A molecular dynamics simulation study of segment B1 of protein G

How adding a single methylene to dihydrofolate reductase can change its conformational dynamics

Studies of the effects of pressure on proteins from piezophilic (pressure-loving) microbes compared with homologous proteins from mesophilic microbes have been relatively rare. Interestingly, such studies of dihydrofolate reductase show that a single-site mutation from an aspartic acid to a glutamic acid can reverse the pressure-dependent monotonic decrease in activity to that in a monotonic pressure-dependent activation. This residue is near the active site but is not thought to directly participate in the catalytic mechanism. Here, the ways that addition of one carbon to the entire protein could lead to such a profound difference in pressure effects are explored using molecular dynamics simulations. The results indicate that the glutamate changes the coupling between a helix and the β-sheet due to the extra flexibility of the side chain, which further changes correlated motions of other regions of the protein.

Structural and molecular analyses of functional epitopes and escape mutants in Japanese encephalitis virus envelope protein domain III

The Japanese encephalitis virus (JEV) is one of the vector borne causes of encephalitis found in southeastern Asia. This positive single-stranded RNA virus is a member of the Flaviviridae family, which notably includes dengue, tick-borne, West Nile, Zika as well as yellow fever, and transmits to humans by infected mosquitos. The main site of interactions for antibodies against this virus is the envelope protein domain III (ED3). The present report investigates the time-dependent structural and conformational changes of JEV ED3 functional epitopes and escape mutants by computer simulations. The results indicate the presence of significant structural differences between the functional epitopes and the escape mutants. Mutation-induced structural/conformational instabilities of this type can decrease the antibody neutralization activity. Among the different escape mutants studied here, Ser40Lys/Asp41Arg appear to be most unstable, while Ser40Glu/Asp41Leu exhibit the lowest structural variations. The highest level of escape mutation observed in Ser40Lys is linked to the relatively higher values of root mean square deviation/fluctuation found in the molecular dynamics simulation of this protein. Secondary-structure deviations and depletion of H bonding are other contributing factors to the protein’s increased instability. Overall, the proteins with residue 41 mutations are found to be structurally more ordered than those with residue 40 mutations. The detailed time-based structural assessment of the mutant epitopes described here may contribute to the development of novel vaccines and antiviral drugs necessary to defend against future outbreaks of JEV escape mutants.

An investigation into non-covalent functionalization of a single-walled carbon nanotube and a graphene sheet with protein G:A combined experimental and molecular dynamics study

Investigation of non-covalent interaction of hydrophobic surfaces with the protein G (PrG) is necessary due to their frequent utilization in immunosensors and ELISA. It has been confirmed that surfaces, including carbonous-nanostructures (CNS) could orient proteins for a better activation. Herein, PrG interaction with single-walled carbon nanotube (SWCNT) and graphene (Gra) nanostructures was studied by employing experimental and MD simulation techniques. It is confirmed that the PrG could adequately interact with both SWCNT and Gra and therefore fine dispersion for them was achieved in the media. Results indicated that even though SWCNT was loaded with more content of PrG in comparison with the Gra, the adsorption of the PrG on Gra did not induce significant changes in the IgG tendency. Several orientations of the PrG were adopted in the presence of SWCNT or Gra; however, SWCNT could block the PrG-FcR. Moreover, it was confirmed that SWCNT reduced the α-helical structure content in the PrG. Reduction of α-helical structure of the PrG and improper orientation of the PrG-SWCNT could remarkably decrease the PrG tendency to the Fc of the IgG. Importantly, the Gra could appropriately orient the PrG by both exposing the PrG-FcR and also by blocking the fragment of the PrG that had tendency to interact with Fab in IgG.

