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PubMed1997

Tertiary structure prediction using mean-force potentials and internal energy functions: successful prediction for coiled-coil geometries.

We report a preliminary study of the use of mean-force potentials (MFPs) for predicting protein tertiary structure. For three leucine zipper sequences, we have calculated ensembles of structures spanning all possible backbone conformations consistent with the canonical coiled-coil geometry. MFPs were measured with the program PROSA. The MFP alone was poor at discriminating the native structure from very divergent structures, and the global minimum of the MFP sometimes occurred far from the native structure. We found that adding an internal energy function (a subset of the CHARMM potential that describes only interactions between backbone atoms), the resultant total energy (CHARMM+PROSA) performed much better; in each case, there was a clear positive correlation between total energy and root-mean-square deviation (RMSD) from the experimental structure, and the lowest-energy structures were about 1 A RMSD from the experimental structures. Thus, we conclude that the combined potential is a powerful method for predicting leucine zippers and is very promising for general 3D structure prediction.

Leucine Zippers↗

PubMed2005

Morpheeins--a new structural paradigm for allosteric regulation.

Classic models for the allosteric regulation of protein function consider an equilibrium among protein structures of constant oligomeric multiplicity. The morpheein (mor-phee'-in) concept expands this model to include a dynamic equilibrium of protein structures wherein a protein monomer can exist in more than one conformation and each monomer conformation dictates a different quaternary structure of finite multiplicity and different functionality. The morpheein concept provides a new framework for understanding allosteric regulation, kinetic cooperativity and hysteresis. Porphobilinogen synthase constitutes a prototype morpheein ensemble comprising several interconverting quaternary structure isoforms; one monomer conformation dictates assembly of a high-activity octamer, whereas an alternative monomer conformation dictates assembly of a low-activity hexamer. It is proposed here that the behavior of some other allosteric enzymes reflect dynamic morpheein equilibrium systems and six candidate proteins are enumerated.

Allosteric Regulation↗

PubMed1993

A Monte Carlo method for conformational analysis of saccharides.

A Metropolis Monte Carlo (MMC) algorithm was applied to explore conformational spaces spanned by the exocyclic dihedral angles of four disaccharides alpha-D-Man(1-->3)-alpha-D-Man(1-->O)Me (1), alpha-D-Man(1-->2)-alpha-D-Man(1-->O)Me (2), methyl beta-cellobioside (3), and methyl beta-maltoside (4). The simulation method uses the HSEA force field and randomly samples the conformational space with an automatic preference for low-energy states. In comparison to a systematic grid search, MMC offers a much more convenient and efficient protocol for the computation of ensemble average values of experimentally accessible NMR parameters such as NOE effects or 3J coupling constants. Energy barriers of a few kcal/mol were found to be surmounted easily when running the simulations with the temperature parameter set at room temperature, whereas passing significantly higher barriers required elevated temperature parameters. Ensemble average NOE values were calculated using the MMC technique and a conventional systematic grid search showing that the MMC method adequately samples the conformational spaces of 1-4. Theoretical NOEs derived for global or local minimum conformations are different from ensemble average values, and it is shown that averaged NOEs agree significantly better with experimental data. Ensemble average NOEs for 1 derived from MMC/HSEA, and previously reported MM2CARB and AMBER calculations all showed good agreement with experimental data, with MMC/HSEA giving the closest fit.

Algorithms↗

PubMed1987

Virtual and solution conformations of oligosaccharides.

