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.     

Determination of conformational equilibrium of peptides in solution by NMR spectroscopy and theoretical conformational analysis: application to the calibration of mean-field solvation models.

Peptides occur in solution as ensembles of conformations rather than in a fixed conformation. The existing energy functions are usually inadequate to predict the conformational equilibrium in solution, because of failure to account properly for solvation, if the solvent is not considered explicitly (which is usually prohibitively expensive). NMR data are therefore widely incorporated into theoretical conformational analysis. Because of conformational flexibility, restrained molecular dynamics (with restraints derived from NMR data), which is usually applied to determine protein conformation is of limited use in the case of peptides. Instead, (a) the restraints are averaged within predefined time windows during molecular dynamics (MD) simulations (time averaging), (b) multiple-copy MD simulations are carried out and the restraints are averaged over the copies (ensemble averaging), or (c) a representative ensemble of sterically feasible conformations is generated and the weights of the conformations are then fitted so that the computed average observables match the experimental data (weight fitting). All these approaches are briefly discussed in this article. If an adequate force field is used, conformations with large statistical weights obtained from the weight-fitting procedure should also have low energies, which can be implemented in force field calibration. Such a procedure is particularly attractive regarding the parameterization of the solvation energy in nonaqueous solvents, e.g., dimethyl sulfoxide, for which thermodynamic solvation data are scarce. A method for calibration of solvation parameters in dimethyl sulfoxide, which is based on this principle was recently proposed by C. Baysal and H. Meirovitch (Journal of the American Chemical Society, 1998, Vol. 120, pp. 800--812), in which the energy gap between the conformations compatible with NMR data and the alternative conformations is maximized. In this work we propose an alternative method based on the principle that the best-fitting statistical weights of conformations should match the Boltzmann weights computed with the force field applied. Preliminary results obtained using three test peptides of varying conformational mobility: H-Ser(1)-Pro(2)-Lys(3)-Leu(4)-OH, Ac-Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)-NH(2), and cyclo(Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)) are presented.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Unrestrained stochastic dynamics simulations of the UUCG tetraloop using an implicit solvation model.

Three unrestrained stochastic dynamics simulations have been carried out on the RNA hairpin GGAC[UUCG] GUCC, using the AMBER94 force field (Cornell et al., 1995. J. Am. Chem. Soc. 117:5179-5197) in MacroModel 5.5 (Mohamadi et al., 1990. J. Comp. Chem. 11:440-467) and either the GB/SA continuum solvation model (Still et al., 1990. J. Am. Chem. Soc. 112:6127-6129) or a linear distance-dependent dielectric (1/R) treatment. The linear distance-dependent treatment results in severe distortion of the nucleic acid structure, restriction of all hydroxyl dihedrals, and collapse of the counterion atmosphere over the course of a 5-ns simulation. An additional vacuum simulation without counterions shows somewhat improved behavior. In contrast, the two GB/SA simulations (1.149 and 3.060 ns in length) give average structures within 1.2 A of the initial NMR structure and in excellent agreement with results of an earlier explicit solvent simulation (Miller and Kollman, 1997. J. Mol. Biol. 270:436-450). In a 3-ns GB/SA simulation starting with the incorrect UUCG tetraloop structure (Cheong et al., 1990. Nature. 346:680-682), this loop conformation converts to the correct loop geometry (Allain and Varani, 1995. J. Mol. Biol. 250:333-353), suggesting enhanced sampling relative to the previous explicit solvent simulation. Thermodynamic effects of 2'-deoxyribose substitutions of loop nucleotides were experimentally determined and are found to correlate with the fraction of time the ribose 2'-OH is hydrogen bonded and the distribution of the hydroxyl dihedral is observed in the GB/SA simulations. The GB/SA simulations thus appear to faithfully represent structural features of the RNA without the computational expense of explicit solvent.     

Understanding the thermodynamic stability of an RNA hairpin and its mutant.

The thermodynamic stability of RNA hairpin loops has been a subject of considerable interest in the recent past (Wimberly et al., 1991). There have been experimental reports indicating that the hairpins with a C(UUCG)G loop sequence are thermodynamically very stable (Wimberly et al., 1991). We used the solution structure of GGAC(UUCG)GUCC (Cheong et al., 1990; Varani et al., 1991) as the starting conformation in our attempt to understand its thermodynamic stability. We carried out molecular dynamics/free energy simulations to understand the basis for the destabilization of the C(UUCG)G loop by mutating cytosine (C7)-->uracil. Because of the limited length of simulation and the presence of kinetic barriers (solvent intervention) to the uracil-->cytosine mutation, all of our computed free energy differences are based on multiple forward simulations. Based on these calculations we find that the cytosine-->uracil mutation in the loop destabilizes it by approximately 1.5kcal/mol relative to that of the reference state, an A-form RNA but with cytosine (C7) looped out. This is the same sign and magnitude as that observed in the thermodynamic studies carried out by Varani et al.(1991). We have carried out free energy component analysis to understand the effect of mutating the cytosine residue to uracil on the thermodynamic stability of the C(UUCG)G hairpin loops. Our calculations show that the most significant contribution to the stability is from the phosphate group linking U5 and U6, which favors the cytosine residue over uracil by about 6.0 kcal/mol. The residues U5, U6, and G8 in the loop region also contribute significantly to the stability. The contributions from the salt and solvent compensate each other, indicating the dynamic nature of interactions of the environment with the nucleic acid system and the coupling between these two components.     

