Statistical mechanical treatment of protein conformation. III. Prediction of protein conformation based on a three-state model.

The method proposed for the evaluation of statistical weights in paper I, and the three-state model [alpha-helical (alpha), extended (epsilon), and other (c) states] formulated in paper II, have been used to develop a procedure to predict the backbone conformations of proteins, based on the concept of the predominant role played by shortrange interactions in determining protein conformation. Conformational probability profiles, in which the probabilities of formation of three consecutive alpha-helical conformations (triad) and of four consecutive extended conformations (tetrad) have been defined relative to their average values over the whole molecule, are calculated for 19 proteins, of which 16 had been used in paper I to evaluate the set of statistical weights of the 20 naturally occurring amino acids. By comparing these conformational probability profiles to experimental x-ray observations, the following results have been obtained: 80% of the alpha-helical regions and 72% of the extended conformational regions have been predicted correctly for the 19 proteins. The percentage of residues predicted correctly is in the range of 53 to 90% for the alpha-helical conformation and in the range of 63 to 88% for the extended conformation for the 19 proteins in the two-state models [alpha-helical (alpha) and other (c) states, and extended (epsilon) and other (c) states]. In the three-state model, the percentage of residues predicted correctly is in the range of 47% to 77 for 19 proteins. These results suggest that the assumption of the dominance of short-range interactions, on which the predictive scheme is based, is a reasonable one. The present predictive method is compared with that of other authors.     

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.     

Use of constrained synthetic amino acids in beta-helix proteins for conformational control

A highly constrained amino acid has been introduced in the turn region of a beta-helix to increase the conformational stability of the native fold for nanotechnological purposes. The influence of this specific amino acid replacement in the final organization of beta-helix motifs has been evaluated by combining ab initio first-principles calculations on model systems and molecular dynamics simulations of entire peptide segments. The former methodology, which has been applied to a sequence containing three amino acids, has been used to develop adjusted templates. Calculations indicated that 1-amino-2,2-diphenylcyclopropanecarboxylic acid, a constrained cyclopropane analogue of phenylalanine, exhibits a strong tendency to form and promote folded conformations. On the other hand, molecular dynamics simulations are employed to probe the ability of such a synthetic amino acid to enhance the conformational stability of the beta-helix motif, which is the first requirement for further protein nanoengineering. A highly regular segment from a naturally occurring beta-helix protein was selected as a potential nanoconstruct module. Simulations of wild type and mutated segments revealed that the ability of the phenylalanine analogue to nucleate turn conformations enhances the conformational stability of the beta-helix motif in isolated peptide segments.     

Active polycondensation: from pep tide chemistry to amino acid based biodegradable polymers

New polycondensation (PC) methods of polymer synthesis using non-traditional active derivative of dicarboxylic acids are reviewed. The new PC methods are named by general name “Active Polycondensation” (APC) to tell them from traditional low-temperature PC. The most of these methods are based on well known in peptide chemistry approaches to the activation of carboxylic groups. In the present paper the syntheses of heterochain polymers of basic classes - polyamides, polyesters, polyurethanes, polyureas, and polybenzazoles by interaction of various active diesters with di- and polyfunctional nucleophiles are discussed in brief. Special attention is given to the synthesis of non-conventional heterochain macromolecular systems, in particular poly(ester amide)s (PEAs), composed of naturally occurring α-amino acids and other non-toxic building blocks like fatty diacids and diols - synthetic analogues of naturally occurring amino acid based polymers - peptides and proteins. The synthesis and properties, biodegradation, and some practical applications of PEAs are discussed in brief.     

Investigation of the conformations of four tetrapeptides by nuclear magnetic resonance and circular dichroism spectroscopy, and conformational energy calculations.

