A Computational Study of the Role of Solvation Effects in Reverse Turn Formation in the Tetrapeptides APGD and APGN

On the foldability of tryptophan-containing tetra- and pentapeptides: an exhaustive molecular dynamics study

Short peptides serve as minimal model systems to decipher the determinants of foldability due to their simplicity arising from their smaller size, their ability to echo protein-like structural characteristics, and their direct implication in force field validation. Here, we describe an effort to identify small peptides that can still form stable structures in aqueous solutions. We followed the in silico folding of a selected set of 8640 tryptophan-containing tetra- and pentapeptides through 15 210 molecular dynamics simulations amounting to a total of 272.46 μs using explicit representation of the solute and full treatment of the electrostatics. The evaluation and sorting of peptides is achieved through scoring functions, which include terms based on interatomic vector distances, atomic fluctuations, and rmsd matrices between successive frames of a trajectory. Highly scored peptides are studied further via successive simulation rounds of increasing simulation length and using different empirical force fields. Our method suggested only a handful of peptides with strong foldability prognosis. The discrepancies between the predictions of the various force fields for such short sequences are also extensively discussed. We conclude that the vast majority of such short peptides do not adopt significantly stable structures in water solutions, at least based on our computational predictions. The present work can be utilized in the rational design and engineering of bioactive peptides with desired molecular properties.

Disorder and order in unfolded and disordered peptides and proteins: a view derived from tripeptide conformational analysis. II. Tripeptides with short side chains populating asx and β-type like turn conformations

In the preceding paper, we found that ensembles of tripeptides with long or bulky chains can include up to 20% of various turns. Here, we determine the structural and thermodynamic characteristics of GxG peptides with short polar and/or ionizable central residues (D, N, C), whose conformational distributions exhibit higher than average percentage (>20%) of turn conformations. To probe the side-chain conformations of these peptides, we determined the (3)J(H(α),H(β)) coupling constants and derived the population of three rotamers with χ1 -angles of -60°, 180° and 60°, which were correlated with residue propensities by DFT-calculations. For protonated GDG, the rotamer distribution provides additional evidence for asx-turns. A comparison of vibrational spectra and NMR coupling constants of protonated GDG, ionized GDG, and the protonated aspartic acid dipeptide revealed that side chain protonation increases the pPII content at the expense of turn populations. The charged terminal groups, however, have negligible influence on the conformational properties of the central residue. Like protonated GDG, cationic GCG samples asx-turns to a significant extent. The temperature dependence of the UVCD spectra and (3)J(H(N)H(α)) constants suggest that the turn populations of GDG and GNG are practically temperature-independent, indicating enthalpic and entropic stabilization. The temperature-independent J-coupling and UVCD spectra of GNG require a three-state model. Our results indicate that short side chains with hydrogen bonding capability in GxG segments of proteins may serve as hinge regions for establishing compact structures of unfolded proteins and peptides.

Molecular modeling of nucleic acid structure: setup and analysis

The last in a set of units by these authors, this unit addresses some important remaining questions about molecular modeling of nucleic acids. It describes how to choose an appropriate molecular mechanics force field; how to set up and equilibrate the system for accurate simulation of a nucleic acid in an explicit solvent by molecular dynamics or Monte Carlo simulation; and how to analyze molecular dynamics trajectories.

A fluid salt-bridging cluster and the stabilization of p53

p53 is a homotetrameric tumor suppressor protein that is found to be mutated in most human cancers. Some of these mutations, particularly mutations to R337, fall in the tetramerization domain and cause defects in tetramer formation leading to loss of function. Mutation to His at this site has been found to destabilize the tetramer in a pH-dependent fashion. In structures of the tetramerization domain determined by crystallography, R337 from one monomer makes a salt bridge with D352 from another monomer, apparently helping to stabilize the tetramer. Here we present molecular dynamics simulations of wild-type p53 and the R337His mutant at several different pH and salt conditions. We find that the 337-352 salt bridge is joined by two other charged side chains, R333 and E349. These four residues do not settle into a fixed pattern of salt bridging, but continue to exchange salt-bridging partners on the nanosecond time scale throughout the simulation. This unusual system of fluid salt bridging may explain the previous finding from alanine scanning experiments that R333 contributes significantly to protein stability, even though in the crystal structure it is extended outward into solvent. This extended conformation of R333 appears to be the result of a specific crystal contact and, this contact being absent in the simulation, R333 turns inward to join its interaction partners. When R337 is mutated to His but remains positively charged, it maintains the original interaction with D352, but the newly observed interaction with E349 is weakened, accounting for the reduced stability of R337H even under mildly acidic conditions. When this His is deprotonated, the interaction with D352 is also lost, accounting for the further destabilization observed under mildly alkaline conditions. Simulations were carried out using both explicit and implicit solvent models, and both displayed similar behavior of the fluid salt-bridging cluster, suggesting that implicit solvent models can capture at least the qualitative features of this phenomenon as well as explicit solvent. Simulations under strongly acidic conditions in implicit solvent displayed the beginnings of the unfolding process, a destabilization of the hydrophobic dimer-dimer interface. Computational alanine scanning using the molecular mechanics Poisson-Boltzmann surface area method showed significant correlation to experimental unfolding data for charged and polar residues, but much weaker correlation for hydrophobic residues.