Experimental and computational studies of the G[UUCG]C RNA tetraloop

In prokaryotic ribosomal RNAs, most UUCG tetraloops are closed by a C-G base-pair. However, this preference is greatly reduced in eukaryotic rRNA species where many UUCG tetraloops are closed by G-C base-pairs. Here, biophysical properties of the C[UUCG]G and G[UUCG]C tetraloops are compared, using experimental and computational methods. Thermal denaturation experiments are used to derive thermodynamic parameters for the wild-type G[UUCG]C tetraloop and variants containing single deoxy substitutions in the loop. A comparison with analogous experiments on the C[UUCG]G motif shows that the two RNA species exhibit similar patterns in response to the substitutions, suggesting that their loop structures are similar. This conclusion is supported by NMR data that suggest that the essential UUCG loop structure is maintained in both tetraloops. However, NMR results show that the G[UUCG]C loop structure is disrupted prior to melting of the stem; this behavior is in contrast to the two-state behavior of the C[UUCG]G molecule. Stochastic dynamics simulations using the GB/SA continuum solvation model, run as a function of temperature, show rare conformational transitions in several G[UUCG]C simulations. These results lead to the conclusion that substitution of a G-C for a C-G closing base-pair increases the intrinsic flexibility of the UUCG loop.     

Ab initio self-consistent field and potential-dependent partial equalization of orbital electronegativity calculations of hydration properties of N-acetyl-N'-methyl-alanineamide

Using a recently developed parallel computation algorithm, ab initio self-consistent field (SCF) calculations were carried out to estimate the relative hydration energies for 12 low-energy conformations of N-acetyl-N'-methyl-alanineamide. The requisite SCF calculations were carried out using 6-31G and 6-31G* basis sets, both in the absence and presence of a perturbing potential arising from a model solvent. The alpha R, alpha L, polyproline II (PII), and pi helical conformations were preferentially stabilized by the solvent potential, whereas conformations with intramolecular hydrogen-bonding C5 and C7 were preferred in the gas phase. Average vicinal nmr coupling constants (JNH-C alpha H), calculated using the total energies of the various solvated conformations, were consistent with observed coupling constants for this peptide in aqueous solution. Substantial alteration of the solute charge density occurred upon equilibration with the reaction field, as was exemplified in changes both in the molecular dipole moments and in atom-centered multipoles, when the molecule was transferred from a medium of low dielectric constant to one of high dielectric constant. In order to model these changes in charge density with an empirical scheme, we have implemented a novel monopolar representation of the solute charge density based on a potential-dependent form of partial equalization of orbital electronegativities (PDPEOE). In the atom-centered point charge PDPEOE representation, charge flows from one region of the solute to another in response to external fields. Hydration energies calculated using the PDPEOE representation are similar to those calculated by the SCF procedure. Also, the PDPEOE calculations yielded changes in molecular dipole moments upon solvation that agreed closely with the changes in the calculated ab initio SCF dipole moments.     

Simulation of Solvation Dynamics in H-Bonding Solvents: Dynamics of Solute–Solvent H-Bonds in Methanol–Water Mixtures

Molecular dynamics (MD) simulations have been undertaken in order to investigate the collective solvent reorganization following an instantaneous electronic charge transfer between distinct atomic sites of diatomic probe molecules immersed in methanol–water mixtures. Our previous studies of solvation dynamics in these mixtures [28,29] are extended here to the analysis of nonequilibrium time-dependent solute–solvent site–site pair distribution functions for the equimolar mixture using two different solute sizes. This has allowed us to obtain a more detailed picture of the solvent reorganization in response to the solute's excitation. Special attention is devoted to the dynamics of rupture and formation of hydrogen bonds between the smaller probe solute and solvent molecules, and its relationship to the molecular mechanisms of solvation dynamics in these systems on distinct time scales. This revised version was published online in June 2006 with corrections to the Cover Date.     

