Statistical mechanical treatment of protein conformation. II. A three-state model for specific-sequence copolymers of amino acids.

A one-dimensional three-state Ising model [involving alpha-helical (alpha), extended (epsilon), and coil (or other) (c) states] for specific-sequence copolymers of amino acids ahs been formulated in order to treat the conformational states of proteins. This model involves four parameters (wh,iota, vh, iota, v episilon, iota, and uc, iota), and requires a 4 X 4 matrix for generating statistical weights. Some problems in applying this model to a specific-sequence copolymer of amino acids are discussed. A nearest-neighbor approximation for treating this three-state model is also formulated; it requires a 3 X 3 matrix, in which the same four parameters appear, but (as with the 4 X 4 matrix treatment) only three parameters (wh, uh, and v epsilon) are required if relative statistical weights are used. The relationship between the present three-state model (3 X 3 matrix treatment) and models of the helix--coil transition is discussed. Then, the three-state model (3 X 3 matrix treatment) is incorporated into an earlier (Tanaka--Scheraga) model of the helix-coil transition, in which asymmetric nucleation of helical sequences is taken into account. A method for calculating molecular averages and conformational-sequence probabilities, P(iota/eta/(rho)), i.e., the probability of finding a sequence of eta residues in a specific conformational state (rho), starting at the iotath position of the chain, is described. Two alternative methods for calculating P(iota/eta/(rho)), that can be applied to a model involving any number of states, are proposed and presented; one is the direct matrix-multiplication method, and the other uses a first-order a priori probability and a conditional probability. In this paper, these calculations are performed with the nearest-neighbor model, and without the feature of asymmetric nucleation. Finally, it is indicated how the three-state model and the methods for computing P(iota/eta/(rho)) can be applied to predict protein conformation.     

Statistical mechanical treatment of protein conformation. I. Conformational properties of amino acids in proteins.

A statistical mechanical (one-dimensional Ising model) treatment, based on the dominance of short-range interactions, is developed in this series of papers; it is intended as an improvement over empirical prediction schemes for obtaining approximate initial conformations of proteins (to be used to try to deduce the native conformation by subsequent energy minimization). In the present paper, the statistical weights for a two-state model (alpha-helical and other conformations) and for a three-state model (alpha-helical, extended, and other conformations) are evaluated from x-ray data on 16 native proteins. The method for evaluating the statistical weights is presented. Asymmetric alpha-helical nucleation parameters are also evaluated for the 20 naturally occurring amino acids. On the basis of these statistical weights, the conformational properties of the twenty naturally occurring amino acids are discussed. The statistical weights evaluated from x-ray data are also discussed in comparison with experimental results on the helix--coil transition in polyamino acids in solution. The predominant role of short-range interactions, and some possible long-range effects in determining the statistical weights, are discussed in conjunction with the mechanism of protein folding.     

A new method for side-chain conformation prediction using a Hopfield network and reproduced rotamers

We present a new side-chain prediction method based on energy minimization using a Hopfield network, focusing on the buried residues of proteins. In this method, the network is composed of automata assigned to each rotamer to restrict side-chain conformational space. We reproduced a rotamer library that enabled us to more widely cover the space for side-chain conformations than those previously produced. The accuracy of the side-chain modeling was estimated by three standards: root mean square deviations (rmsds) between the modeled and the crystal structures, the percentages of correctly predicted side-chain torsion angles, and the percentages of correctly predicted hydrogen bonds. The average rmsd for buried side chains of 21 proteins was 1.10 Å. The value was almost always improved relative to the previous works. The percentage of side-chain X₁ angles for buried residues was 87.3%. By considering the hydrogen bond energy, the average percentage of correctly predicted hydrogen bonds rose from 33% without hydrogen bond energy to 52% with the bond energy. We applied this method to homology modeling, where the protein backbone used to predict side-chain conformations deviates from the correct conformation, and could predict side-chain conformations as correctly as those using the correct backbones. © 1996 by John Wiley & Sons, Inc.     

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.     