Kinetics and thermodynamics of type VIII beta-turn formation: a CD, NMR, and microsecond explicit molecular dynamics study of the GDNP tetrapeptide

We report an experimental and theoretical study on type VIII beta-turn using a designed peptide of sequence GDNP. CD and NMR studies reveal that this peptide exists in equilibrium between type VIII beta-turn and extended conformations. Extensive MD simulations give a description of the free energy landscape of the peptide in which we retrieve the same two main conformations suggested by the experiments. The free energy difference between the two conformational states is very small and the transition between them occurs within a few kT at 300 K on a nanosecond timescale. The equilibrium is mainly driven by entropic contribution, which favors extended conformations over beta-turns. This confirms other theoretical studies showing that beta-turns are marginally stable in water solution because of the larger entropy of the extended state unless some stabilizing interactions exist. Our observations may be extended to any type of beta-turn and have important consequences for protein folding. A comparison of our MD and CD results also suggests a possible type VIII beta-turn CD signature indicated by one main band at 200 nm, close to that of random coil, and a fairly large shoulder at 220 nm. Last, our results clearly show that the XXXP motif can only fold into a type VIII beta-turn, which is consistent with its fairly strong propensity for this type of turn. This important finding may help for peptide design and is in line with recent studies on bioactive elastin peptides.

Accelerated Poisson-Boltzmann calculations for static and dynamic systems

We report here an efficient implementation of the finite difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approximations, including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calculations and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielectric model for a system tested, HIV Protease, making it a strong candidate for solution-phase molecular dynamics simulations. Further, the finite difference method includes all intrasolute electrostatic interactions, whereas the distance dependent dielectric calculations use a 15-A cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approximation to the Poisson-Boltzmann method.

Stability and amino acid preferences of type VIII reverse turn: the most common turn in peptides?

Free energies of the alpha(r)beta and betabeta conformations of 14 tetrapeptides, based on the sequence SALN and protein X-ray structures, were calculated using molecular dynamics simulations and MM-PBSA calculations. The alphaalpha conformations of five of the tetrapeptides were also studied. SALN has been earlier shown by molecular dynamics simulations and NMR spectroscopy to have a tendency to form an alpha(r)beta turn. The gas-phase energy of the molecular mechanical force field (CHARMM), the electrostatic and non-polar solvation free energies and solute entropies were used to explain the free energy differences of the alphaalpha, betabeta and alpha(r)beta conformations of the peptides. The alpha(r)beta conformation of SALN and SATN was predicted to be slightly more stable than the extended conformation (betabeta), in agreement with experimental results. The SALN mutants SAIN, SAVN, SATN, SSIN and MSHV, were also predicted to be potential alpha(r)beta turn-forming peptides. We report also revised positional potentials for the type VIII turn, based on a non-homologous set of protein structures. This protein databank analysis confirms the main results of the earlier analyses and reveals several new amino acid residues with a significant positional preference. The results of this work led us to suggest that the alpha(r)beta turn may be the most common turn type in peptides. Such turns may be readily formed in aqueous solution and thereby play important roles in the protein folding process by serving as an initiation point for structure formation.