Predicting the orientation of protein G B1 on hydrophobic surfaces using Monte Carlo simulations

A Monte Carlo algorithm was developed to predict the most likely orientations of protein G B1, an immunoglobulin G (IgG) antibody-binding domain of protein G, adsorbed onto a hydrophobic surface. At each Monte Carlo step, the protein was rotated and translated as a rigid body. The assumption about rigidity was supported by quartz crystal microbalance with dissipation monitoring experiments, which indicated that protein G B1 adsorbed on a polystyrene surface with its native structure conserved and showed that its IgG antibody-binding activity was retained. The Monte Carlo simulations predicted that protein G B1 is likely adsorbed onto a hydrophobic surface in two different orientations, characterized as two mutually exclusive sets of amino acids contacting the surface. This was consistent with sum frequency generation (SFG) vibrational spectroscopy results. In fact, theoretical SFG spectra calculated from an equal combination of the two predicted orientations exhibited reasonable agreement with measured spectra of protein G B1 on polystyrene surfaces. Also, in explicit solvent molecular dynamics simulations, protein G B1 maintained its predicted orientation in three out of four runs. This work shows that using a Monte Carlo approach can provide an accurate estimate of a protein orientation on a hydrophobic surface, which complements experimental surface analysis techniques and provides an initial system to study the interaction between a protein and a surface in molecular dynamics simulations.

Multiscale simulations of protein G B1 adsorbed on charged self-assembled monolayers

The orientation of an antibody plays an important role in the development of immunosensors. Protein G is an antibody binding protein, which specifically targets the Fc fragment of an antibody. In this work, the orientation of prototypical and mutated protein G B1 adsorbed on positively and negatively charged self-assembled monolayers was studied by parallel tempering Monte Carlo and all-atom molecular dynamics simulations. Both methods present generally similar orientation distributions of protein G B1 for each kind of surface. The root-mean-square deviation, DSSP, gyration radius, eccentricity, dipole moment, and superimposed structures of protein G B1 were analyzed. Moreover, the orientation of binding antibody was also predicted in this work. Simulation results show that with the same orientation trends, the mutant exhibits narrower orientation distributions than does the prototype, which was mainly caused by the stronger dipole of the mutant. Both kinds of proteins adsorbed on charged surfaces were induced by the competition of electrostatic interaction and vdW interaction; the electrostatic interaction energy dominated the adsorption behavior. The protein adsorption was also largely affected by the distribution of charged residues within the proteins. Thus, the prototype could adsorb on a negatively charged surface, although it keeps a net charge of -4 e. The mutant has imperfect opposite orientation when it adsorbed on oppositely charged surfaces. For the mutant on a carboxyl-functionalized self-assembled monolayer (COOH-SAM), the orientation was the same as that inferred by experiments. While for the mutant on amine-functionalized self-assembled monolayer (NH2-SAM), the orientation was induced by the competition between attractive interactions (led by ASP40 and GLU56) and repulsive interactions (led by LYS10); thus, the perfect opposite orientation could not be obtained. On both surfaces, the adsorbed protein could retain its native conformation. The desired orientation of protein G B1, which would increase the efficiency of binding antibodies, could be obtained on a negatively charged surface adsorbed with the prototype. Further, we deduced that with the packing density of 12,076 protein G B1 domain per μm(2), the efficiency of the binding IgG would be maximized. The simulation results could be applied to control the orientation of protein G B1 in experiments and to provide a better understanding to maximize the efficiency of antibody binding.

GB1 is not a two-state folder: identification and characterization of an on-pathway intermediate

The folding pathway of the small α/β protein GB1 has been extensively studied during the past two decades using both theoretical and experimental approaches. These studies provided a consensus view that the protein folds in a two-state manner. Here, we reassessed the folding of GB1, both by experiments and simulations, and detected the presence of an on-pathway intermediate. This intermediate has eluded earlier experimental characterization and is distinct from the collapsed state previously identified using ultrarapid mixing. Failure to identify the presence of an intermediate affects some of the conclusions that have been drawn for GB1, a popular model for protein folding studies.