The possibility that observed nuclear Overhauser enhancements and bulk longitudinal relaxation times, parameters measured by 1H NMR and often employed in determining the preferred solution conformation of biologically important molecules, are the result of averaging over many conformational states is quantitatively evaluated. Of particular interest was to ascertain whether certain 1H NMR determined conformations are "virtual" in nature; i.e., the fraction of the population of molecules actually found at any time within the subset of conformational space defined as the "solution conformation" is vanishingly small. A statistical mechanics approach was utilized to calculate an ensemble average relaxation matrix from which (NOE)'s and (T1)'s are calculated. Model glycosidic linkages in four oligosaccharides were studied. The solution conformation at any glycosidic linkage is properly represented by a normalized, Boltzmann distribution of conformers generated from an appropriate potential energy surface. The nature of the resultant population distributions is such that 50% of the molecular population is found within 1% of available microstates, while 99% of the molecular population occupies about 10% of the ensemble microstates, a number roughly equal to that sterically allowed. From this analysis we conclude that in many cases quantitative interpretation of NMR relaxation data, which attempts to define a single set of allowable torsion angle values consistent with the observed data, will lead to solution conformations that are either virtual or reflect torsion angle values possessed by a minority of the molecular population. On the other hand, calculation of ensemble average NMR relaxation data yields values in agreement with experimental results. Observed values of NMR relaxation data are the result of the complex interdependence of the population distribution and NOE (or T1) surfaces in conformational space. In conformational analyses, NMR data can therefore be used to test different population distributions calculated from empirical potential energy functions.

Algorithms↗

PubMed2002

Optimally informative backbone structural propensities in proteins.

We use basic ideas from information theory to extract the maximum amount of structural information available in protein sequence data. From a non-redundant set of protein X-ray structures, we construct local-sequence-dependent [phi,psi] distributions that summarize the influence of local sequence on backbone conformation. These distributions, approximations of actual backbone propensities in the folded protein, have the following properties: (1) They compensate for the problem of scarce data by an optimized combination of local-sequence-dependent and single-residue specific distributions; (2) They use multi-residue information; (3) They exploit similarities in the local coding properties of amino acids by collapsing the amino acid alphabet to streamline local sequence description; (4) They are designed to contain the maximum amount of local structural information the data set allows. Our methodology is able to extract around 30 cnats of information from the protein data set out of a total 387 cnats of initial uncertainty or entropy in a finely discretized [phi,psi] dihedral angle space (18 x 18 structural states), or about 7.8%. This was achieved at the hexamer length scale; shorter as well as longer fragments produce reduced information gains. The automatic clustering of amino acids into groups, a component of the optimization procedure, reveals patterns consistent with their local coding properties. While the overall information gain from local sequence is small, there are some local sequences that have significantly narrower structural distributions than others. Distribution width varies from at least 20% less than the average overall entropy to at least 14% above. This spread is an expression of the influence of local sequence on the conformational propensities of the backbone chain. The optimal ensemble of local-sequence-specific backbone distributions produced is useful as a guide to structural predictions from sequence, as well as a tool for further explorations of the nature of the local protein code.

Algorithms↗

PubMedDate not supplied

Disaccharide conformational flexibility. II. Molecular dynamics simulations of sucrose.

Molecular dynamics simulations have been used to study the motions in vacuum of the disaccharide sucrose. Ensembles of trajectories were calculated for each of the five local minimum energy conformations identified in the adiabatic conformational energy mapping of this molecule. The model sucrose molecules were found to exhibit a variety of motions, although the global minimum energy conformation was found to be dynamically stable, and no transitions away from this structure were observed to occur spontaneously. In all but one of these vacuum trajectories, the intramolecular hydrogen bond between residues was maintained, in accord with recent nmr studies of this molecule in aqueous solution. Considerable flexibility of the furanoid ring was found in the trajectories. No "flips" to the opposite puckering for this ring were found in the simulations starting from the global minimum, although such a transition was observed for a trajectory initiated with one of the higher local minimum energy conformations. Overall, the observed structural fluctuations were consistent with the experimental picture of sucrose as a relatively rigid molecule.

Carbohydrate Conformation↗

PubMed1996

Protein folding for realists: a timeless phenomenon.

