, and two proteins, the bovine pancreatic trypsin inhibitor and the B1 immunoglobin-binding domain of streptococcal protein G. Molecular dynamics simulations of these biomolecules, using a slightly modified Amber force field, provide stable and meaningful trajectories in overall agreement with experiments and all-atom simulations. Correlations with respect to Poisson-Boltzmann electrostatic solvation free energies are also presented to discuss the parameterization of the model and its consequences.

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.

Free energy surfaces of β-hairpin and α-helical peptides generated by replica exchange molecular dynamics with the AGBNP implicit solvent model

We have studied the potential of mean force of two peptides, one known to adopt a beta-hairpin and the other an alpha-helical conformation in solution. These peptides are, respectively, residues 41-56 of the C-terminus (GEWTYDDATKTFTVTE) of the B1 domain of protein G and the 13 residue C-peptide (KETAAAKFERQHM) of ribonuclease A. Extensive canonical ensemble sampling has been performed using a parallel replica exchange method. The effective potential employed in this work consists of the OPLS all-atom force field (OPLS-AA) and an analytical generalized Born (AGB) implicit solvent model including a novel nonpolar solvation free energy estimator (NP). An additional dielectric screening parameter has been incorporated into the AGBNP model. In the case of the beta-hairpin, the nonpolar solvation free energy estimator provides the necessary effective interactions for the collapse of the hydrophobic core (W43, Y45, F52, and V54), which the more commonly used surface-area-dependent nonpolar model does not provide. For both the beta-hairpin and the alpha-helix, increased dielectric screening reduces the stability of incorrectly formed salt bridges, which tend to disrupt the formation of the hairpin and helix, respectively. The fraction of beta-hairpin and alpha-helix content we obtained using the AGBNP model agrees well with experimental results. The thermodynamic stability of the beta-hairpin from protein G and the alpha-helical C-peptide from ribonuclease A as modeled with the OPLS-AA/AGBNP effective potential reflects the balance between the nonpolar effective potential terms, which drive compaction, and the polar and hydrogen bonding terms, which promote secondary structure formation.

MMTSB Tool Set: enhanced sampling and multiscale modeling methods for applications in structural biology

We describe the Multiscale Modeling Tools for Structural Biology (MMTSB) Tool Set (https://mmtsb.scripps.edu/software/mmtsbToolSet.html), which is a novel set of utilities and programming libraries that provide new enhanced sampling and multiscale modeling techniques for the simulation of proteins and nucleic acids. The tool set interfaces with the existing molecular modeling packages CHARMM and Amber for classical all-atom simulations, and with MONSSTER for lattice-based low-resolution conformational sampling. In addition, it adds new functionality for the integration and translation between both levels of detail. The replica exchange method is implemented to allow enhanced sampling of both the all-atom and low-resolution models. The tool set aims at applications in structural biology that involve protein or nucleic acid structure prediction, refinement, and/or extended conformational sampling. With structure prediction applications in mind, the tool set also implements a facility that allows the control and application of modeling tasks on a large set of conformations in what we have termed ensemble computing. Ensemble computing encompasses loosely coupled, parallel computation on high-end parallel computers, clustered computational grids and desktop grid environments. This paper describes the design and implementation of the MMTSB Tool Set and illustrates its utility with three typical examples--scoring of a set of predicted protein conformations in order to identify the most native-like structures, ab initio folding of peptides in implicit solvent with the replica exchange method, and the prediction of a missing fragment in a larger protein structure.

Solution structure of the ubiquitin-binding domain in Swa2p from Saccharomyces cerevisiae

The SWA2/AUX1 gene has been proposed to encode the Saccharomyces cerevisiae ortholog of mammalian auxilin. Swa2p is required for clathrin assembly/dissassembly in vivo, thereby implicating it in intracellular protein and lipid trafficking. While investigating the 287-residue N-terminal region of Swa2p, we found a single stably folded domain between residues 140 and 180. Using binding assays and structural analysis, we established this to be a ubiquitin-associated (UBA) domain, unidentified by bioinformatics of the yeast genome. We determined the solution structure of this Swa2p domain and found a characteristic three-helix UBA fold. Comparisons of structures of known UBA folds reveal that the position of the third helix is quite variable. This helix in Swa2p UBA contains a bulkier tyrosine in place of smaller residues found in other UBAs and cannot pack as close to the second helix. The molecular surface of Swa2p UBA has a mostly negative potential, with a single hydrophobic surface patch found also in the UBA domains of human protein, HHR23A. The presence of a UBA domain implicates Swa2p in novel roles involving ubiquitin and ubiquitinated substrates. We propose that Swa2p is a multifunctional protein capable of recognizing several proteins through its protein-protein recognition domains.

Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures

This study compares generalized Born (GB) and Poisson (PB) methods for calculating electrostatic solvation energies of proteins. A large set of GB and PB implementations from our own laboratories as well as others is applied to a series of protein structure test sets for evaluating the performance of these methods. The test sets cover a significant range of native protein structures of varying size, fold topology, and amino acid composition as well as nonnative extended and misfolded structures that may be found during structure prediction and folding/unfolding studies. We find that the methods tested here span a wide range from highly accurate and computationally demanding PB-based methods to somewhat less accurate but more affordable GB-based approaches and a few fast, approximate PB solvers. Compared with PB solvation energies, the latest, most accurate GB implementations were found to achieve errors of 1% for relative solvation energies between different proteins and 0.4% between different conformations of the same protein. This compares to accurate PB solvers that produce results with deviations of less than 0.25% between each other for both native and nonnative structures. The performance of the best GB methods is discussed in more detail for the application for force field-based minimizations or molecular dynamics simulations.

AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling

We have developed an implicit solvent effective potential (AGBNP) that is suitable for molecular dynamics simulations and high-resolution modeling. It is based on a novel implementation of the pairwise descreening Generalized Born model for the electrostatic component and a new nonpolar hydration free energy estimator. The nonpolar term consists of an estimator for the solute-solvent van der Waals dispersion energy designed to mimic the continuum solvent solute-solvent van der Waals interaction energy, in addition to a surface area term corresponding to the work of cavity formation. AGBNP makes use of a new parameter-free algorithm to calculate the scaling coefficients used in the pairwise descreening scheme to take into account atomic overlaps. The same algorithm is also used to calculate atomic surface areas. We show that excellent agreement is achieved for the GB self-energies and surface areas in comparison to accurate, but much more expensive, numerical evaluations. The parameter-free approach used in AGBNP and the sensitivity of the AGBNP model with respect to large and small conformational changes makes the model suitable for high-resolution modeling of protein loops and receptor sites as well as high-resolution prediction of the structure and thermodynamics of protein-ligand complexes. We present illustrative results for these kinds of benchmarks. The model is fully analytical with first derivatives and is computationally efficient. It has been incorporated into the IMPACT molecular simulation program.

Efficient evaluation of the effective dielectric function of a macromolecule in aqueous solution

We propose an analytical approach to calculate the effective dielectric function of proteins in aqueous solution. The screening effect if quantified by a measure of enclosure which is based on the distribution of solute atomic volumes around a pair of charges in a macromolecule. For protein conformations that vary significantly in size and shape, a comparison with finite difference Poisson calculations shows that pair interaction energies, their sums and solvation energies are well reproduced. The approach rivals the speed of simple distance dependent dielectric functions and the accuracy of the generalized Born model.

Proton Binding to Proteins: pKa Calculations with Explicit and Implicit Solvent Models

Ionizable residues play important roles in protein structure and activity, and proton binding is a valuable reporter of electrostatic interactions in these systems. We use molecular dynamics free energy simulations (MDFE) to compute proton pKa shifts, relative to a model compound in solution, for three aspartate side chains in two proteins. Simulations with explicit solvent and with an implicit, dielectric continuum solvent are reported. The implicit solvent simulations use the generalized Born (GB) model, which provides an approximate, analytical solution to Poisson's equation. With explicit solvent, the direction of the pKa shifts is correct in all three cases with one force field (AMBER) and in two out of three cases with another (CHARMM). For two aspartates, the dielectric response to ionization is found to be linear, even though the separate protein and solvent responses can be nonlinear. For thioredoxin Asp26, nonlinearity arises from the presence of two substates that correspond to the two possible orientations of the protonated carboxylate. For this side chain, which is partly buried and has a large pKa upshift, very long simulations are needed to correctly sample several slow degrees of freedom that reorganize in response to the ionization. Thus, nearby Lys57 rotates to form a salt bridge and becomes buried, while three waters intercalate along the opposite edge of Asp26. Such strong and anisotropic reorganization is very difficult to predict with Poisson-Boltzmann methods that only consider electrostatic interactions and employ a single protein structure. In contrast, MDFE with a GB dielectric continuum solvent, used for the first time for pKa calculations, can describe protein reorganization accurately and gives encouraging agreement with experiment and with the explicit solvent simulations.