beta-hairpin-forming peptides; models of early stages of protein folding

Formation of beta-hairpins is considered the initial step of folding of many proteins and, consequently, peptides constituting the beta-hairpin sequence of proteins (the beta-hairpin-forming peptides) are considered as models of early stages of protein folding. In this article, we discuss the results of experimental studies (circular-dichroism, infrared and nuclear magnetic resonance spectroscopy, and differential scanning calorimetry) of the structure of beta-hairpin-forming peptides excised from the B1 domain of protein G, which are known to fold on their own. We demonstrate that local interactions at the turn sequence and hydrophobic interactions between nonpolar residues are the dominant structure-determining factors, while there is no convincing evidence that stable backbone hydrogen bonds are formed in these peptides in aqueous solution. Consequently, the most plausible mechanism for folding of the beta-hairpin sequence appears to be the broken-zipper mechanism consisting of the following three steps: (i) bending the chain at the turn sequence owing to favorable local interactions, (ii) formation of loose hydrophobic contacts between nonpolar residues, which occur close to the contacts in the native structure of the protein but not exactly in the same position and, finally, (iii) formation of backbone hydrogen bonds and locking the hydrophobic contacts in the native positions as a hydrophobic core develops, sufficient to dehydrate the backbone peptide groups. This mechanism provides sufficient uniqueness (contacts form between residues that become close together because the chain is bent at the turn position) and robustness (contacts need not occur at once in the native positions) for folding a beta-hairpin sequence.

Three-dimensional molecular theory of solvation coupled with molecular dynamics in Amber

We present the three-dimensional molecular theory of solvation (also known as 3D-RISM) coupled with molecular dynamics (MD) simulation by contracting solvent degrees of freedom, accelerated by extrapolating solvent-induced forces and applying them in large multi-time steps (up to 20 fs) to enable simulation of large biomolecules. The method has been implemented in the Amber molecular modeling package, and is illustrated here on alanine dipeptide and protein G.

Procrustean rotation in concert with principal component analysis of molecular dynamics trajectories: Quantifying global and local differences between conformational samples

Given the principal component analysis (PCA) of a molecular dynamics (MD) conformational trajectory for a model protein, we perform orthogonal Procrustean rotation to "best fit" the PCA squared-loading matrix to that of a target matrix computed for a related but different molecular system. The sum of squared deviations of the elements of the rotated matrix from those of the target, known as the error of fit (EOF), provides a quantitative measure of the dissimilarity between the two conformational samples. To estimate precision of the EOF, we perform bootstrap resampling of the molecular conformations within the trajectories, generating a distribution of EOF values for the system and target. The average EOF per variable is determined and visualized to ascertain where, locally, system and target sample properties differ. We illustrate this approach by analyzing MD trajectories for the wild-type and four selected mutants of the beta1 domain of protein G.

Simulation of NMR data reveals that proteins' local structures are stabilized by electronic polarization

Molecular dynamics simulations of NMR backbone relaxation order parameters have been carried out to investigate the polarization effect on the protein's local structure and dynamics for five benchmark proteins (bovine pancreatic trypsin inhibitor, immunoglobulin-binding domain (B1) of streptococcal protein G, bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and hen egg white lysozyme). In order to isolate the polarization effect from other interaction effects, our study employed both the standard AMBER force field (AMBER03) and polarized protein-specific charges (PPCs) in the MD simulations. The simulated order parameters, employing both the standard nonpolarizable and polarized force fields, are directly compared with experimental data. Our results show that residue-specific order parameters at some specific loop and turn regions are significantly underestimated by the MD simulations using the standard AMBER force field, indicating hyperflexibility of these local structures. Detailed analysis of the structures and dynamic motions of individual residues reveals that the hyperflexibility of these local structures is largely related to the breaking or weakening of relevant hydrogen bonds. In contrast, the agreement with the experimental results is significantly improved and more stable local structures are observed in the MD simulations using the polarized force field. The comparison between theory and experiment provides convincing evidence that intraprotein hydrogen bonds in these regions are stabilized by electronic polarization, which is critical to the dynamical stability of these local structures in proteins.

Conformation and dynamics of the three-helix bundle UBA domain of p62 from experiment and simulation

The ubiquitin associated domain of p62 is a small three-helix bundle of approximately 50 residues that mediates the recognition of polyubiquitin chains and ubiquitylated substrates. The solution structure of a 52 residue construct containing this domain has been characterized using heteronuclear nuclear magnetic resonance (NMR) methods. The resulting ensemble of NMR-derived structures was used in molecular dynamics (MD) simulations to investigate the equilibrium conformation and dynamics of this domain. NOE and (15)N relaxation data have been used to validate the structural ensemble produced by the MD simulations and show a good correlation for residues in regions of secondary structure. A similar approach was taken using an ensemble of structures from the MD simulations to calculate electronic circular dichroism (CD) and IR spectra from first principles with an encouraging correlation with the experimental CD and IR data.