Future research on protein folding must confront two serious dilemmas. (1) It may never be possible to observe at high resolution the very important structures that form in the first few milliseconds of the refolding reaction. (2) The energy functions used to predict structure from sequence will always be approximations of the true energy function. One strategy to resolve both dilemmas is to view protein folding from a different perspective, one that no longer emphasizes time and unique trajectories through conformation space. Instead, free energy replaces time as the reaction coordinate, and ensembles of equilibrium states of partially folded proteins are analyzed in place of trajectories of one protein chain through conformation space, either in vitro or in silico. Initial characterization of the folding of staphylococcal nuclease within this alternative conceptual framework has led to an equilibrium folding pathway with several surprising features. In addition to the finding of two bundles of four hydrophobic segments containing both native and non-native interactions, a gradient in relative stability of different substructures has been identified, with the most stable interactions located toward the amino terminus and the least stable toward the carboxy terminus. Hydrophobic bundles with up-down topology and stability gradients may be two examples of numerous tactics used by proteins to facilitate rapid folding and minimize aggregation. As NMR methods for structural analysis of partially folded proteins are refined, higher resolution descriptions of the structure and dynamics of the polypeptide chain outside the native state may provide many insights into the processes and energetics underlying the self-assembly of folded structure.

Forecasting↗

PubMed1999

A molecular dynamics study of the 41-56 beta-hairpin from B1 domain of protein G.

The structural and dynamical behavior of the 41-56 beta-hairpin from the protein G B1 domain (GB1) has been studied at different temperatures using molecular dynamics (MD) simulations in an aqueous environment. The purpose of these simulations is to establish the stability of this hairpin in view of its possible role as a nucleation site for protein folding. The conformation of the peptide in the crystallographic structure of the protein GB1 (native conformation) was lost in all simulations. The new equilibrium conformations are stable for several nanoseconds at 300K (>10 ns), 350 K (>6.5 ns), and even at 450 K (up to 2.5 ns). The new structures have very similar hairpin-like conformations with properties in agreement with available experimental nuclear Overhauser effect (NOE) data. The stability of the structure in the hydrophobic core region during the simulations is consistent with the experimental data and provides further evidence for the role played by hydrophobic interactions in hairpin structures. Essential dynamics analysis shows that the dynamics of the peptide at different temperatures spans basically the same essential subspace. The main equilibrium motions in this subspace involve large fluctuations of the residues in the turn and ends regions. Of the six interchain hydrogen bonds, the inner four remain stable during the simulations. The space spanned by the first two eigenvectors, as sampled at 450 K, includes almost all of the 47 different hairpin structures found in the database. Finally, analysis of the hydration of the 300 K average conformations shows that the hydration sites observed in the native conformation are still well hydrated in the equilibrium MD ensemble.

Amino Acid Sequence↗

PubMed2005

Cages, baskets, ladders, and tubes: conformational studies of polyhedral oligomeric silsesquioxanes.

The conformational flexibility of a series of cage, basket, ladder, and tube polyhedral oligomeric silsesquioxanes (POSS) has been examined using the Low Mode:Monte Carlo conformational search method in conjunction with the MM3/GBSA(CHCl3) surface. An ensemble of low energy structures was generated and used to explore the molecular shape and flexibility of each system. The results indicate that, except for the ladder molecule, the incompletely condensed systems that are studied are relatively rigid. Even in cases where the molecule is able to adopt numerous low energy conformations, the overall shape remains cage-like and the conformations differ only by small angles or substituent orientations. The ladder molecule is the most flexible and this ensemble clusters into two families: one that is cage-like and the other that is more open and ladder-like. The conformational flexibilities in the gas and solvent phases, as approximated using the GBSA continuum solvent model, are very similar.

Journal Article↗

PubMed1998

Obligatory steps in protein folding and the conformational diversity of the transition state.