DFTMD studies of glucose and epimers: anomeric ratios, rotamer populations, and hydration energies

Results are presented from density functional molecular dynamics (DFTMD) simulations, based on constant energy dynamics, of glucose and its cyclic form of 6-carbon epimers. Both in vacuo and an implicit solvent method (COSMO) were examined, including simulations of low-energy conformations of each molecule. Analysis of the DFTMD results includes the following: energies averaged over the simulation time, calculated anomeric ratios, hydroxyl and hydroxymethyl rotamer populations, and hydration energies. Hydrogen-bonding networks persistence times were examined, and the effects of solvation on rotamer populations were described. Anomeric ratios calculated from energy optimization of an ensemble of low-energy conformers are compared to those obtained from ensemble averages from molecular dynamics, with dynamics simulations giving populations in best agreement with experimental anomeric ratios. Ensemble results in vacuo were not in agreement with experimental anomeric ratios or hydroxymethyl populations, producing in some cases reversal of the α:β ratios. The difficulty in obtaining correct α:β ratios increases with the number of axial groups; the mono-axial epimers being best represented, epimers with two axial groups being more difficult, and the epimers with three axial hydroxyl groups being most difficult to analyze, the result of a large number of very strong hydrogen-bonding networks that form the ensemble of low-energy conformations in the multi-axial structures.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Implicit solvent models

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.     

Atomic-scale analysis of the solvation thermodynamics of hydrophobic hydration.

Molecular dynamics simulations are used to model the transfer thermodynamics of krypton from the gas phase into water. Extra long, nanosecond simulations are required to reduce the statistical uncertainty of the calculated "solvation" enthalpy to an acceptable level. Thermodynamic integration is used to calculate the "solvation" free energy, which together with the enthalpy is used to calculate the "solvation" entropy. A comparison series of simulations are conducted using a single Lennard-Jones sphere model of water to identify the contribution of hydrogen bonding to the thermodynamic quantities. In contrast to the classical "iceberg" model of hydrophobic hydration, the favorable enthalpy change for the transfer process at room temperature is found to be due primarily to the strong van der Waals interaction between the solute and solvent. Although some stabilization of hydrogen bonding does occur in the solvation shell, this is overshadowed by a destabilization due to packing constraints. Similarly, whereas some of the unfavorable change in entropy is attributed to the reduced rotational motion of the solvation shell waters, the major component is due to a decrease in the number of positional arrangements associated with the translational motions.     

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.     

Structure of a small RNA hairpin.

The hairpin stem-loop form of the RNA oligonucleotide rCGC(UUU)GCG has been studied by NMR spectroscopy. In 10 mM phosphate buffer this RNA molecule forms a unimolecular hairpin with a stem of three base pairs and a loop of three uridines, as judged by both NMR and UV absorbance melting behavior. Distance and torsion angle restraints were determined using homonuclear proton-proton and heteronuclear proton-phosphorus 2-D NMR. These values were used in restrained molecular dynamics to determine the structure of the hairpin. The stem has characteristics of A-form geometry, although distortion from A-form occurs in the 3'-side of the stem, presumably to aid in accommodating the small loop. The loop nucleotides adopt C2'-endo conformations. NOE's strongly suggest stacking of the uracils with the stem, especially the first uracil on the 5'-side of the loop. The reversal of the chain direction in the loop seems to occur between U5 and U6. Loop structures produced by molecular dynamics simulations had a wide range of conformations and did not show stacking of the uracils. A flexible loop with significant dynamics is consistent with all the data.     

Combined theoretical studies on solvation and hydrogen bond interactions in glycine tripeptide

The theoretical conformational analysis of glycine tripeptide (GT) has been carried out by molecular dynamics (MD) method in order to find minimum energy conformations. The MD studies on GT with water have been carried out for over 10 ns with a time step of 2 fs using fixed charge force field (AMBER ff03). By adding the solvation effect using water as a solvent, the GT conformers identified in this study exhibit α-helical conformation. Compared with the earlier reports, this MD study is able to identify the energetically favourable GT conformations. The obtained geometry of the five most stable GT conformations was optimised using the density functional theory method at B3LYP/6-311G** level of theory. Subsequently, the effects of solvation on the conformational characteristics of five most stable GT conformers with four water molecules (the number of water molecules in the first solvation shell of GT obtained from MD study) were investigated using the same method and the same level of theory. The effect of microsolvation on the fifth GT conformer has been studied with a cluster of 11 water molecules as the first hydration shell which generates folded structure. The interaction energies of all the complexes are calculated by correcting the basis set superposition error. The strong hydrogen bond mainly contributes to the interaction energies. The atoms in molecules theory and natural bond orbital analysis were used to study the origin of H-bonds. A good correlation between the structural parameters and the properties of charge density is found. NMR calculations show that the C = O carbons of the amine groups of the first and middle glycine fragments have maximum chemical shifts.