NMR study and molecular dynamics simulations of optimized β-hairpin fragments of protein G

The stability and structure of several beta-hairpin peptide variants derived from the C-terminus of the B1 domain of protein G were investigated by a number of experimental and computational techniques. Our analysis shows that the structure and stability of this hairpin can be greatly affected by one or a few simple mutations. For example, removing an unfavorable charge near the N-terminus of the peptide (Glu42 to Gln or Thr) or optimization of the N-terminal charge-charge interactions (Gly41 to Lys) both stabilize the peptide, even in water. Furthermore, a simple replacement of a charged residue in the turn (Asp47 to Ala) changes the beta-turn conformation. Finally, we show that the effects of combining these single mutations are additive, suggesting that independent stabilizing interactions can be isolated and evaluated in a simple model system. Our results indicate that the structure and stability of this beta-hairpin peptide can be modulated in numerous ways and thus contributes toward a more complete understanding of this important model beta-hairpin as well as to the folding and stability of larger peptides and proteins.

Folding pathway of the b1 domain of protein G explored by multiscale modeling

The understanding of the folding mechanisms of single-domain proteins is an essential step in the understanding of protein folding in general. Recently, we developed a mesoscopic CA-CB side-chain protein model, which was successfully applied in protein structure prediction, studies of protein thermodynamics, and modeling of protein complexes. In this research, this model is employed in a detailed characterization of the folding process of a simple globular protein, the B1 domain of IgG-binding protein G (GB1). There is a vast body of experimental facts and theoretical findings for this protein. Performing unbiased, ab initio simulations, we demonstrated that the GB1 folding proceeds via the formation of an extended folding nucleus, followed by slow structure fine-tuning. Remarkably, a subset of native interactions drives the folding from the very beginning. The emerging comprehensive picture of GB1 folding perfectly matches and extends the previous experimental and theoretical studies.

Model-free analysis for large proteins at high magnetic field strengths

Protein backbone dynamics is often characterized using model-free analysis of three sets of (15)N relaxation data: longitudinal relaxation rate (R1), transverse relaxation rate (R2), and (15)N-{H} NOE values. Since the experimental data is limited, a simplified model-free spectral density function is often used that contains one Lorentzian describing overall rotational correlation but not one describing internal motion. The simplified spectral density function may be also used in estimating the overall rotational correlation time, by making the R2/R1 largely insensitive to internal motions, as well as used as one of the choices in the model selection protocol. However, such approximation may not be valid for analysis of relaxation data of large proteins recorded at high magnetic field strengths since the contribution to longitudinal relaxation from the Lorentzian describing the overall rotational diffusion of the molecule is comparably small relative to that describing internal motion. Here, we quantitatively estimate the errors introduced by the use of the simplified spectral density in model-free analysis for large proteins at high magnetic field strength.

Long dynamics simulations of proteins using atomistic force fields and a continuum representation of solvent effects: calculation of structural and dynamic properties