We have analyzed the existence of obligatory steps in the folding reaction of the alpha-spectrin SH3 domain by mutating Asp 48 (D48G), which is at position i+3 of an isolated two-residue type II' beta-turn. Calorimetry and X-ray analysis show an entropic stabilizing effect resulting from local changes at the dihedral angles of the beta-turn. Kinetic analysis of D48G shows that this beta-turn is fully formed in the transition state, while there is no evidence of its formation in an isolated fragment. Introduction of several mutations in the D48G protein reveals that the local stabilization has not significantly altered the transition state ensemble. All these results, together with previous analysis of other alpha-spectrin and src SH3 mutants, indicate that: (i) in the folding reaction there could be obligatory steps which are not necessarily part of the folding nucleus; (ii) transition state ensembles in beta-sheet proteins could be quite defined and conformationally restricted ('mechanic folding nucleus'); and (iii) transition state ensembles in some proteins could be evolutionarily conserved.

Amino Acid Sequence↗

PubMed2003

Conformational interconversion in compstatin probed with molecular dynamics simulations.

Compstatin is a 13-residue cyclic peptide that has the potential to become a therapeutic agent against unregulated complement activation. In our effort to understand the structural and dynamic characteristics of compstatin that form the basis for rational and combinatorial optimization of structure and activity, we performed 1-ns molecular dynamics (MD) simulations. We used as input in the MD simulations the ensemble of 21 lowest energy NMR structures, the average minimized structure, and a global optimization structure. At the end of the MD simulations we identified five conformations, with populations ranging between 9% and 44%. These conformations are as follows: 1) coil with alphaR-alphaR beta-turn, as was the conformation of the initial ensemble of NMR structures; 2) beta-hairpin with epsilon-alphaR beta-turn; 3) beta-hairpin with alphaR-alphaR beta-turn; 4) beta-hairpin with alphaR-beta beta-turn; and 5) alpha-helical. Conformational switch was possible with small amplitude backbone motions of the order of 0.1-0.4 A and free energy barrier crossing of 2-11 kcal/mol. All of the 21 MD structures corresponding to the NMR ensemble possessed a beta-turn, with 14 structures retaining the alphaR-alphaR beta-turn type, but the average minimized structure and the global optimization structures were converted to alpha-helical conformations. Overall, the MD simulations have aided to gain insight into the conformational space sampled by compstatin and have provided a measure of conformational interconversion. The calculated conformers will be useful as structural and possibly dynamic templates for optimization in the design of compstatin using structure-activity relations (SAR) or dynamics-activity relations (DAR).

Computer Simulation↗

PubMed1994

Significance of root-mean-square deviation in comparing three-dimensional structures of globular proteins.

In the study of globular protein conformations, one customarily measures the similarity in three-dimensional structure by the root-mean-square deviation (RMSD) of the C alpha atomic coordinates after optimal rigid body superposition. Even when the two protein structures each consist of a single chain having the same number of residues so that the matching of C alpha atoms is obvious, it is not clear how to interpret the RMSD. A very large value means they are dissimilar, and zero means they are identical in conformation, but at what intermediate values are they particularly similar or clearly dissimilar? While many workers in the field have chosen arbitrary cutoffs, and others have judged values of RMSD according to the observed distribution of RMSD for random structures, we propose a self-referential, non-statistical standard. We take two conformers to be intrinsically similar if their RMSD is smaller than that when one of them is mirror inverted. Because the structures considered here are not arbitrary configurations of point atoms, but are compact, globular, polypeptide chains, our definition is closely related to similarity in radius of gyration and overall chain folding patterns. Being strongly similar in our sense implies that the radii of gyration must be nearly identical, the root-mean-square deviation in interatomic distances is linearly related to RMSD, and the two chains must have the same general fold. Only when the RMSD exceeds this level can parts of the polypeptide chain undergo nontrivial rearrangements while remaining globular. This enables us to judge when a prediction of a protein's conformation is "correct except for minor perturbations", or when the ensemble of protein structures deduced from NMR experiments are "basically in mutual agreement".

Protein Conformation↗

PubMed1999

Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach.

The equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two-dimensional Ising model in the presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to putting the equilibrium ensemble approach to work. A method by which to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely, the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open to both possibilities. A critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite-size data.

Journal Article↗

PubMed1990

Structure of the hydration shells of oligo(dA-dT).oligo(dA-dT) and oligo(dA).oligo(dT) tracts in B-type conformation on the basis of Monte Carlo calculations.

Monte Carlo simulations [(N, V, T)-ensemble] were performed for the hydration shell of poly(dA-dT).poly(dA-dT) in canonical B form and for the hydration shell of poly(dA).poly(dT) in canonical B conformation and in a conformation with narrow minor groove, highly inclined bases, but with a nearly zero-inclined base pair plane (B' conformation). We introduced helical periodic boundary conditions with a rather small unit cell and a limited number of water molecules to reduce the dimensionality of the configuration space. The coordinates of local maxima of water density and the properties of one- and two-membered water bridges between polar groups of the DNA were obtained. The AT-alternating duplex hydration mirrors the dyad symmetry of polar group distribution. At the dApdT step, a water bridge between the two carbonyl oxygens O2 of thymines is formed as in the central base-pair step of Dickerson's dodecamer. In the major groove, 5-membered water chains along the tetranucleotide pattern d(TATA).d(TATA) are observed. The hydration geometry of poly(dA).poly(dT) in canonical B conformation is distinguished by autonomous primary hydration of the base-pair edges in both grooves. When this polymer adopts a conformation with highly inclined bases and narrow minor groove, the water density distribution in the minor groove is in excellent agreement with Dickerson's spine model. One local maximum per base pair of the first layer is located near the dyad axis between adjacent base pairs, and one local maximum per base pair in the second shell lies near the dyad axis of the base pair itself. The water bridge between the two strands formed within the first layer was observed with high probability. But the water molecules of the second layer do not have a statistically favored orientation necessary for bridging first layer waters. In the major groove, the hydration geometry of the (A.T) base-pair edge resembles the main features of the AT-pair hydration derived from other sequences for the canonical B form. The preference of the B' conformation for oligo(dA).oligo(dT) tracts may express the tendency to common hydration of base-pair edges of successive base pairs in the grooves of B-type DNA. The mean potential energy of hydration of canonical B-DNA was estimated to be -60 to -80 kJ/mole nucleotides in dependence on the (G.C) contents. Because of the small system size, this estimation is preliminary.

Base Sequence↗

PubMed1999

Folding dynamics of the B1 domain of protein G explored by ultrarapid mixing.

For many proteins, compact conformations are known to accumulate in advance of the rate-limiting step in folding. To understand the nature and significance of these early conformational events, we employed ultrarapid mixing methods to fully characterize the kinetics of folding of the 57-residue B1 domain of protein G. Continuous-flow fluorescence measurements exhibit a major exponential phase on the submillisecond time scale (600-700 micros), which is followed by a slower phase with a denaturant-dependent time constant (2-30 ms) observable by conventional stopped-flow measurements. The combined kinetic traces quantitatively account for the total change in Trp 43 fluorescence upon folding, including the previously unresolved 'burst phase' signal. The denaturant dependence of the two rate constants and their relative amplitudes are fully consistent with a three-state mechanism, U right harpoon over left harpoon I right harpoon over left harpoon N, where I is a productive intermediate with native-like fluorescence properties. The relatively slow rate and exponential time course of the initial folding phase indicates that a substantial free energy barrier is encountered during chain condensation, resulting in a partially organized ensemble of states distinct from the initial unfolded conformations.

Fluorescence↗

PubMed2000

Side-chain conformational entropy in protein unfolded states.