Proton nuclear magnetic resonance and circular dichroism studies were carried out on aqueous solutions of the tetrapeptide Asp-Lys-Thr-Gly (which appears as a bend at residues 35-38 of alpha-chymotrypsin) and its sequence variants Gly-Thr-Asp-Lys, Asp-Lys-Gly-Thr, and Lys-Thr-Gly-Asp; the N and C termini of all four tetrapeptides were blocked with CH3CO and NHCH3 groups, respectively. The spectroscopic data suggest that bend conformations may exist, to some extent, among the distributions of conformations in the first, third, and fourth, but not in the second, tetrapeptide. This result is consistent with empirical probabilities for the prediction of bend conformations in proteins. Conformational energy calculations on these four tetrapeptides support the indications from the experimental data. It thus appears that, because of short-range interactions, the tendency toward bend formation exists in short peptides, provided that both the composition and amino acid sequence are energetically favorable for bend formation.     

Designed Heme-Cage β-Sheet Miniproteins

The structure and function of naturally occurring proteins are governed by a large number of amino acids (≥100). The design of miniature proteins with desired structures and functions not only substantiates our knowledge about proteins but can also contribute to the development of novel applications. Excellent progress has been made towards the design of helical proteins with diverse functions. However, the development of functional β-sheet proteins remains challenging. Herein, we describe the construction and characterization of four-stranded β-sheet miniproteins made up of about 19 amino acids that bind heme inside a hydrophobic binding pocket or “heme cage” by bis-histidine coordination in an aqueous environment. The designed miniproteins bound to heme with high affinity comparable to that of native heme proteins. Atomic-resolution structures confirmed the presence of a four-stranded β-sheet fold. The heme–protein complexes also exhibited high stability against thermal and chaotrope-induced unfolding.     

Conformations of Biopolymers

Discussion of the history of biopolymers is focused on proteins and polypeptides. Rubber elasticity is discussed from the early days onward, when the first and second laws of thermodynamics were established. Insight in the elasticity of elastin, an amorphous protein occurring in ligaments and arteries, is followed against this background. Denatured proteins also fit in this category. At present, the random-coil state that underlies the elasticity is rather well understood as a result of the new methods of analyzing the dimensions in terms of the conformations of the residues. Subsequently, the discovery of the α-helix, as well as that of the other helical structures of DNA and collagen, is described. The conversion to random coils is followed with emphasis on our insight into the cooperative nature of the transition. Finally, the least understood globular proteins are considered. Major progress was made with the successful analysis of x-ray patterns. The native state is characterized by closely packed residues in complicated, but unique, patterns. The conversion to random coils (denaturation) is sharp, not unlike a phase transition. Although the native state is rather closely packed, some mobility still exists. The implication of this mobility for enzymatic action is hinted at.     

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.     

Effects of amino acid phi,psi propensities and secondary structure interactions in modulating H alpha chemical shifts in peptide and protein beta-sheet.

H alpha chemical shifts are often used as indicators of secondary structure formation in protein structural analysis and peptide folding studies. On the basis of NMR analysis of model beta-sheet and alpha-helical peptides, together with a statistical analysis of protein structures for which NMR data are available, we show that although the gross pattern of H alpha chemical shifts reflects backbone torsion angles, longer range effects from distant amino acids are the dominant factor determining experimental chemical shifts in beta-sheets of peptides and proteins. These show context-dependent variations that aid structural assignment and highlight anomalous shifts that may be of structural significance and provide insights into beta-sheet stability.     

Application of 1-aminocyclohexane carboxylic acid to protein nanostructure computer design

Conformationally restricted amino acids are promising candidates to serve as basic pieces in redesigned protein motifs which constitute the basic modules in synthetic nanoconstructs. Here we study the ability of constrained cyclic amino acid 1-aminocyclohexane-1-carboxylic acid (Ac6c) to stabilize highly regular beta-helical motifs excised from naturally occurring proteins. Calculations indicate that the conformational flexibility observed in both the ring and the main chain is significantly higher than that detected for other 1-aminocycloalkane-1-carboxylic acids (Acnc, where n refers to the size of the ring) with smaller cycles. Incorporation of Ac6c into the flexible loops of beta-helical motifs indicates that the stability of such excised building blocks as well as the nanoassemblies derived from them is significantly enhanced. Thus, the intrinsic Ac6c tendency to adopt folded conformations combined with the low structural strain of the cyclohexane ring confers the ability to both self-adapt to the beta-helix motif and to stabilize the overall structure by absorbing part of its conformational fluctuations. Comparison with other Acnc residues indicates that the ability to adapt to the targeted position improves considerably with the ring size, i.e., when the rigidity introduced by the strain of the ring decreases.     

