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

Tyrosine triad at the interface between the Rieske iron-sulfur protein, cytochrome c1 and cytochrome c2 in the bc1 complex of Rhodobacter capsulatus

A triad of tyrosine residues (Y152-154) in the cytochrome c(1) subunit (C1) of the Rhodobacter capsulatus cytochrome bc(1) complex (BC1) is ideally positioned to interact with cytochrome c(2) (C2). Mutational analysis of these three tyrosines showed that, of the three, Y154 is the most important, since its mutation to alanine resulted in significantly reduced levels, destabilization, and inactivation of BC1. A second-site revertant of this mutant that regained photosynthetic capacity was found to have acquired two further mutations-A181T and A200V. The Y152Q mutation did not change the spectral or electrochemical properties of C1, and showed wild-type enzymatic C2 reduction rates, indicating that this mutation did not introduce major structural changes in C1 nor affect overall activity. Mutations Y153Q and Y153A, on the other hand, clearly affect the redox properties of C1 (e.g. by lowering the midpoint potential as much as 117 mV in Y153Q) and the activity by 90% and 50%, respectively. A more conservative Y153F mutant on the other hand, behaves similarly to wild-type. This underscores the importance of an aromatic residue at position Y153, presumably to maintain close packing with P184, which modeling indicates is likely to stabilize the sixth heme ligand conformation.

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.

Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations

A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two-dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic-simulation sample of the atomic configurations of the molecule. The torsional-angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal-rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis-stilbene are found to be much more strongly correlated than those in trans-stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine.

Structural details, pathways, and energetics of unfolding apomyoglobin

Protein folding is often difficult to characterize experimentally because of the transience of intermediate states, and the complexity of the protein-solvent system. Atomistic simulations, which could provide more detailed information, have had to employ highly simplified models or high temperatures, to cope with the long time scales of unfolding; direct simulation of folding is even more problematic. We report a fully atomistic simulation of the acid-induced unfolding of apomyoglobin in which the protonation of acidic side-chains to simulate low pH is sufficient to induce unfolding at room temperature with no added biasing forces or other unusual conditions; and the trajectory is validated by comparison to experimental characterization of intermediate states. Novel insights provided by their analysis include: characterization of a dry swollen globule state forming a barrier to initial unfolding or final folding; observation of cooperativity in secondary and tertiary structure formation and its explanation in terms of dielectric environments; and structural details of the intermediate and the completely unfolded states. These insights involve time scales and levels of structural detail that are presently beyond the range of experiment, but come within reach through the simulation methods described here. An implicit solvation model is used to analyze the energetics of protein folding at various pH and ionic strength values, and a reasonable estimate of folding free energy is obtained. Electrostatic interactions are found to disfavor folding.

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.

Identifying native-like protein structures using physics-based potentials

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

Continuum solvent molecular dynamics study of flexibility in interleukin-8

Generalized Born continuum solvent methods have been shown to provide a reasonable description of the equilibrium thermodynamics of aqueous solvation in a variety of applications to peptides, proteins, and nucleic acids. Here we study the performance of these methods in molecular dynamics simulations of interleukin-8, comparing nanosecond-length explicit solvent simulations with those using the generalized Born model. In general, the simulations show similar results, although movement away from the initial NMR-determined structure and average fluctuations about the mean are slightly higher for the continuum solvent results. In both simulations, the two helices that are packed on top of the core sheet move closer together, resulting in a structure that more closely resembles the X-ray structure. Principal-component (quasiharmonic) analysis is used to analyze the motions of these helices in both of the simulations and in the NMR ensemble of structures. Prospects for making more general use of continuum solvent models in protein dynamics simulations are discussed.

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.

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.

Significance of aromatic-backbone amide interactions in protein structure

Weakly polar interactions between aromatic rings of amino acids and hydrogens of backbone amides (Ar-HN) have been shown to support local structures in proteins. Their role in secondary structures, however, has not been elucidated. To investigate the relationship between Ar-HN interaction and the stability of local and secondary structures of polypeptides and to improve the prediction of this interaction based on amino acid sequence, the structures of 560 nonhomologous proteins, from the Protein Data Bank, were searched for Ar-HN interactions between the aromatic ring of each Phe, Tyr, and Trp residue at position i and the backbone amide group of any residue, except Pro, at the positions i, i - 1, i - 2, i - 3, i + 1, i + 2, and i + 3. Ar-HN interactions were identified by calculating the chemical shift of the amide hydrogen caused by the proximal aromatic ring. Ar(i)-HN(i + 1, i + 2 and i + 3) interactions were more common (7.10%, 2.08%, and 0.54%, respectively) than were Ar(i)-HN(i - 1, i - 2, and i - 3) interactions (0.66%, <0.1%, and 0.18%, respectively). The value of the chi(1) torsion angle of the aromatic residue in position i depended on the direction of the Ar-HN interaction. The position of the aromatic ring in Ar(i)-HN(i + 1, i + 2, and i + 3) interactions was mostly trans, in Ar(i)-HN(i - 1, i - 2, and i - 3) interactions mainly gauche(-), and in Ar(i)-HN(i) interactions mostly gauche(+). The analyses of the secondary structures of the protein fragments containing Ar-HN interactions showed that Ar-HN interactions were in all types of secondary structures. Search results suggest that Ar-HN interactions have a stabilizing effect on all types of secondary structures.

