Assessment of Four Theoretical Approaches to Predict Protein Flexibility in the Crystal Phase and Solution.

In this paper, we evaluated the ability of four coarse-grained methods to predict protein flexible regions with potential biological importance, UNRES-flex, UNRES-DSSP-flex (based on the united residue model of polypeptide chains without and with secondary structure restraints, respectively), CABS-flex (based on the C-α, C-ß, and side chain model), and nonlinear rigid block normal mode analysis (NOLB) with a set of 100 protein structures determined by NMR spectroscopy or X-ray crystallography, with all secondary structure types. End regions with high fluctuations were excluded from analysis. The Pearson and Spearman correlation coefficients were used to quantify the conformity between the calculated and experimental fluctuation profiles, the latter determined from NMR ensembles and X-ray B-factors, respectively. For X-ray structures (corresponding to proteins in a crowded environment), NOLB resulted in the best agreement between the predicted and experimental fluctuation profiles, while for NMR structures (corresponding to proteins in solution), the ranking of performance is CABS-flex > UNRES-DSSP-flex > UNRES-flex > NOLB; however, CABS-flex sometimes exaggerated the extent of small fluctuations, as opposed to UNRES-DSSP-flex.

Molecular simulations of rhodopsin tetrameter.

Di/oligomerization of G-protein coupled receptors (GPCRs) is well established, however very little is known regarding the interaction details. Current paper presents results of molecular dynamics simulations of theoretical model of rhodopsin tetramer with transducine (Gt) in lipid bilayer. Ligand-protein and receptor-receptor interactions have been proposed.

Dynamic Formation and Breaking of Disulfide Bonds in Molecular Dynamics Simulations with the UNRES Force Field.

Many proteins contain disulfide bonds that are usually essential for maintaining function and a stable structure. Several algorithms attempt to predict the arrangement of disulfide bonds in the context of protein structure prediction, but none can simulate the entire process of oxidative folding, including dynamic formation and breaking of disulfide bonds. In this work, a potential function developed to model disulfide bonds is coupled with the united-residue (UNRES) force field, and used in both canonical and replica exchange molecular dynamics simulations to produce complete oxidative folding pathways. The potential function is obtained by introducing a transition barrier that separates the bonded and nonbonded states of the half-cystine residues. Tests on several helical proteins show that improved predictions are obtained when dynamic disulfide-bond formation and breaking are considered. The effect of the disulfide bonds on the folding kinetics is also investigated, particularly their role in stabilizing folding intermediates, resulting in slower folding.

Physics-based protein-structure prediction using a hierarchical protocol based on the UNRES force field: assessment in two blind tests.

Recent improvements in the protein-structure prediction method developed in our laboratory, based on the thermodynamic hypothesis, are described. The conformational space is searched extensively at the united-residue level by using our physics-based UNRES energy function and the conformational space annealing method of global optimization. The lowest-energy coarse-grained structures are then converted to an all-atom representation and energy-minimized with the ECEPP/3 force field. The procedure was assessed in two recent blind tests of protein-structure prediction. During the first blind test, we predicted large fragments of alpha and alpha+beta proteins [60-70 residues with C(alpha) rms deviation (rmsd) <6 A]. However, for alpha+beta proteins, significant topological errors occurred despite low rmsd values. In the second exercise, we predicted whole structures of five proteins (two alpha and three alpha+beta, with sizes of 53-235 residues) with remarkably good accuracy. In particular, for the genomic target TM0487 (a 102-residue alpha+beta protein from Thermotoga maritima), we predicted the complete, topologically correct structure with 7.3-A C(alpha) rmsd. So far this protein is the largest alpha+beta protein predicted based solely on the amino acid sequence and a physics-based potential-energy function and search procedure. For target T0198, a phosphate transport system regulator PhoU from T. maritima (a 235-residue mainly alpha-helical protein), we predicted the topology of the whole six-helix bundle correctly within 8 A rmsd, except the 32 C-terminal residues, most of which form a beta-hairpin. These and other examples described in this work demonstrate significant progress in physics-based protein-structure prediction.

The protein folding problem: global optimization of the force fields.

The evolutionary development of a theoretical approach to the protein folding problem, in our laboratory, is traced. The theoretical foundations and the development of a suitable empirical all-atom potential energy function and a global optimization search are examined. Whereas the all-atom approach has thus far succeeded for relatively small molecules and for alpha-helical proteins containing up to 46 residues, it has been necessary to develop a hierarchical approach to treat larger proteins. In the hierarchical approach to single- and multiple-chain proteins, global optimization is carried out for a simplified united residue (UNRES) description of a polypeptide chain to locate the region in which the global minimum lies. Conversion of the UNRES structures in this region to all-atom structures is followed by a local search in this region. The performance of this approach in successive CASP blind tests for predicting protein structure by an ab initio physics-based method is described. Finally, a recent attempt to compute a folding pathway is discussed.