Long dynamics simulations were carried out on the B1 immunoglobulin-binding domain of streptococcal protein G (ProtG) and bovine pancreatic trypsin inhibitor (BPTI) using atomistic descriptions of the proteins and a continuum representation of solvent effects. To mimic frictional and random collision effects, Langevin dynamics (LD) were used. The main goal of the calculations was to explore the stability of tens-of-nanosecond trajectories as generated by this molecular mechanics approximation and to analyze in detail structural and dynamical properties. Conformational fluctuations, order parameters, cross correlation matrices, residue solvent accessibilities, pKa values of titratable groups, and hydrogen-bonding (HB) patterns were calculated from all of the trajectories and compared with available experimental data. The simulations comprised over 40 ns per trajectory for ProtG and over 30 ns per trajectory for BPTI. For comparison, explicit water molecular dynamics simulations (EW/MD) of 3 ns and 4 ns, respectively, were also carried out. Two continuum simulations were performed on each protein using the CHARMM program, one with the all-atom PAR22 representation of the protein force field (here referred to as PAR22/LD simulations) and the other with the modifications introduced by the recently developed CMAP potential (CMAP/LD simulations). The explicit solvent simulations were performed with PAR22 only. Solvent effects are described by a continuum model based on screened Coulomb potentials (SCP) reported earlier, i.e., the SCP-based implicit solvent model (SCP-ISM). For ProtG, both the PAR22/LD and the CMAP/LD 40-ns trajectories were stable, yielding C(alpha) root mean square deviations (RMSD) of about 1.0 and 0.8 A respectively along the entire simulation time, compared to 0.8 A for the EW/MD simulation. For BPTI, only the CMAP/LD trajectory was stable for the entire 30-ns simulation, with a C(alpha) RMSD of approximately 1.4 A, while the PAR22/LD trajectory became unstable early in the simulation, reaching a C(alpha) RMSD of about 2.7 A and remaining at this value until the end of the simulation; the C(alpha) RMSD of the EW/MD simulation was about 1.5 A. The source of the instabilities of the BPTI trajectories in the PAR22/LD simulations was explored by an analysis of the backbone torsion angles. To further validate the findings from this analysis of BPTI, a 35-ns SCP-ISM simulation of Ubiquitin (Ubq) was carried out. For this protein, the CMAP/LD simulation was stable for the entire simulation time (C(alpha) RMSD of approximately 1.0 A), while the PAR22/LD trajectory showed a trend similar to that in BPTI, reaching a C(alpha) RMSD of approximately 1.5 A at 7 ns. All the calculated properties were found to be in agreement with the corresponding experimental values, although local deviations were also observed. HB patterns were also well reproduced by all the continuum solvent simulations with the exception of solvent-exposed side chain-side chain (sc-sc) HB in ProtG, where several of the HB interactions observed in the crystal structure and in the EW/MD simulation were lost. The overall analysis reported in this work suggests that the combination of an atomistic representation of a protein with a CMAP/CHARMM force field and a continuum representation of solvent effects such as the SCP-ISM provides a good description of structural and dynamic properties obtained from long computer simulations. Although the SCP-ISM simulations (CMAP/LD) reported here were shown to be stable and the properties well reproduced, further refinement is needed to attain a level of accuracy suitable for more challenging biological applications, particularly the study of protein-protein interactions.

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.

Optimal combination of theory and experiment for the characterization of the protein folding landscape of S6: how far can a minimalist model go?

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present a new methodology that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape. We prove that this new procedure allows a simplified protein model to reproduce remarkably well (correlation coefficient > 0.9) all experimental data available on free energies differences upon single mutations for S6 ribosomal protein and two circular permutants. Our results confirm and quantify the hypothesis, recently formulated on the basis of experimental data, that the folding landscape of protein S6 is strongly affected by an atypical distribution of contact energies.

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.

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.

Evidence of turn and salt bridge contributions to beta-hairpin stability: MD simulations of C-terminal fragment from the B1 domain of protein G

We ran and analyzed a total of eighteen, 10 ns molecular dynamics simulations of two C-terminal beta-hairpins from the B1 domain of Protein G: twelve runs for the last 16 residues and six runs for the last 15 residues, G41-E56 and E42-E56, respectively. Based on their CalphaRMS deviation from the starting structure and the pattern of stabilizing interactions (hydrogen bonds, hydrophobic contacts, and salt bridges), we were able to classify the twelve runs on G41-E56 into one of three general states of the beta-hairpin ensemble: 'Stable', 'Unstable', and 'Unfolded'. Comparing the specific interactions between these states, we find that on average the stable beta-hairpin buries 287 A(2) of hydrophobic surface area, makes 13 hydrogen bonds, and forms 3 salt-bridges. We find that the hydrophobic core prefers to make some specific contacts; however, this core does not require optimal packing. Side-chain hydrogen bonds stabilize the beta-hairpin turn with strong stabilizing interactions primarily due to the carboxyl of D46 with contributions from T49 hydroxyl. Buoyed by the strength of the hydrophobic core, other hydrogen bonds, primarily main-chain, guide the beta-hairpin into registration by forming a loose network of interactions, making an approximately constant number of hydrogen bonds from a pool of possible candidates. In simulations on E42-E56, where the salt bridge closing the termini is not favored, we observe that all the simulations show no 'Stable' behavior, but are 'Unstable' or 'Unfolded'. We can estimate that the salt-bridge between the termini provides approximately 1.3 kcal/mol. Altogether, the results suggest that the beta-hairpin folds beginning at the turn, followed by hydrophobic collapse, and then hydrogen bond formation. Salt bridges help to stabilize the folded conformations by inhibiting unfolded states.