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.

Molecular dynamics simulations of beta-hairpin folding

Molecular dynamics simulations of beta-hairpin folding have been carried out with a solvent-referenced potential at 274 K. The model peptide V4DPGV4 formed stable beta-hairpin conformations and the beta-hairpin ratio calculated by the DSSP algorithm was about 56% in the 50-ns simulation. Folding into beta-hairpin conformations is independent of the initial conformations. The simulations provided insights into the folding mechanism. The hydrogen bond often formed in a beta-turn first, and then propagated by forming more hydrogen bonds along the strands. Unfolding and refolding occurred repeatedly during the simulations. Both the hydrogen bonding and the hydrophobic interaction played important roles in forming the ordered structure. Without the hydrophobic effect, stable beta-hairpin conformations did not form in the simulations. With the same energy functions, the alanine-based peptide (AAQAA)3Y folded into helical conformations, in agreement with experiments. Folding into an alpha-helix or a beta-hairpin is amino acid sequence-dependent.

Dissecting the stability of a beta-hairpin peptide that folds in water: NMR and molecular dynamics analysis of the beta-turn and beta-strand contributions to folding

NMR studies of the folding and conformational properties of a beta-hairpin peptide, several peptide fragments of the hairpin, and sequence-modified analogues, have enabled the various contributions to beta-hairpin stability in water to be dissected. Temperature and pH-induced unfolding studies indicate that the folding-unfolding equilibrium approximates to a two-state model. The hairpin is highly resistant to denaturation and is still significantly folded in 7 M urea at 298 K. Thermodynamic analysis shows the hairpin to fold in water with a significant change in heat capacity, however, DeltaCp degrees in 7 M urea is reduced. V/Y-->A mutations on one strand of the hairpin reduce folding to <10 %, consistent with a hydrophobic stabilisation model. We show that in a truncated peptide (residues 6-16) lacking the hydrophobic residues on one beta-strand, the type I' Asn-Gly turn in the sequence SINGKK is significantly populated in water in the absence of interstrand hydrophobic contacts. Unrestrained molecular dynamics simulations of unfolding, using an explicit solvation model, show that the conformation of the NG turn persists for longer than the AG analogue, which has a much lower propensity for type I' turn formation from a data base analysis of preferred turns. The origin of the high stability of the Asn-Gly turn is not entirely clear; data base analysis of 66 NG turns, together with molecular dynamics simulations, reveals no participation of the Asn side-chain in turn-stabilising interactions with the peptide backbone. However, hydration analysis of the molecular dynamics simulations reveals a pocket of "high density" water bridging between the Asn side-chain and peptide main-chain that suggests solvent-mediated interactions may play an important role in modulating phi,psi propensities in the NG turn region.

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.

On the pH-conformational dependence of the unblocked SYPYD peptide

Simulations were carried out for an unblocked pentapeptide with the sequence Ser-Tyr-Pro-Tyr-Asp (SYPYD) with explicit consideration of the coupling between the conformation of the molecule and the ionization equilibria at a given pH. The available NMR experimental data indicate a high preference for the cis isomeric turn-like form of Tyr-Pro at intermediate pH (approximately 6) and a destabilization of the cis form at both high (approximately 9) and low (approximately 3) pH. In order to identify the source of the stability of the conformation of this pentapeptide as a function of pH, Monte Carlo simulations were used to generate an ensemble of low-energy conformations at different pH values (viz. 3, 6 and 9). The total free energy function used in these calculations includes terms that account for the solvation free energy and free energy of ionization. These terms are evaluated by means of a fast multigrid boundary element (MBE) method. In good qualitative agreement with the experiments, our results indicate that the Boltzmann averaged population of the cis isomeric form of the pentapeptide has a maximum (45 %) at pH 6 and is significantly smaller (25 % and 23 %) for higher and lower pH values, respectively, following the trend of the experimental data. Also, the degree of charge for the lowest-energy conformations, as well as the contribution of electrostatic interactions to the stability of the preferred conformations, vary widely at the different pH values. Different kinds of packing of the aromatic side-chains of Tyr2 and Tyr4 against the proline ring are observed at different pH values, indicating that their contribution to the stability of the low-energy conformations is also pH-dependent. In summary, our results provide a basis for discussing the nature of the interactions that stabilize turn-like conformations of the peptide SYPYD as a function of pH.