Fe3+-hydroxamate as immobilized metal affinity-adsorbent for protein chromatography

The adsorbent glycinehydroxamate-Sepharose 6B, charged with Fe3+ under specified conditions, is reported. It was used at various pH values for chromatography of the following proteins: lysozyme, cytochrome c, avidin, bovine pancreatic RNase, myoglobin, ovalbumin and human serum albumin. The common naturally occurring amino acids were tested for their interactions with the new sorbent under neutral conditions.     

Ab initio polypeptide structure prediction

The biological activity of a polypeptide strongly depends on its 3D structure. Ab initio prediction of the native structure from the sequence of amino acids has long motivated the development of an optimum energy model such that interactions present in the native conformation are stronger than those present in nonnative conformations and of algorithms capable of finding the basin of lowest free energy among an astronomically large number of possible conformations. Despite recent progress in our understanding of the factors responsible for both polypeptide stability and formation, computer simulations of polypeptide models are still far from being practical software tools for biologists. In this work, state-of-the-art computer simulations aimed at ab initio structure prediction in aqueous solution are reviewed and their strengths and weaknesses are highlighted. Received: 23 June 1999 / Accepted: 20 September 1999 / Published online: 15 December 1999     

sDFIRE: Sequence‐specific statistical energy function for protein structure prediction by decoy selections

An important unsolved problem in molecular and structural biology is the protein folding and structure prediction problem. One major bottleneck for solving this is the lack of an accurate energy to discriminate near‐native conformations against other possible conformations. Here we have developed sDFIRE energy function, which is an optimized linear combination of DFIRE (the Distance‐scaled Finite Ideal gas Reference state based Energy), the orientation dependent (polar‐polar and polar‐nonpolar) statistical potentials, and the matching scores between predicted and model structural properties including predicted main‐chain torsion angles and solvent accessible surface area. The weights for these scoring terms are optimized by three widely used decoy sets consisting of a total of 134 proteins. Independent tests on CASP8 and CASP9 decoy sets indicate that sDFIRE outperforms other state‐of‐the‐art energy functions in selecting near native structures and in the Pearson's correlation coefficient between the energy score and structural accuracy of the model (measured by TM‐score). © 2016 Wiley Periodicals, Inc.     

Position‐Dependent Effects of Fluorinated Amino Acids on the Hydrophobic Core Formation of a Heterodimeric Coiled Coil

Systematic model investigations of the molecular interactions of fluorinated amino acids within native protein environments substantially improve our understanding of the unique properties of these building blocks. A rationally designed heterodimeric coiled coil peptide (VPE/VPK) and nine variants containing amino acids with variable fluorine content in either position a16 or d19 within the hydrophobic core were synthesized and used to evaluate the impact of fluorinated amino acid substitutions within different hydrophobic protein microenvironments. The structural and thermodynamic stability of the dimers were examined by applying both experimental (CD spectroscopy, FRET, and analytical ultracentrifugation) and theoretical (MD simulations and MM‐PBSA free energy calculations) methods. The coiled coil environment imposes position‐dependent conformations onto the fluorinated side chains and thus affects their packing and relative orientation towards their native interaction partners. We find evidence that such packing effects exert a significant influence on the contribution of fluorine‐induced polarity to coiled coil folding.     

Foldable subunits of helix protein

Detection of foldable subunits in proteins is an important approach to understand their evolutions and find building motifs for de novo protein design. Using united-residue model, we simulated the folding of a six-helix protein with a length of 120 amino acids (C-terminal domain of Ku86). The folding behaviors, structural topology and sequence repetition of this protein all suggest that it may have a two-fold quasi-repetition or symmetry in its sequence and structure. Therefore, we simulated the folding of its two halves (1–60 and 61–120 amino acids) and find that they can fold into native conformations independently. It is also found that their folding behaviors are very similar to other three-helix bundles. This suggests that this protein may be divided into two foldable halves.     