Protein molecular dynamics with the generalized Born/ACE solvent model

Implicit solvent models are increasingly important for the study of proteins in aqueous solution. Here, the generalized Born (GB) solvent polarization model as implemented in the analytical ACE potential [Schaefer and Karplus (1996) J Phys Chem 100:1578] is used to perform molecular dynamics simulations of two small, homologous proteins: the immunoglobulin-binding domain of streptococcal protein G and the Ras binding domain of Raf. Several model parameterizations are compared through more than 60 ns of simulation. Results are compared with two simpler solvent models-an accessible surface area model and a distant-dependent dielectric model, with finite-difference Poisson calculations, with existing explicit solvent simulations, and with experimental data. The simpler models yield stable but distorted structures. The best GB/ACE implementation uses a set of atomic Voronoi volumes reported recently, obtained by averaging over a large database of crystallographic protein structures. A 20% reduction is applied to the volumes, compensating in an average sense for an excessive de-screening of individual charges inherent in the ACE self-energy and for an undersolvation of dipolar groups inherent in the GB screening function. This GB/ACE parameterization yields stable trajectories on the 0.5-1-ns time scale that deviate moderately (approximately 1.5-2.5 A) from the X-ray structure, reproduce approximately the surface distribution of charged, polar, and hydrophobic groups, and reproduce accurately backbone flexibility as measured by amide NMR-order parameters. Over longer time scales (1.5-3 ns), some of the protein G runs escape from the native energy basin and deviate strongly (3 A) from the native structure. The conformations sampled during the transition out of the native energy basin are overstabilized by the GB/ACE solvation model, as compared with a numerical treatment of the full dielectric continuum model.

Beta-hairpin folding simulations in atomistic detail using an implicit solvent model

We have used distributed computing techniques and a supercluster of thousands of computer processors to study folding of the C-terminal beta-hairpin from protein G in atomistic detail using the GB/SA implicit solvent model at 300 K. We have simulated a total of nearly 38 micros of folding time and obtained eight complete and independent folding trajectories. Starting from an extended state, we observe relaxation to an unfolded state characterized by non-specific, temporary hydrogen bonding. This is followed by the appearance of interactions between hydrophobic residues that stabilize a bent intermediate. Final formation of the complete hydrophobic core occurs cooperatively at the same time that the final hydrogen bonding pattern appears. The folded hairpin structures we observe all contain a closely packed hydrophobic core and proper beta-sheet backbone dihedral angles, but they differ in backbone hydrogen bonding pattern. We show that this is consistent with the existing experimental data on the hairpin alone in solution. Our analysis also reveals short-lived semi-helical intermediates which define a thermodynamic trap. Our results are consistent with a three-state mechanism with a single rate-limiting step in which a varying final hydrogen bond pattern is apparent, and semi-helical off-pathway intermediates may appear early in the folding process. We include details of the ensemble dynamics methodology and a discussion of our achievements using this new computational device for studying dynamics at the atomic level.

From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding

Beginning with simplified lattice and continuum "minimalist" models and progressing to detailed atomic models, simulation studies have augmented and directed development of the modern landscape perspective of protein folding. In this review we discuss aspects of detailed atomic simulation methods applied to studies of protein folding free energy surfaces, using biased-sampling free energy methods and temperature-induced protein unfolding. We review studies from each on systems of particular experimental interest and assess the strengths and weaknesses of each approach in the context of "exact" results for both free energies and kinetics of a minimalist model for a beta-barrel protein. We illustrate in detail how each approach is implemented and discuss analysis methods that have been developed as components of these studies. We describe key insights into the relationship between protein topology and the folding mechanism emerging from folding free energy surface calculations. We further describe the determination of detailed "pathways" and models of folding transition states that have resulted from unfolding studies. Our assessment of the two methods suggests that both can provide, often complementary, details of folding mechanism and thermodynamics, but this success relies on (a) adequate sampling of diverse conformational regions for the biased-sampling free energy approach and (b) many trajectories at multiple temperatures for unfolding studies. Furthermore, we find that temperature-induced unfolding provides representatives of folding trajectories only when the topology and sequence (energy) provide a relatively funneled landscape and "off-pathway" intermediates do not exist.