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search procedure

A procedure that finds the most probable conformational states of a protein chain is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. The conformation of the entire chain is represented by a sequence of single-residue conformational states; the distinct conformations in this representation are called “chain-states.” The first article in this series described a procedure that computes tripeptide conformational probabilities from the amino acid sequence using pattern recognition techniques. The procedure described in this article uses the tripeptide probabilities to estimate the probabilities of the chain-states. The chain-state probability estimator is a product of conditional and marginal probabilities (obtained from the tripeptide probabilities), with a penalty factor to eliminate conformations containing α-helices and ?-strands of excessive length. The probability estimator considers short-range conformational information, medium-range sequence information and some simple long-range information (through the restrictions on helix and strand lengths). Energy minimization calculations can be carried out in the region of conformational space corresponding to a particular chain-state. By selecting the most probable chain-states, the search can be focused on the most probable, or “important,” regions of the conformational space. These energy calculations are described in the third article of the series. The complete procedure described by the three articles is called PRISM, for pattern recognition-based importance sampling minimization.     

Diverse fragment clustering and water exclusion identify protein hot spots

Simulated annealing of chemical potential located the highest affinity positions of eight organic probes and water on eight static structures of hen egg white lysozyme (HEWL) in various conformational states. In all HELW conformations, a diverse set of organic probes clustered in the known binding site (hot spot). Fragment clusters at other locations were excluded by tightly-bound waters so that only the hot-spot cluster remained in each case. The location of the hot spot was correctly predicted irrespective of the protein conformation and without accounting for protein flexibility during the simulations. Any one of the static structures could have been used to locate the hot spot. A site on a protein where a diversity of organic probes is calculated to cluster, but where water specifically does not bind, identifies a potential small-molecule binding site or protein-protein interaction hot spot.     

Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure

A procedure that generates random conformations of a protein chain, and then applies energy minimization to find the structure of lowest energy, is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. Each state corresponds to a rectangular region in the ?, ψ map. The conformation of an entire chain is then represented by a sequence of single-residue conformational states. The distinct “chain-states” in this representation correspond to multidimensional rectangular regions in the conformational space of the whole protein. A set of highly-probable chain-states can be predicted from the amino acid sequence using the pattern recognition procedure developed in the first two articles of this series. The importance-sampling minimization procedure of the present article is then used to explore the regions of conformational space corresponding to each of these chain-states. The importance-sampling procedure generates a number of random conformations within a particular multidimensional rectangular region, sampling most densely from the most probable, or “important,” sections of the ?, ψ map. All values of ? and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ? and Φ are generated from bivariate gaussian distributions that are determined from known X-ray structures. Separate gaussian distributions are used for proline residues in the α and ? states, for glycine residues in the α, ?, α*, and ?* states, and for ordinary residues involved in 29 different tripeptide conformations. Energy minimization is then applied to the randomly-generated structures to optimize interactions and to improve packing. The final energy values are used to select the best structures. The importance-sampling minimization procedure is tested on the avian pancreatic polypeptide, using chain-states predicted from the amino acid sequence. The conformation having the lowest energy is very similar to the X-ray conformation.     

Independence of photoproduct formation on DNA conformation.

Abstract— In an ethanolic solution native T7 DNA can undergo conformational transitions from the B conformation (0% ethanol) to the C-like (60% w/w ethanol) and the A (80% w/w ethanol) conformations. We have investigated the formation of three classes of thymine-derived photoproducts in T7 DNA irradiated (280 nm) in the B, C-like, and A conformations, which were monitored by circular dichroism measurements. We find that the predominant class of thymine-derived photoproducts in any conformational state is cyclobutyl dipyrimidines. While the ‘spore product,’ 5-thyminyl-5,6-dihydrothymine, which belongs to another class of photoproductsf does form in native DNA in the A conformation, its yield in denatured DNA at 80% ethanol is the same as that in native DNA. The yield of pyrimidine adduct, a third photoproduct class, is a maximum at 50–60% ethanol. This effect of ethanol is probably not due to the ethanol-induced C-like conformation, however, since pyrimidine adduct formation is not enhanced when T7 DNA is irradiated in the C conformation in 6 M CsCl or in intact phage. We conclude from these and other data in the literature that the degree of hydration rather than the conformational state is the critical factor in determining which of the photoproducts will form in native DNA.     