The investigation of the effects of counterions in protein dynamics simulations.

Molecular simulations able to exactly represent solvated charged proteins are helpful in understanding protein dynamics, structure and function. In the present study we have used two different starting structures of papain (a typical, stable, globular protein of intermediate net charge) and different modeling procedures to evaluate some effects of counterions in simulations. A number of configurations have been generated and relaxed for each system by various combinations of constrained simulated annealing and molecular dynamics procedures, using the AMBER force field. The analysis of trajectories shows that the simulations of solvated proteins are moderately sensitive to the presence of counterions. However, this sensitivity is highly dependent on the starting model and different procedures of equilibration used. The neutralized systems tend to evince smaller root mean square deviations regardless of the system investigated and the simulation procedure used. The results of parameterized fitting of the simulated structures to the crystallographic data, giving quantitative measure of the total charge influence on the stability of various elements of the secondary structure, revealed a clear scatter of different reactions of various systems' secondary structures to counterions addition: some systems apparently were stabilized when neutralized, while the others were not. Thus, one cannot unequivocally state, despite consideration of specific simulation conditions, whether protein secondary structures are more stable when they have neutralized charges. This suggests that caution should be taken when claiming the stabilizing effect of counterions in simulations other than those involving small, unstable polypeptides or highly charged proteins.

Conformation-family Monte Carlo: a new method for crystal structure prediction.

A new global optimization method, Conformation-family Monte Carlo, has been developed recently for searching the conformational space of macromolecules. In the present paper, we adapted this method for prediction of crystal structures of organic molecules without assuming any symmetry constraints except the number of molecules in the unit cell. This method maintains a database of low energy structures that are clustered into families. The structures in this database are improved iteratively by a Metropolis-type Monte Carlo procedure together with energy minimization, in which the search is biased toward the regions of the lowest energy families. The Conformation-family Monte Carlo method is applied to a set of nine rigid and flexible organic molecules by using two popular force fields, AMBER and W99. The method performed well for the rigid molecules and reasonably well for the molecules with torsional degrees of freedom.

Synthesis, activity on NK-3 tachykinin receptor and conformational solution studies of scyliorhinin II analogs modified at position 16.

Two analogs of a tachykinin family peptides - scyliorhinin II (ScyII): [Aib(16)]ScyII and [Sar(16)]ScyII were synthesized by the solid-phase method using Fmoc chemistry. Conformational studies in water and DMSO-d(6) on these peptides were performed using a combination of two-dimensional NMR and theoretical conformational analysis. The solution structure of the peptides studied is interpreted as an equilibrium of several conformers with different statistical weights. The structure of [Sar(16)]ScyII in water appeared to be more flexible, especially in the C-terminal fragment. A better defined structure for this analog was obtained in DMSO-d(6), in which the analysis resulted in a family of conformers with similar shapes. Some of these conformers were characterized by the presence of a 3(10)-helix in the N-terminal fragment and middle part of the molecule. The introduction of the Aib residue in position 16 significantly rigidifies the structure. For [Aib(16)]ScyII in both solvent systems very similar populations of conformations were obtained which are characterized by the presence of a 3(10)-helix in the 13-18 fragment. A common structural motif was found in conformationally constrained Cys(7)-Cys(13) fragment, which resembles the Greek letter 'omega'. The differences in the solution structure of the C-terminal fragment of the peptides studied are responsible for their specificity. [Aib(16)]ScyII showed 25% the agonistic activity of selective NK-3 agonist - senktide, but it also showed antagonist effect vs. this peptide, whereas [Sar(16)]ScyII appeared to be a full agonist of NK-3 tachykinin receptor.

Fluorescence decay time distribution analysis of cyclic enkephalin analogues; influence of solvent and Leu configuration in position 5 on conformation.

Lifetime distribution analysis were performed to study the influence of Leu configuration in position 5 on changes of the peptide chain of cyclic analogues of enkephalins containing a fluorescence donor and acceptor in different solvents. The configuration change of Leu5 in all the analogues of enkephalins studied which contain donor-acceptor pairs has no apparent influence on Trp lifetime distributions. In contrast, there is a significant solvent effect on the shape of lifetime distribution.

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.

Influence of solvent and configuration of residues at positions 2 and 3 on distance and mobility of pharmacophore groups at positions 1 and 4 in cyclic enkephalin analogues.

The analgesic activity of opioid peptides is mainly connected with their affinity and selectivity for the mu-receptors. The biological activity of cyclic opioid analogues depends on mutual orientation and conformational freedom of aromatic pharmacophore groups at positions 1 and 4. The distance and distance distributions between chromophores at positions 1 [Phe(p-NO(2)), p-nitrophenylalanine] and 4 [Nal, beta-(2-naphthyl)alanine], which constitute an energy donor-acceptor pair, were calculated based on measured fluorescence intensity decays of a donor (Nal). The influence of the solvent and configuration of the residues at position 2 and 3 on donor-acceptor distance distribution and mobility of pharmacophore groups at position 1 and 4 in cyclic enkephalin analogues are discussed.