Sequence-dependent correction of random coil NMR chemical shifts.

Random coil chemical shifts are commonly used to detect secondary structure elements in proteins in chemical shift index calculations. While this technique is very reliable for folded proteins, application to unfolded proteins reveals significant deviations from measured random coil shifts for certain nuclei. While some of these deviations can be ascribed to residual structure in the unfolded protein, others are clearly caused by local sequence effects. In particular, the amide nitrogen, amide proton, and carbonyl carbon chemical shifts are highly sensitive to the local amino acid sequence. We present a detailed, quantitative analysis of the effect of the 20 naturally occurring amino acids on the random coil shifts of (15)N(H), (1)H(N), and (13)CO resonances of neighboring residues, utilizing complete resonance assignments for a set of five-residue peptides Ac-G-G-X-G-G-NH(2). The work includes a validation of the concepts used to derive sequence-dependent correction factors for random coil chemical shifts, and a comprehensive tabulation of sequence-dependent correction factors that can be applied for amino acids up to two residues from a given position. This new set of correction factors will have important applications to folded proteins as well as to short, unstructured peptides and unfolded proteins.     

STATISTICAL PROPERTIES OF LONG-RANGE CONTACTS IN GLOBULAR PROTEINS

The analysis of residue-residue contacts in protein structures can shed some light on our understanding of the folding and stability of proteins. In this paper, we study the statistical properties of long-range and short-range residue-residue contacts of 91 globular proteins using CSU software and analyze the importance of long-range contacts in globular protein structure. There are many short-range and long-range contacts in globular proteins, and it is found that the average number of long-range contacts per residue is 5.63 and the percentage of residue-residue contacts which are involved in long-range ones is 59.4%. In more detail, the distribution of long-range contacts in different residue intervals is investigated and it is found that the residues occurring in the interval range of 4-10 residues apart in the sequence contribute more long-range contacts to the stability of globular protein. The number of long-range contacts per residue, which is a measure of ability toform residue-residue contacts, is also calculated for 20 different amino acid residues. It is shown that hydrophobic residues (including Leu, Val, Ile, Met, Phe, Tyr, Cys and Trp) having a large number of long-range contacts easily form long-range contacts, while the hydrophilic amino acids (including Ala, Gly, Thr, His, Glu, Gln, Asp, Asn, Lys, Ser, Arg, and Pro) form long-range contacts with more difficulty. The relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of short-range and long-range contacts per residue for 20 amino acid residues is also studied. An approximately linear relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of long-range contacts per residue CL is found and can be expressed as     

Intraresidue distribution of energy in proteins

Boltzmann-like distributions appear in many properties and energy-related quantities of proteins. A few examples are hydrophobicity, various types of side-chain/side-chain interactions, proline isomerization, hydrogen bonds, internal cavities, interactions at the level of specific atom types, and the propensity of the phi/'phi' ratio. Here, we conjecture that the Boltzmann hypothesis also holds for the intra-residue energy distribution. We confirm the conjecture by calculating the energies of 41,672 residues of the structures of highly resolved proteins, where at least 12 out of 20 naturally occurring amino acids follow Boltzmann's law. We further examine the entire set of all residue energies and find that the convolution of the individual distributions gives a Poisson function, which is followed by approximately 50% of individual proteins' structures.     

Inference of the solvation energy parameters of amino acids using maximum entropy approach

We present a novel technique, based on the principle of maximum entropy, for deriving the solvation energy parameters of amino acids from the knowledge of the solvent accessible areas in experimentally determined native state structures as well as high quality decoys of proteins. We present the results of detailed studies and analyze the correlations of the solvation energy parameters with the standard hydrophobic scale. We study the ability of the inferred parameters to discriminate between the native state structures of proteins and their decoy conformations.