Interfacial water structure controls protein conformation

A phenomenological theory of salt-induced Hofmeister phenomena is presented, based on a relation between protein solubility in salt solutions and protein-water interfacial tension. As a generalization of previous treatments, it implies that both kosmotropic salting out and chaotropic salting in are manifested via salt-induced changes of the hydrophobic/hydrophilic properties of protein-water interfaces. The theory is applied to describe the salt-dependent free energy profiles of proteins as a function of their water-exposed surface area. On this basis, three classes of protein conformations have been distinguished, and their existence experimentally demonstrated using the examples of bacteriorhodopsin and myoglobin. The experimental results support the ability of the new formalism to account for the diverse manifestations of salt effects on protein conformation, dynamics, and stability, and to resolve the puzzle of chaotropes stabilizing certain proteins (and other anomalies). It is also shown that the relation between interfacial tension and protein structural stability is straightforwardly linked to protein conformational fluctuations, providing a keystone for the microscopic interpretation of Hofmeister effects. Implications of the results concerning the use of Hofmeister effects in the experimental study of protein function are discussed.     

The theory of viscoelastic characteristics of a highly stretched macromolecule in single molecule AFM

The theory for the deformation of a model macromolecule stretched by its ends under the action of high constant and low periodic forces is constructed. The macromolecule is composed of monomer units in three conformational states. The proposed theory describes the regime of a severe stretching of a macromolecule extended to a length close to its contour length, when its extension proceeds via conformational transitions between different states of monomer units. The structural parameters of the monomer unit are found to correlate with viscoelastic characteristics, which are calculated from the experimental results on the deformation of an individual macromolecule obtained by the frequency atomic force microscopy. For a monomer unit with three conformations, the force dependences of viscoelastic characteristics (effective coefficients of elasticity and friction) can show one or two minima. When the experimental dependences of the above parameters show two minima, the monomer unit can have three or more equilibrium states. With the knowledge of the viscoelastic characteristics of a macromolecule, it is possible to unequivocally estimate all structural parameters of a monomer unit for its three-state conformational model. When the force dependence of viscoelastic characteristics show only one minimum, the monomer unit can have two or more states and analysis of the corresponding viscoelastic characteristics at the minimum makes it possible to select between two- and three-state conformational models. Then, for the three-state model, experimental data allow the prediction of only equilibrium parameters of the monomer unit (position of the minima and energy); dynamic parameters (positions and height of barriers between equilibrium states) remain indeterminate. The proposed theory is used for the interpretation of the viscoelastic characteristics of dextran obtained by single-molecule AFM experiments. The three-state conformational model of a dextran unit is shown to agree better with the experimental data than with the two-state conformational model.     

Chain conformation in two-dimensional dense state

In an effort to provide evidence concerning the conformation of many chains in strict two-dimensional (2D) dense state, we synthesized polymer chains of diameter of nanometers through an anionic polymerization process. The conformational characteristics of the long chain molecules in films of thickness h corresponding to the chain diameter a were directly obtained from atomic force microscopy observations. In 2D dispersed state, the conformations of the long chain molecules were typical Gaussian. However, in 2D dense state the long chain molecules were strongly interpenetrated. Their conformations were largely perturbed by the presence of neighbor chains and were not Gaussian. This result was in contradiction with the segregated globule model predicted by de Gennes. The central reason is that 2D space cannot be filled to normal density with 2D Gaussian globules; either the area must be greatly increased with consequently large voids, or the globule conformation must be expanded by allowing chains to interpenetrate each other.     

Raman spectroscopic characterization of secondary structure in natively unfolded proteins: alpha-synuclein