Recent improvements in prediction of protein structure by global optimization of a potential energy function.

Recent improvements of a hierarchical ab initio or de novo approach for predicting both alpha and beta structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic alpha-helical protein of 70 residues was predicted to within 4.3 A alpha-carbon (C(alpha)) rms deviation (rmsd) whereas, for other alpha-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 A C(alpha) rmsd. Whereas beta structures can now be predicted with the new procedure, the success rate for alpha/beta- and beta-proteins is lower than that for alpha-proteins at present. For the beta portions of alpha/beta structures, the C(alpha) rmsd's are less than 6.0 A for contiguous fragments of 30-40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a C(alpha) rmsd less than 6.0 A. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.

Influence of solvents and leucine configuration at position 5 on tryptophan fluorescence in cyclic enkephalin analogues.

The fluorescence decay of tryptophan is a sensitive indicator of its local environment within a peptide or protein. In this study we carried out fluorescence measurements of the tryptophan residue of cyclic enkephalin analogues of a general formula X-c[D-Dab(2)-Gly(3)-Trp(4)-Y(5)] where X = Cbz or H and Y = D- or L-Leu, in four solvents [water, methanol, acetonitrile, and dimethyl sulfoxide (DMSO)]. An analysis of the tryptophan fluorescence decays using a discrete-exponential model indicates that tryptophan fluorescence decay can be described by a double exponential function in all solvents studied. Lifetime distribution analysis yields a bimodal distribution in protic solvents (water and methanol), whereas an asymmetric, unimodal distribution in an aprotic solvent (DMSO) and uni- or bimodal distributions in acetonitrile solution, depending on leucine configuration. The data are interpreted in terms of the rotamer model, in which the modality and the relative proportions of the lifetime components are related to the population distribution of tryptophan chi(1) rotamers about the C(alpha)--C(beta) bond. The chirality of the Leu(5) residue and solvent properties affect the local environment of the tryptophan residue and therefore influence the distribution of side-chain rotamers. These results are consistent with the results of theoretical conformational calculations.

Solution conformational study of Scyliorhinin I analogues with conformational constraints by two-dimensional NMR and theoretical conformational analysis.

Two analogues of Scyliorhinin I (Scyl), a tachykinin with N-MeLeu in position 8 and a 1,5-disubstituted tetrazole ring between positions 7 and 8, introduced in order to generate local conformational constraints, were synthesized using the solid-phase method. Conformational studies in water and DMSO-d6 were performed on these peptides using a combination of the two-dimensional NMR technique and theoretical conformational analysis. The algorithm of conformational search consisted of the following three stages: (i) extensive global conformational analysis in order to find all low-energy conformations; (ii) calculation of the NOE effects and vicinal coupling constants for each of the low energy conformations; (iii) determining the statistical weights of these conformations by means of a nonlinear least-squares procedure, in order to obtain the best fit of the averaged simulated spectrum to the experimental one. In both solvents the three-dimensional structure of the analogues studied can be interpreted only in terms of an ensemble of multiple conformations. For [MeLeu8]Scyl, the C-terminal 6-10 fragment adopts more rigid structure than the N-terminal one. In the case of the analogue with the tetrazole ring in DMSO-d6 the three-dimensional structure is characterized by two dominant conformers with similar geometry of their backbones. They superimpose especially well (RMSD = 0.28 A) in the 6-9 fragments. All conformers calculated in both solvents superimpose in their C-terminal fragments much better than those of the first analogue. The results obtained indicate that the introduction of the tetrazole ring into the Scyl molecule rigidifies its structure significantly more than that of MeLeu.

Molecular simulation study of cooperativity in hydrophobic association.

To investigate the cooperativity of hydrophobic interactions, the potential of mean force of two- and three-molecule methane clusters in water was determined by molecular dynamics simulations using two methods: umbrella-sampling with the weighted histogram analysis method and thermodynamic integration. Two water models, TIP3P and TIP4P, were used, while each methane molecule was modeled as a united atom. It was found that the three-body potential of mean force is not additive, i.e., it cannot be calculated as a sum of two-body contributions, but requires an additional three-body cooperative term. The cooperative term, which amounts to only about 10% of the total hydrophobic association free energy, was found to increase the strength of hydrophobic association; this finding differs from the results of earlier Monte Carlo studies with the free energy perturbation method of Rank and Baker (1997). As in the work of Rank and Baker, the solvent contribution to the potential of mean force was found to be well approximated by the molecular surface of two methane molecules. Moreover, we also found that the cooperative term is well represented by the difference between the molecular surface of the three-methane cluster and those of all three pairs of methane molecules. In addition, it was found that, while there is a cooperative contribution to the hydrophobic association free energy albeit a small one, the errors associated with the use of pairwise potentials are comparable to or larger than this contribution.