The largest force disfavoring the folding of a protein is the loss of conformational entropy. A large contribution to this entropy loss is due to the side-chains, which are restricted, although not immobilized, in the folded protein. In order to accurately estimate the loss of side-chain conformational entropy that occurs upon folding it is necessary to have accurate estimates of the amount of entropy possessed by side-chains in the ensemble of unfolded states. A new scale of side-chain conformational entropies is presented here. This scale was derived from Monte Carlo computer simulations of small peptide models. It is demonstrated that the entropies are independent of host peptide length. This new scale has the advantage over previous scales of being more precise with low standard errors. Better estimates are obtained for long (e.g., Arg and Lys) and rare (e.g., Trp and Met) side-chains. Excellent agreement with previous side-chain entropy scales is achieved, indicating that further advancements in accuracy are likely to be small at best. Strikingly, longer side-chains are found to possess a smaller fraction of the theoretical maximum entropy available than short side-chains. This indicates that rotations about torsions after chi(2) are significantly affected by side-chain interactions with the polypeptide backbone. This finding invalidates previous assumptions about side-chain-backbone interactions. Proteins 2000;40:443-450.

Amino Acids↗

PubMed1993

Sampling of the conformations of the d(CGCTGCGGC) hairpin in solution by two-dimensional nuclear magnetic resonance and theoretical methods.

Most NMR studies of DNA oligomers have focused on rigid structures that show a strong preference for one or a small set of ground-state conformations. There is an increasing interest in extending NMR methods to investigate DNA systems in which this preference does not exist. A DNA hairpin is one such system where a large number of low-energy structures coexist in solution. In this article we show how 1D/2D NMR data of the d(C1-G2-C3-T4-G5-C6-G7-G8-C9) hairpin are used to map the conformational space of this molecule. First, we characterize the gross morphology of the hairpin by monitoring the exchangeable imino signals in the molecule. Second, we extract a set of inter-proton distances (i.e., the average values and the associated dispersions) for various pairwise interactions by performing full-matrix NOESY simulation with respect to the observed NOESY data for mixing times of 250 and 100 ms. Third, we use these distances as structural constraints to perform a 300-ps molecular dynamics simulation at 500 K. Fourth, we extract 600 snapshots (one after every 0.5 ps) from the MD trajectory and perform constrained energy minimization to map local minima on the sampled energy surface (we call this the rapid temperature quenching step). Fifth, we assign 600 structures to 14 disjoint clusters such that conformationally similar hairpins belong to the same cluster while conformationally distinct hairpins belong to different clusters. Finally, we interpret the NOESY data in terms of conformationally distinct structures by recalculating NOESY contributions taken from representative structures of different clusters. Our analyses clearly demonstrate that the NMR data correspond to an ensemble of distinct structures, i.e., a set of energetically stable but conformationally distinct structures that satisfies the constraints of loop folding in the d(C1-G2-C3-T4-G5-C6-G7-G8-C9) hairpin. Two types of loop folding consistent with NMR data are obtained: (i) a hairpin with two G.C pairs in the stem and four residues in the loop and (ii) a hairpin with two G.C pairs and a reverse wobble G.T pair in the stem plus two residues in the loop.

Base Sequence↗

PubMed2006

Methionine oxidation of monomeric lambda repressor: the denatured state ensemble under nondenaturing conditions.

Although poorly understood, the properties of the denatured state ensemble are critical to the thermodynamics and the kinetics of protein folding. The most relevant conformations to cellular protein folding are the ones populated under physiological conditions. To avoid the problem of low expression that is seen with unstable variants, we used methionine oxidation to destabilize monomeric lambda repressor and predominantly populate the denatured state under nondenaturing buffer conditions. The denatured ensemble populated under these conditions comprises conformations that are compact. Analytical ultracentrifugation sedimentation velocity experiments indicate a small increase in Stokes radius over that of the native state. A significant degree of alpha-helical structure in these conformations is detected by far-UV circular dichroism, and some tertiary interactions are suggested by near-UV circular dichroism. The characteristics of the denatured state populated by methionine oxidation in nondenaturing buffer are very different from those found in chemical denaturant.

Circular Dichroism↗