Solvent density and long-range dipole field around a DNA-binding protein studied by molecular dynamics

The distribution and orientation of solvent around a DNA-binding protein, 434 Cro, were investigated by molecular dynamics simulations with a periodic-boundary condition. The protein was treated in two states: charged and neutral. The computed high-density sites of the solvent around the protein correlated well with the experimentally determined crystal-water sites, in both the charged and neutral states. A local density map, introduced to investigate the solvent density around the highly mobile regions of the protein, showed a hydration shell around hydrophobic sidechains and hydrogen-bondable sites around hydrophilic sidechains, and also showed that the solvent density is sensitive to the slight concaves of the sidechain surface. The long-range solvent-dipole field was observed around the protein, where the pattern of the dipole ordering was considerably different between the charged and neutral states. A local solvent-dipole field was introduced, and the pattern of the dipole ordering was different between the hydrophobic and hydrophilic sidechains. The dipole field from the charged state provided a higher correlation to the electrostatic field obtained from the Poisson-Boltzmann's equation than that from the neutral state, although the correlation become weak quickly for the both states with increasing the protein-solvent distance.

A surprising simplicity to protein folding

The polypeptide chains that make up proteins have thousands of atoms and hence millions of possible inter-atomic interactions. It might be supposed that the resulting complexity would make prediction of protein structure and protein-folding mechanisms nearly impossible. But the fundamental physics underlying folding may be much simpler than this complexity would lead us to expect folding rates and mechanisms appear to be largely determined by the topology of the native (folded) state, and new methods have shown great promise in predicting protein-folding mechanisms and the three-dimensional structures of proteins.

Synthesis, folding, and structure of the beta-turn mimic modified B1 domain of streptococcal protein G

The mechanism of beta-sheet formation remains a fundamental issue in our understanding of the protein folding process, but is hampered by the often encountered kinetic competition between folding and aggregation. The role of local versus nonlocal interactions has been probed traditionally by mutagenesis of both turn and strand residues. Recently, rigid organic molecules that impose a correct chain reversal have been introduced in several small peptides to isolate the importance of the long-range interactions. Here, we present the incorporation of a well-studied beta-turn mimic, designated as the dibenzofuran-based (DBF) amino acid, in the B1 domain of streptococcal protein G (B1G), and compare our results with those obtained upon insertion of the same mimic into the N-terminal beta-hairpin of B1G (O Melnyk et al., 1998, Lett Pept Sci 5:147-150). The DBF-B1G domain conserves the structure and the functional and thermodynamical properties of the native protein, whereas the modified peptide does not adopt a native-like conformation. The nature of the DBF flanking residues in the modified B1G domain prevents the beta-turn mimic from acting as a strong beta-sheet nucleator, which reinforces the idea that the native beta-hairpin formation is not driven by the beta-turn formation, but by tertiary interactions.

Exploring the origins of topological frustration: design of a minimally frustrated model of fragment B of protein A

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This G-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht phi values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate phi, whereas highly frustrated systems display a bimodal distribution peaked at low and high phi values. The distribution of phi values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at phi = 0.3 with tails extending to low and high phi values, indicating the presence of a small amount of topological frustration. The contacts with high phi values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of phi values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration.

Protein dynamics simulations from nanoseconds to microseconds

There have been a number of advances in atomic resolution simulations of biomolecules during the past few years. These have arisen partly from improvements to computer power and partly from algorithmic improvements. There have also been advances in measuring time-dependent fluctuations in proteins using NMR spectroscopy, revealing the importance of fluctuations in the microsecond to millisecond time range. Progress has also been made in measuring how far the simulations are able to represent the accessible phase space that is available to the protein in its native state, in solution, at room temperature. Another area of development is the simulation of protein unfolding at atomic resolution.

Discrete molecular dynamics studies of the folding of a protein-like model

BACKGROUND

Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from insensitivity to the geometrical properties of the proteins (lattice models), whereas others are computationally heavy (traditional molecular dynamics).