Theoretical studies of binding modes of two covalent inhibitors of cysteine proteases.

Physiological and pathological roles of cysteine proteases make them important targets for inhibitor development. Although highly potent inhibitors of this group of enzymes are known, their major drawback is a lack of sufficient specificity. Two cysteine protease covalent inhibitors, viz. (i) Z-RL-deoxo-V-peptide-epoxysuccinyl hybrid, and (ii) Z-RLVG-methyl-, have been developed and modeled in the catalytic pocket of papain, an archetypal thiol protease. A number of configurations have been generated and relaxed for each system using the AMBER force field. The catalytic pockets S3 and S4 appear rather elusive in view of the observed inhibitors' flexibility. This suggest rather limited chances for the development of selective structure-based inhibitors of thiol proteases, designed to exploit differences in the structure of catalytic pockets of various members of this family.

Molecular dynamics simulation studies of lipid bilayer systems.

The main structural element of biological membranes is a liquid-crystalline lipid bilayer. Other constituents, i.e. proteins, sterols and peptides, either intercalate into or loosely attach to the bilayer. We applied a molecular dynamics simulation method to study membrane systems at various levels of compositional complexity. The studies were started from simple lipid bilayers containing a single type phosphatidylcholine (PC) and water molecules (PC bilayers). As a next step, cholesterol (Chol) molecules were introduced to the PC bilayers (PC-Chol bilayers). These studies provided detailed information about the structure and dynamics of the membrane/water interface and the hydrocarbon chain region in bilayers built of various types of PCs and Chol. This enabled studies of membrane systems of higher complexity. They included the investigation of an integral membrane protein in its natural environment of a PC bilayer, and the antibacterial activity of magainin-2. The latter study required the construction of a model bacterial membrane which consisted of two types of phospholipids and counter ions. Whenever published experimental data were available, the results of the simulations were compared with them.

Binding modes of a new epoxysuccinyl-peptide inhibitor of cysteine proteases. Where and how do cysteine proteases express their selectivity?

Papain from Carica papaya, an easily available cysteine protease, is the best-studied representative of this family of enzymes. The three dimensional structure of papain is very similar to that of other cysteine proteases of either plant (actinidin, caricain, papaya protease IV) or animal (cathepsins B, K, L, H) origin. As abnormalities in the activities of mammalian cysteine proteases accompany a variety of diseases, there has been a long-lasting interest in the development of potent and selective inhibitors for these enzymes. A covalent inhibitor of cysteine proteases, designed as a combination of epoxysuccinyl and peptide moieties, has been modeled in the catalytic pocket of papain. A number of its configurations have been generated and relaxed by constrained simulated annealing-molecular dynamics in water. A clear conformational variability of this inhibitor is discussed in the context of a conspicuous conformational diversity observed earlier in several solid-state structures of other complexes between cysteine proteases and covalent inhibitors. The catalytic pockets S2 and even more so S3, as defined by the pioneering studies on the papain-ZPACK, papain-E64c and papain-leupeptin complexes, appear elusive in view of the evident flexibility of the present inhibitor and in confrontation with the obvious conformational scatter seen in other examples. This predicts limited chances for the development of selective structure-based inhibitors of thiol proteases, designed to exploit the minute differences in the catalytic pockets of various members of this family. A simultaneous comparison of the three published proenzyme structures suggests the enzyme's prosegment binding loop-prosegment interface as a new potential target for selective inhibitors of papain-related thiol proteases.

Essential dynamics/factor analysis for the interpretation of molecular dynamics trajectories.

Subject of this work is the analysis of molecular dynamics (MD) trajectories of neurophysins I (NPI) and II (NPII) and their complexes with the neurophyseal nonapeptide hormones oxytocin (OT) and vasopresssin (VP), respectively, simulated in water. NPs serve in the neurosecretory granules as carrier proteins for the hormones before their release to the blood. The starting data consisted of two pairs of different trajectories for each of the (NPII/VP)2 and (NPI/OT)2 heterotetramers and two more trajectories for the NPII2 and NPI2 homodimers (six trajectories in total). Using essential dynamics which, to our judgement, is equivalent to factor analysis, we found that only about 10 degrees of freedom per trajectory are necessary and sufficient to describe in full the motions relevant for the function of the protein. This is consistent with these motions to explain about 90% of the total variance of the system. These principal degrees of freedom represent slow anharmonic motional modes, clearly pointing at distinguished mobility of the atoms involved in the protein's functionality.