ES/IS: estimation of conformational free energy by combining dynamics simulations with explicit solvent with an implicit solvent continuum model

This paper reviews a recently developed method for calculating the total conformational free energy of a solute macromolecule in water solvent. The method consists of a relatively short simulation by molecular dynamics with explicit solvent molecules (ES) to produce a set of microstates of the macroscopic conformation. Conformational internal solute energy and entropy are obtained from the simulation, the latter in the quasi-harmonic approximation by analysis of the covariance matrix. The implicit solvent (IS) surface energy-dielectric continuum model is used to calculate the average solvation free energy as the sum of the free energies of creating the solute-size hydrophobic cavity, of the van der Waals solute-solvent interactions and of the polarization of water solvent by the solute's charges. We have earlier applied this method to calculate the conformational free energy of native and intentionally misfolded globular conformations of proteins (the EMBL set of deliberately misfolded proteins), and have obtained good discrimination in favor of the native conformations in all instances. These results are summarized and further analyzed to show that, on average, three major component terms of the free energy all contribute in favor of discrimination. We discuss possible improvements of the ES/IS method. It is shown how the force field can be made self-consistent by adapting the parameters for calculation of surface and polarization free energies closely to the molecular mechanics force field used in the dynamics simulation, using established simulation methods to compute free energies for cavity formation and a charging process with the molecular mechanics force field to provide a set of (quasi-experimental) reference data that can be used to refine the parameters of the continuum models. The molecular surface area together with a microscopic surface free energy near 70 cal/(mol A2) is found to be a consistent descriptor of the cavity free energy. Preliminary results indicate that a linear-response approximation for the polarization of water solvent reaction near typical polar and charged protein groups is accurate to within approximately 90%.

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.

Comparison of ring current methods for use in molecular modeling refinement of NMR derived three-dimensional structures

A comparison between three different methods commonly used to estimate ring current effects on chemical shifts is presented. Haigh-Mallion, Johnson-Bovey, and classical point-dipole approximations were used to estimate the ring current contribution to chemical shifts for protons in several proteins for which both detailed X-ray crystal structures and chemical shift assignments were available. For the classical point-dipole model, new proportionality constants were calculated by fitting to ring current estimations from both the quantum-mechanical Haigh-Mallion and semiclassical Johnson-Bovey methods and compared with the previously used point-dipole constant of Perkins and Dwek. Statistical analysis of the predictions obtained by all methods indicates that the point-dipole approximation parametrized against quantum-mechanical data is superior to the previously used classical model, comparable to Johnson-Bovey calculations, and slightly poorer than predictions from the Haigh-Mallion theory. The implementation of a pseudoenergy penalty term for use in structure refinement from chemical shift data based on the classical point-dipole model is described, and its usefulness in cases where other NMR information is limited is discussed with a specific example.

Side-chain effects on peptidyl-prolyl cis/trans isomerisation

Peptidyl-prolyl cis/trans isomerisation has been frequently found as a rate limiting step in the folding of proteins. In order to determine whether the nature of the amino acid preceding proline controls the probability of cis prolyl bonds in native proteins, systematic studies on the thermodynamics and kinetics of the prolyl isomerisation in the pentapeptide series Ac-Ala-Xaa-Pro-Ala-Lys-NH2 were performed. All proteinogenic amino acids were substituted in the position preceding proline. When measured by 1H-NMR and CD spectroscopy both isomers proved to be devoid of ordered structure in the whole series of the oligopeptides in aqueous solution. Thus, isomerization rates and cis/trans ratios calculated from solvent jump and 1H-NMR magnetisation transfer experiments exclusively reflect the side-chain effects of the Xaa position in the peptide series. There is a rough correlation between the cis content in the oligopeptides and the propensity of Xaa-Pro cis prolyl bonds in proteins. This correlation suggests that the prolyl bond conformation is mainly determined by local effects in proteins. The rate constants kc-->t of pentapeptides containing unionised amino acids preceding proline range from 3.2 x 10(-3) s-1 (Xaa = Ala) to 0.5 x 10(-3) s-1 (Xaa = Trp) at 4 degrees C. Proline clustering led to an isomerisation cycle indicating considerable influence on the isomerisation rates of the peptide bond conformations flanking the rotating bond. Both tyrosine and histidine specifically reduce isomerisation rates severalfold by deprotonation of their respective side-chains.