The application of Raman spectroscopy to characterize natively unfolded proteins has been underdeveloped, even though it has significant technical advantages. We propose that a simple three-component band fitting of the amide I region can assist in the conformational characterization of the ensemble of structures present in natively unfolded proteins. The Raman spectra of alpha-synuclein, a prototypical natively unfolded protein, were obtained in the presence and absence of methanol, sodium dodecyl sulfate (SDS), and hexafluoro-2-propanol (HFIP). Consistent with previous CD studies, the secondary structure becomes largely alpha-helical in HFIP and SDS and predominantly beta-sheet in 25% methanol in water. In SDS, an increase in alpha-helical conformation is indicated by the predominant Raman amide I marker band at 1654 cm(-1) and the typical double minimum in the CD spectrum. In 25% HFIP the amide I Raman marker band appears at 1653 cm(-1) with a peak width at half-height of approximately 33 cm(-1), and in 25% methanol the amide I Raman band shifts to 1667 cm(-1) with a peak width at half-height of approximately 26 cm(-1). These well-characterized structural states provide the unequivocal assignment of amide I marker bands in the Raman spectrum of alpha-synuclein and by extrapolation to other natively unfolded proteins. The Raman spectrum of monomeric alpha-synuclein in aqueous solution suggests that the peptide bonds are distributed in both the alpha-helical and extended beta-regions of Ramachandran space. A higher frequency feature of the alpha-synuclein Raman amide I band resembles the Raman amide I band of ionized polyglutamate and polylysine, peptides which adopt a polyproline II helical conformation. Thus, a three-component band fitting is used to characterize the Raman amide I band of alpha-synuclein, phosvitin, alpha-casein, beta-casein, and the non-A beta component (NAC) of Alzheimer's plaque. These analyses demonstrate the ability of Raman spectroscopy to characterize the ensemble of secondary structures present in natively unfolded proteins.     

The study of protein conformation in solution via direct sampling by desorption electrospray ionization mass spectrometry

The direct sampling feature of liquid sample desorption electrospray ionization (DESI) allows the ionization of liquid samples without adding acids/organic solvents (i.e., without sample pretreatment). As a result, it provides a new approach for probing protein conformation in solution. In this study, it has been observed that native protein ions are generated from proteins in water by DESI. Interestingly, the intensities of the resulting protein ions appear to be higher than those generated by ESI of the proteins in water or in ammonium acetate. For protein solutions that already contain acids/organic solvents, DESI can be used to investigate the influences of these denaturants on protein conformations and the obtained results are in good agreement with spectroscopic data. In addition, online monitoring of protein conformational changes by DESI is feasible; for instance, heat-induced unfolding of ubiquitin can be traced with DESI in water without influences of organic solvents/acids. This DESI method provides a new alternative tool for the study of protein conformation in solution.     

A new protein conformation indicator based on biarsenical fluorescein with an extended benzoic acid moiety.

We demonstrate herein a new protein conformation indicator based on biarsenical fluorescein with an extended benzoic acid moiety. The present indicator is reactive to a genetically introduced tetracysteine motif (Cys-Cys-Xaa-Xaa-Cys-Cys, where Xaa is a noncysteine amino acid) of proteins. Compared to the original biarsenical fluorescein (FlAsH) and the biarsenical Nile red analogue (BArNile), the present indicator exhibited larger fluorescence intensity changes in response to Ca(2+)-induced conformational rearrangements of calmodulin. A calculation of the highest occupied molecular orbital (HOMO) level of the benzoic acid moiety of the indicator molecule supports possible involvement of a photoinduced electron transfer (PET) process. These results indicate that the present indicator is useful for sensitive detection of protein conformational changes.     

Conformational study of the structure of free 18-crown-6

A conformational search was performed for 18-crown-6 using the CONLEX method at the MM3 level. To have a more accurate energy order of the predicted conformations, the predicted conformations were geometry optimized at the HF/STO-3G level and the 198 lowest energy conformations, according to the HF/STO-3G energy order, were geometry optimized at the HF/6-31+G level. In addition, the 47 nonredundant lowest energy conformations, according to the MP2/6-31+G energy order at the HF/6-31+G optimized geometry, hereafter the MP2/6-31+G//HF/6-31+G energy order, were geometry optimized at the B3LYP/6-31+G level. According to the MP2/6-31+G//B3LYP/6-31+G energy order, three conformations had energies lower than the experimentally known Ci conformation of 18c6. At the MP2/6-31+G//B3LYP/6-31+G level, the S6 lowest energy conformation is more stable by 1.96 kcal/mol than this Ci conformation. This was confirmed by results at the MP2/6-31+G level with an energy difference of 1.84 kcal/mol. Comparison between the structure of the S6 conformation of 18c6 and the S4 lowest energy conformation of 12-crown-4, as well as other important conformations of both molecules, is made. It is concluded that the correlation energy is necessary to have an accurate energy order of the predicted conformations. A rationalization of the conformational energy order in terms of the hydrogen bonding and conformational dihedral angles is given. It is also suggested that to have a better energy order of the predicted conformations at the MM3 level, better empirical force fields corresponding to the hydrogen bond interactions are needed.     