RESULTS

We used the recently proposed approach of Zhou and Karplus to study the folding of a protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding <--> unfolding transition. In addition, we demonstrate the ability to study the core of the model protein.

CONCLUSIONS

The algorithm along with the model of interresidue interactions can serve as a tool for studying the thermodynamics and kinetics of protein models.

Mechanics and dynamics of B1 domain of protein G: role of packing and surface hydrophobic residues

The structural organization of the B1 domain of streptococcal protein G (PGA) has been probed using molecular dynamics simulations, with a particular emphasis on the role of the solvent exposed Ile6 residue. In addition to the native protein (WT-PGA), three single-mutants (I6G-PGA, I6F-PGA, and I6T-PGA), one double-mutant (I6T,T53G-PGA), and three isolated peptide fragments (corresponding to the helix and the two beta-hairpins) were studied in the presence of explicit water molecules. Comparative analysis of the various systems showed that the level of perturbation was directly related to the hydrophobicity and the size of the side chain of residue 6, the internal rigidity of the proteins decreasing in the order I6T-PGA > I6G-PGA > WT-PGA > I6F-PGA. The results emphasized the importance of residue 6 in controlling both the integrity of the sheet's surface and the orientation of the helix in relation to the sheet by modulation of surface/core interactions. The effects of mutations were delocalized across the structure, and glycine residues, in particular, absorbed most of the introduced strain. A qualitative structural decomposition of the native fold into elementary building-blocks was achieved using principal component analysis and mechanical response matrices. Within this framework, internal motions of the protein were described as coordinated articulations of these structural units, mutations affecting mostly the amplitude of the motions rather than the structure/location of the building-blocks. Analysis of the isolated peptidic fragments suggested that packing did not play a determinant role in defining the elementary building-blocks, but that chain topology was mostly responsible.

Calculations on folding of segment B1 of streptococcal protein G

We present an investigation of the folding thermodynamics and mechanism of segment B1 of streptococcal protein G. Molecular dynamics simulations of the fully solvated protein are used to probe thermodynamically significant states at different stages of folding. We performed several unfolding simulations to generate a database of initial conditions. The database is analyzed and clustered. The cluster centers extracted from this database were then used as starting points for umbrella sampling of the folding free energy landscape under folding conditions. The resulting sampling was combined with the weighted histogram analysis method. One and two-dimensional free energy surfaces were constructed along several order parameters and used to analyze the folding process. Our findings indicate that an initial collapse precedes the formation of significant native structure. Elements of local structure originate in the regions of the protein shown to have higher H/2H exchange protection factors in early stages of folding. A non-native contact, observed experimentally at the N terminus of the alpha-helix in a peptide excised from the protein, is seen to pre-organize the chain in early stages of folding. Collapse and early structure formation yields a compact globule with a significant number of water molecules present. Desolvation of the protein core is coincident with the final stages of folding from the compact state.

Molecular picture of folding of a small alpha/beta protein

We characterize, at the atomic level, the mechanism and thermodynamics of folding of a small alpha/beta protein. The thermodynamically significant states of segment B1 of streptococcal protein G (GB1) are probed by using the statistical mechanical methods of importance sampling and molecular dynamics. From a thermodynamic standpoint, folding commences with overall collapse, accompanied by formation of approximately 35% of the native structure. Specific contacts form at the loci experimentally inferred to be structured early in folding kinetics studies. Our study reveals that these initially structured regions are not spatially adjacent. As folding progresses, fluid-like nonlocal native contacts form, with many contacts forming and breaking as the structure searches for the native conformation. Although the alpha-helix forms early, the beta-sheet forms concomitantly with the overall topology. Water is present in the protein core up to a late stage of folding, lubricating conformational transitions during the search process. Once 80% of the native contacts have formed, water is squeezed from the protein interior and the structure descends into the native manifold. Examination of the onset of side-chain mobility within our model indicates side-chain motion is most closely linked to the overall volume of the protein and no sharp order-disorder transition appears to occur. Exploration of models for hydrogen deuterium exchange show qualitative agreement with equilibrium measurement of hydrogen/deuterium protection factors.