Integrating folding kinetics and protein function: biphasic kinetics and dual binding specificity in a WW domain

Because of the association of beta-sheet formation with the initiation and propagation of amyloid diseases, model systems have been sought to further our understanding of this process. WW domains have been proposed as one such model system. Whereas the folding of the WW domains from human Yes-associated protein (YAP) and Pin have been shown to obey single-exponential kinetics, the folding of the WW domain from formin-binding protein (FBP) 28 has been shown to proceed via biphasic kinetics. From an analysis of free-energy landscapes from atomic-level molecular dynamics simulations, the biphasic folding kinetics observed in the FBP WW domain may be traced to the ability of this WW domain to adopt two slightly different forms of packing in its hydrophobic core. This conformational change is propagated along the peptide backbone and affects the position of a tryptophan residue shown in other WW domains to play a key role in binding. The WW domains of Pin and YAP do not support more than one type of packing each, leading to monophasic folding kinetics. The ability of the FBP WW domain to assume two different types of packing may, in turn, explain the capacity of this WW domain to bind two classes of ligand, a property that is not shared by other WW domains. These findings lead to the hypothesis that lability with respect to conformations separated by an observable barrier as a requirement for function is incompatible with the ability of a protein to fold via single-exponential kinetics.

Designing human m1 muscarinic receptor-targeted hydrophobic eigenmode matched peptides as functional modulators

A new proprietary de novo peptide design technique generated ten 15-residue peptides targeting and containing the leading nontransmembrane hydrophobic autocorrelation wavelengths, "modes", of the human m(1) muscarinic cholinergic receptor, m(1)AChR. These modes were also shared by the m(4)AChR subtype (but not the m(2), m(3), or m(5) subtypes) and the three-finger snake toxins that pseudoirreversibly bind m(1)AChR. The linear decomposition of the hydrophobically transformed m(1)AChR amino acid sequence yielded ordered eigenvectors of orthogonal hydrophobic variational patterns. The weighted sum of two eigenvectors formed the peptide design template. Amino acids were iteratively assigned to template positions randomly, within hydrophobic groups. One peptide demonstrated significant functional indirect agonist activity, and five produced significant positive allosteric modulation of atropine-reversible, direct-agonist-induced cellular activation in stably m(1)AChR-transfected Chinese hamster ovary cells, reflected in integrated extracellular acidification responses. The peptide positive allosteric ligands produced left-shifts and peptide concentration-response augmentation in integrated extracellular acidification response asymptotic sigmoidal functions and concentration-response behavior in Hill number indices of positive cooperativity. Peptide mode specificity was suggested by negative crossover experiments with human m(2)ACh and D(2) dopamine receptors. Morlet wavelet transformation of the leading eigenvector-derived, m(1)AChR eigenfunctions locates seven hydrophobic transmembrane segments and suggests possible extracellular loop locations for the peptide-receptor mode-matched, modulatory hydrophobic aggregation sites.

Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation

An efficient concerted rotation algorithm for use in Monte Carlo statistical mechanics simulations is applied to fold three polypeptides, U(1-17)T9D, alpha(1), and trpzip2, which exhibit native beta-hairpin and alpha-helix folds. The method includes flexible bond and dihedral angles, and a Gaussian bias is applied with driver bond and dihedral angles to optimize the sampling efficiency. Solvation in water is implemented with the generalized Born (GBSA) model. The computed lowest-energy manifolds for the folded structures of the two beta-hairpins agree closely with the corresponding NMR structures. In the case of the alpha(1) peptide, the folded alpha-helical state, which is observed as oligomers in concentrated solution and crystals, is not stable in isolation. The computed preference for random coil structures is in agreement with NMR experiments at low concentration. The fact that native states can be located on high dimensional energy surfaces starting from extended conformations shows that the present methodology samples all relevant parts of the conformational space. The OPLS-AA force field with the GBSA solvent model was also found to perform well in leading to clear energetic separation of the correctly folded structures from misfolded structures for the two peptides that form beta-turns.