The dynamics, structure, and conformational free energy of proline-containing antifreeze glycoprotein

Recent NMR studies of the solution structure of the 14-amino acid antifreeze glycoprotein AFGP-8 have concluded that the molecule lacks long-range order. The implication that an apparently unstructured molecule can still have a very precise function as a freezing inhibitor seems startling at first consideration. To gain insight into the nature of conformations and motions in AFGP-8, we have undertaken molecular dynamics simulations augmented with free energy calculations using a continuum solvation model. Starting from 10 different NMR structures, 20 ns of dynamics of AFGP were explored. The dynamics show that AFGP structure is composed of four segments, joined by very flexible pivots positioned at alanine 5, 8, and 11. The dynamics also show that the presence of prolines in this small AFGP structure facilitates the adoption of the poly-proline II structure as its overall conformation, although AFGP does adopt other conformations during the course of dynamics as well. The free energies calculated using a continuum solvation model show that the lowest free energy conformations, while being energetically equal, are drastically different in conformations. In other words, this AFGP molecule has many structurally distinct and energetically equal minima in its energy landscape. In addition, conformational, energetic, and hydrogen bond analyses suggest that the intramolecular hydrogen bonds between the N-acetyl group and the protein backbone are an important integral part of the overall stability of the AFGP molecule. The relevance of these findings to the mechanism of freezing inhibition is discussed.

A classical and ab initio study of the interaction of the myosin triphosphate binding domain with ATP

We used classical molecular mechanics (MM) simulations and quantum mechanical (QM) structural relaxations to examine the active site of myosin when bound to ATP. Two conformations of myosin have been determined by x-ray crystallography. In one, there is no direct interaction between switch 2 and the nucleotide (open state). In the other (closed state), the universally conserved switch 2 glycine forms a hydrogen bond with a gamma-phosphate oxygen. MM simulations indicate that the two states are thermodynamically stable and allow us to investigate the extent to which the P-loop, switch 1, and switch 2 are involved in hydrolysis. We find that the open structure has a higher affinity for ATP than the closed structure, and that ATP is distorted toward a transition state by interactions with the protein. We also examine how the structure of the binding site changes with either MgATP or CaATP as the nucleotide in myosin in the open conformer. Our analyses suggest that higher CaATPase rates occur because the leaving phosphate (P(i)) group is more weakly bound and dissociation occurs faster. Finally, we validate the use of a particular formulation of a QM methodology (Car-Parrinello) to further refine the structures of the active site.

Stereochemical, structural, and thermodynamic origins of stability differences between stereoisomeric benzo[a]pyrene diol epoxide deoxyadenosine adducts in a DNA mutational hot spot sequence

Benzo[a]pyrene (BP), a prototype polycyclic aromatic hydrocarbon (PAH), can be metabolically activated to the enantiomeric benzo[a]pyrene diol epoxides (BPDEs), (+)-(7R,8S,9S,10R)-7,8-dihydroxy-9,10-epoxy-7,8,9,10-tetrahydrobenzo[a]pyrene and the (-)-(7S,8R,9R,10S) enantiomer. These can react with adenine residues in DNA, to produce the stereoisomeric 10S (+)- and 10R (-)-trans-anti-[BP]-N(6)-dA adducts. High-resolution NMR solution studies indicate that in DNA duplexes the 10R (-) adduct is intercalated on the 5'-side of the modified adenine, while the 10S (+) adduct is disordered, exhibits multiple adduct conformations, and is positioned on the 3'-side of the modified adenine. Duplexes containing the 10S (+) adduct positioned at A within codon 61 of the human N-ras sequence CAA are thermodynamically less stable and more easily excised by human DNA repair enzymes than those containing the 10R (-) adduct. However, the molecular origins of these differences are not understood and represent a fascinating opportunity for elucidating structure-function relationships. We have carried out a computational investigation to uncover the structural and thermodynamic origins of these effects in the 11-mer duplex sequence d(CGGACAAGAAG).d(CTTCTTGTCCG) by performing a 2-ns molecular dynamics simulation using NMR solution structures as the basis for the starting models. Then, we applied the MM-PBSA (molecular mechanics Poisson-Boltzmann surface area) method to compute free energy differences between the stereoisomeric adducts. The 10R (-) isomer is more stable by approximately 13 kcal/mol, of which approximately 10 kcal/mol is enthalpic, which agrees quite well with their observed differences in thermodynamic stability. The lower stability of the 10S (+) adduct is due to diminished stacking by the BP moiety in the intercalation pocket, more helix unwinding, and a diminished quality of Watson-Crick base pairing. The latter stems from conformational heterogeneity involving a syn-anti equilibrium of the glycosidic bond in the modified adenine residue. The lower stability and conformational heterogeneity of the 10S (+) adduct may play a role in its enhanced susceptibility to nucleotide excision repair.