Quantitative measurement of protease ligand conformation

The tendency for protease ligands to bind in an extended conformation has been suggested as an important factor for the identification of compounds of medicinal importance. Here we present a novel graph-theoretical method giving a quantitative measure of ligand conformation, and through application of this method to a representative set of protease ligands in bound and unbound conformations, derive the result that protease ligands are more extended in conformation when in their bound state. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Conformational elasticity theory of chain molecules

This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (i) the molecular model is the rotational isomeric state (RIS) model; (ii) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (iii) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experi     

Temperature selectivity effects in reversed-phase liquid chromatography due to conformation differences between helical and non-helical peptides

In order to characterize the effect of temperature on the retention behaviour and selectivity of separation of polypeptides and proteins in reversed-phase high-performance liquid chromatography (RP-HPLC), the chromatographic properties of four series of peptides, with different peptide conformations, have been studied as a function of temperature (5-80 degrees C). The secondary structure of model peptides was based on either the amphipathic alpha-helical peptide sequence Ac-EAEKAAKEX(D/L)EKAAKEAEK-amide, (position X being in the centre of the hydrophobic face of the alpha-helix), or the random coil peptide sequence Ac-X(D/L)LGAKGAGVG-amide, where position X is substituted by the 19 L- or D-amino acids and glycine. We have shown that the helical peptide analogues exhibited a greater effect of varying temperature on elution behaviour compared to the random coil peptide analogues, due to the unfolding of alpha-helical structure with the increase of temperature during RP-HPLC. In addition, temperature generally produced different effects on the separations of peptides with different L- or D-amino acid substitutions within the groups of helical or non-helical peptides. The results demonstrate that variations in temperature can be used to effect significant changes in selectivity among the peptide analogues despite their very high degree of sequence homology. Our results also suggest that a temperature-based approach to RP-HPLC can be used to distinguish varying amino acid substitutions at the same site of the peptide sequence. We believe that the peptide mixtures presented here provide a good model for studying temperature effects on selectivity due to conformational differences of peptides, both for the rational development of peptide separation optimization protocols and a probe to distinguish between peptide conformations.     

Aggregation of polyalanine in a hydrophobic environment

The dimerization of polyalanine peptides in a hydrophobic environment was explored using replica exchange molecular dynamics simulations. A nonpolar solvent (cyclohexane) was used to mimic, among other hydrophobic environments, the hydrophobic interior of a membrane in which the peptides are fully embedded. Our simulations reveal that while the polyalanine monomer preferentially adopts a beta-hairpin conformation, dimeric phases exist in an equilibrium between random coil, alpha-helical, beta-sheet, and beta-hairpin states. A thermodynamic characterization of the dimeric phases reveals that electric dipole-dipole interactions and optimal side-chain packing stabilize alpha-helical conformations, while hydrogen bond interactions favor beta-sheet conformations. Possible pathways leading to the formation of alpha-helical and beta-sheet dimers are discussed.     

Molecular dynamics simulations of conserved Hox protein hexapeptides. I. Folding behavior in water solution

Molecular dynamics simulations of hexapeptides TFDWMK and LFPWMR; the highly conserved regions of Hox proteins Hox B1 and Hox B8, respectively, are carried out starting from extended structures to investigate their conformational space in water solution. In addition, we have studied TADWMK and TADAMK, where the aromatic residues Phenylalanine and Tryptophan were successively substituted for Alanine to investigate effects from the presence/absence of aromatic amino acids and interactions between them to folding behavior. The backbone of the hexapeptides in all simulations folds to a similar conformation found in experimental studies in solution. Intramolecular, hydrophobically driven interactions between the aromatic residues and internal hydrogen bonds are found to stabilize the conformations.