Molecular dynamics study of the energetic, mechanistic, and structural implications of a closed phosphate tube in ncd

The switch 1 region of myosin forms a lid over the nucleotide phosphates as part of a structure known as the phosphate-tube. The homologous region in kinesin-family motors is more open, not interacting with the nucleotide. We used molecular dynamics (MD) simulations to examine a possible displacement of switch 1 of the microtubule motor, ncd, from the open conformation to the closed conformation seen in myosin. MD simulations were done of both the open and the closed conformations, with either MgADP or MgATP at the active site. All MD structures were stable at 300 K for 500 ps, implying that the open and closed conformers all represented local minima on a global free energy surface. Free energy calculations indicated that the open structure was energetically favored with MgADP at the active site, suggesting why only the open structure has been captured in crystallographic work. With MgATP, the closed and open structures had roughly equal energies. Simulated annealing MD showed the transformation from the closed phosphate-tube ncd structure to an open configuration. The MD simulations also showed that the coordination of switch 1 to the nucleotide dramatically affected the position of both the bound nucleotide and switch 2 and that a closed phosphate-tube may be necessary for catalysis.

Generalized born models of macromolecular solvation effects

It would often be useful in computer simulations to use a simple description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation, and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efficiency. Here we give an overview of one such approximation, the generalized Born model, which is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids. We discuss its strengths and weaknesses, both for its fidelity to the underlying continuum model and for its ability to replace explicit consideration of solvent molecules in macromolecular simulations. We focus particularly on versions of the generalized Born model that have a pair-wise analytical form, and therefore fit most naturally into conventional molecular mechanics calculations.

Predicting relative binding free energies of tacrine-huperzine A hybrids as inhibitors of acetylcholinesterase

The binding of the 9-methyl derivative of tacrine-huperzine A hybrid to Torpedo californica acetylcholinesterase (AChE) has been studied by computational methods. Molecular dynamics simulations have been performed for the AChE-drug complex considering two different ionization states of the protein and two different orientations of the drug in the binding pocket, which were chosen from a previous screening procedure. Analysis of structural fluctuations and of the pattern of interactions between drug and enzyme clearly favor one binding mode for the tacrine-huperzine A hydrid, which mixes effectively some of the binding features of tacrine and huperzine A. The differences in inhibitory activity for a series of related derivatives have been successfully predicted by free energy calculations, which reinforces the confidence in the binding mode and its usefulness for molecular modeling studies. The same techniques have been used to make de novo predictions for a new 3-fluoro-9-ethyl derivative, which can be used to verify a posteriori the goodness of the binding mode. Finally, we have also investigated the effect of replacing Phe300 in the Torpedo californica enzyme by Tyr, which is present in the human AChE. The results indicate that the Phe330-->Tyr mutation is expected to have little effect on the binding affinities. Overall, the whole of results supports the validity of the putative binding model to explain the binding of tacrine-huperzine A hybrids to AChE.

Explicit and implicit water simulations of a beta-hairpin peptide

The conformational properties of a beta-hairpin peptide (YITNSDGTWT) were studied by using both explicit and implicit water simulations. The conformational space of the peptide was scanned by using a restricted hydrogen-bonding search method. The search method used generated the conformational space with enough diversity and good representation of beta-hairpin structures. By using a total surface area-based treatment of hydrophobic interactions, implicit water simulations failed to discriminate between experimental beta-hairpin structures from the rest of the conformers present in the authors' conformation library. However, with inclusion of vibrational free energy and accounting separately for polar and nonpolar surface areas, the nuclear magnetic resonance structure was ranked successfully as the most stable conformation. There is a loose correlation between the conformational energies by the continuum model and the conformational energies by explicit water simulation for conformers with similar structures. However, in terms of solvation energy, both approaches have a much better correlation. By using proper treatment of surface effect (partition of the surface area into polar and nonpolar areas) and including vibrational free-energy contribution, the continuum models should be reliable. Furthermore, the authors found that, for this peptide, beta-hairpin structures have large vibrational entropy that contributes decisively to the stability of folded beta-hairpin structures. Proteins 1999;37:73-87.

Continuum solvent studies of the stability of RNA hairpin loops and helices

We apply continuum solvent models to investigate the relative stability of various conformational forms for two RNA sequences, GGAC(UUCG)GUCC and GGUG(UGAA)CACC. In the first part, we compare alternate hairpin conformations to explore the reliability of these models to discriminate between different local conformations. A second part looks at the hairpin-duplex conversion for the UUCG sequence, identifying major contributors to the thermodynamics of a much large scale transition. Structures were taken as snapshots from multi-nanosecond molecular dynamics simulations computed in a consistent fashion using explicit solvent and with long-range electrostatics accounted for using the Particle-Mesh Ewald procedure. The electrostatic contribution to solvation energies were computed using both a finite-difference Poisson-Boltzmann (PB) model and a pairwise Generalized Born model; non-electrostatic contributions were estimated with a surface-area dependent term. To these solvation free energies were added the mean solute internal energies (determined from a molecular mechanics potential) and estimates of the solute entropy (from a harmonic analysis). Consistent with experiment and with earlier solvated molecular dynamics simulations, the UUCG hairpin was found to prefer conformers close to a recent NMR structure determination in preference to those from an earlier NMR study. Similarly, results for the UGAA hairpin favored an NMR-derived structure over that to be expected for a generic GNRA hairpin loop. Experimental free energies are not known for the hairpin/duplex conversion, but must be close to zero since hairpins are seen in solution and duplexes in crystals; out calculations find a value near zero and illustrate the expected interplay of solvation, salt effects and entropy in affecting this equilibrium.

Molecular dynamics and continuum solvent studies of the stability of polyG-polyC and polyA-polyT DNA duplexes in solution

Molecular dynamics simulation in explicit solvent and continuum solvent models are applied to investigate the relative stability of A- and B-form helices for two DNA sequences, dA10-dT10 and dG10-dC10 in three structural forms. One structural form is based on an unrestrained molecular dynamics (MD) trajectory starting from a canonical B-DNA structure, the second is based on a MD trajectory starting in a canonical B-DNA structure with the sugars constrained to be C2'-endo and the third simulation started from a canonical A-DNA structure with the sugars constrained to C3'-endo puckers. For the energetic analysis, structures were taken as snapshots from nanosecond length molecular dynamics simulations computed in a consistent fashion in explicit solvent, applying the particle mesh Ewald method and the Cornell et al. force field. The electrostatic contributions to solvation free energies are computed using both a finite-difference Poisson-Boltzmann model and a pairwise Generalized Born model. The non-electrostatic contributions to the solvation free energies are estimated with a solvent accessible surface area dependent term. To estimate the gas phase component of the relative free energy between the various structures, the mean solute internal energies (determined with the Cornell et al. molecular mechanics potential including all pairwise interactions within the solute) and estimates of the solute entropy (using a harmonic approximation) were used. Consistent with experiment, the polyG-polyC (GC) structures are found to be much more A-phillic than the polyA-polyT (AT) structures, the latter being quite A-phobic. The dominant energy components responsible for this difference comes from the internal and van der Waal energies. A perhaps less appreciated difference between the GC and AT rich sequences is suggested by the calculated salt dependence which demonstrates a significantly enhanced ability to drive GC rich sequences towards an A-form structure compared to AT rich sequences. In addition to being A-phobic, the AT structure also has a noticably larger helical repeat than GC and other mixed sequence duplexes, consistent with experiment. Analysis of the average solvent density from the trajectories shows hydration patterns in qualitative agreement with experiment and previous theoretical treatments.

Thermodynamics of a reverse turn motif. Solvent effects and side-chain packing

The linear pentapeptide, Ala-Tyr-cis-Pro-Tyr-Asp-NMA (AYPYD) is known to have a significant population of type VI turn conformers in aqueous solvent. We have carried out theoretical studies of the conformational energetics of this peptide using a potential of mean force (PMF) consisting of the AMBER/OPLS empirical potential energy function, a macroscopic electrostatic model of polar solvation, and a surface area-based model of non-polar solvation. Conformers were taken from molecular dynamics simulations reported elsewhere, or generated by a random search method reported here. The chain entropy of folding was calculated by a systematic search of accessible dihedral angle space. The intra-peptide component was found to strongly favor folding and was nearly cancelled by the polar solvation term which disfavored folding. The non-polar solvation term had little effect. Fluctuations about the average value of the PMF were small and in accord with estimates from a simple harmonic model. When applied to conformers generated by a random search, the PMF selected a conformer close to the NMR-determined structure as the lowest energy conformer. The conformer with the second-lowest energy was extended, but was found to fold rapidly to the turn state in a subsequent molecular dynamics study, and may be an important state on the folding-unfolding pathway. Averages of the PMF were combined with the entropy estimates to provide an estimate of the free energy of folding that is in reasonable agreement with experimental results. In terms of the interplay between backbone electrostatic interactions and the packing of apolar side-chains, this peptide provides a model for the energetics of protein folding, and therefore makes a useful test case for calculations.