Theory of protein molecule self-organization. I. Thermodynamic parameters of local secondary structures in the unfolded protein chain

This paper presents the results of a stereochemical analysis of local interactions in unfolded protein chains (sterical repulsions, hydrogen, and hydrophobic bonds, etc.) by means of space-filling modeles. On the basis of this analysis, an evaluation is made of thermodynamic parameters controlling the building-in of all the 20 natural amino acid residues in all the physically possible position of local secondary structures (α-helices, including α-helices with short fragments of helices 3₁₀ at the C-terminus; β-bends of different types, helices 3₁₀, and their combinations) as well as thermodynamic parameters of separate hydrogen bonds of polar side groups with the neighbor peptide groups (“local contacts”). The accuracy of the obtained results is discussed.     

Theory of protein molecule self-organization. II. A comparison of calculated thermodynamic parameters of local secondary structures with experiments

Constants of the helix–coil transition for all natural amino acid residues are evaluated on the basis of thermodynamic parameters obtained in paper I of this series. The specific effects at the termini of the helices are also considered as well as the parameters controlling the formation of β-bends in the unfolded protein chain. Evaluated s constants of the helix–coil transition agree with the experimental data on helix–coil transitions of synthetic polypeptides in water. Only a very qualitative correlation exists between s constants (both experimental and theoretical) and the occurrence of corresponding residues in internal turns of α-helices in globular proteins: residues with s > 1 occur in helices as a rule more often than residues with s < 1. At the same time a direct correlation is demonstrated between theoretical parameters of residue incorporation into α-helical termini and β-bends in an unfolded polypeptide chain and the occurrence of residues in corresponding positions of the globular protein secondary structures.     

Residue solvent accessibilities in the unfolded polypeptide chain.

The difference of solvent accessibilities in the native and unfolded states of the protein is used as a measure of the hydrophobic contribution to the free energy of folding. We present a new approximation of amino acids solvent accessibilities in the unfolded state based on the 1-ns molecular dynamics simulation of Ala-X-Ala tripeptides at a temperature of 368 K. The standard accessibility values averaged from the molecular dynamics study are significantly lower from those previously obtained by considering only selected conformations of Ala-X-Ala tripeptides.     

A new type of secondary structure: mobile conformation of polypeptide chain. Data bank for protein structures

As a result of statistical analysis of Protein Data Bank a new type of secondary structure was found in globular proteins. It is mobile (M) conformation, characterised by noncooperative hydration and the increased dynamical properties of the chain. Percentage distribution of amino acid residues between the main secondary structure types is 42.7% for alpha-helix, 19.6% for beta-structure and 19.1% for M-conformation. The most frequently occurring amino acids for M-conformation are proline, cysteine and serine. Fragments of mobile conformation seem to play a major part in local and domain dynamics of protein globule.     

A pentapeptide-based method for protein secondary structure prediction

We present a new method for protein secondary structure prediction, based on the recognition of well-defined pentapeptides, in a large databank. Using a databank of 635 protein chains, we obtained a success rate of 68.6%. We show that progress is achieved when the databank is enlarged, when the 20 amino acids are adequately grouped in 10 sets and when more pentapeptides are attributed one of the defined conformations, alpha-helices or beta-strands. The analysis of the model indicates that the essential variable is the number of pentapeptides of well-defined structure in the database. Our model is simple, does not rely on arbitrary parameters and allows the analysis in detail of the results of each chosen hypothesis.     

The chain effect. Part III. Induction of secondary structure in copolymerizations

Studies of the properties of copolymers of N-carboxy sarcosine anhydride with other N-carboxy α-amino acid anhydrides have shown that the secondary structure may be a function of the type of initiator used. In particular, when polysarcosine is the initiator, and the “chain effect” becomes possible, blocklike character appears in the copolymer. This is the result of selective and rapid polymerization of N-unsubstituted N-carboxy α-amino acid anhydrides by the chain-effect mechanism. In suitable circumstances, therefore, the latter may be used to induce order into copolymerizations of this type.     

Relationship between chain collapse and secondary structure formation in a partially folded protein

Chain collapse and secondary structure formation are frequently observed during the early stages of protein folding. Is the chain collapse brought about by interactions between secondary structure units or is it due to polymer behavior in a poor solvent (coil‐globule transition)? To answer this question, we measured small‐angle X‐ray scattering for a series of β‐lactoglobulin mutants under conditions in which they assume a partially folded state analogous to the folding intermediates. Mutants that were designed to disrupt the secondary structure units showed the gyration radii similar to that of the wild type protein, indicating that chain collapse is due to coil‐globule transitions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 651–658, 2014.     

A water molecule participates in the secondary structure of hyaluronan.

The structure of hyaluronan was investigated in water/dimethyl sulphoxide mixtures by using high-field n.m.r. and space-filling molecular models. The secondary structure previously established in detail in 'dry' dimethyl sulphoxide [Heatley, Scott & Hull (1984) Biochem. J. 220, 197-205] undergoes changes on addition of water, compatible with the incorporation of a water bridge between the uronate carboxylate and acetamido NH groups. Molecular models show that such a configuration is highly probable, and saturation-transfer experiments yield rates of NH proton exchange that support this proposed structure. The existence of two distinct stable configurations for hyaluronan, in water-rich and water-poor conditions respectively, may have biological implications, e.g. during its biosynthesis in cell membranes. There are extensive hydrophobic regions in both forms, which may be important for interactions with e.g., membranes, proteins and itself.     

蛋白质二级结构预测方法的评价

目前评价蛋白质二级结构预测方法主要考虑预测准确率,并没有充分考虑方法自身参数对方法的影响。本文提出一种新型评价方法,将内在评价与外在评价相结合评价预测方法的优劣。以基于混合并行遗传算法的蛋白质二级结构预测方法为例,通过内在评价,合理选取内在参数——切片长度和组内类别数,有效提高预测准确率,同时,通过外在评价,与其他基于随机算法的蛋白质二级结构预测算法比较和与CASP所提供的结论比较,说明了方法的有效性与正确性,以此验证内在评价和外在评价的客观性、公正性和全面性。     

Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure.

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.     

Comparison of an exact and a simulation method for calculating gene extinction probabilities in pedigrees

A comparison is made between a much used simulation method, commonly called gene dropping, and the exact computational technique of peeling. These methods are illustrated using the problem of finding the distribution of the number of distinct ancestral genes surviving at an autosomal locus. Each method is used on several real zoo pedigrees, of varying size and complexity, and the results are compared. Gene dropping is found to be a good approximation to peeling, but for all but the most complex pedigrees surveyed, peeling is preferable. The relationship between heterozygosity and allelic variability is investigated.     

Heat capacity of proteins. II. Partial molar heat capacity of the unfolded polypeptide chain of proteins: protein unfolding effects

Using the heat capacity values for amino acid side-chains and the peptide unit determined in the accompanying paper, we calculated the partial heat capacities of the unfolded state for four proteins (apomyoglobin, apocytochrome c, ribonuclease A, lysozyme) in aqueous solution in the temperature range from 5 to 125 degrees C, with an assumption that the constituent amino acid residues contribute additively to the integral heat capacity of a polypeptide chain. These ideal heat capacity functions of the extended polypeptide chains were compared with the calorimetrically determined heat capacity functions of the heat and acid-denatured proteins. The average deviation of the experimental functions from the calculated ideal ones in the whole studied temperature range does not exceed the experimental error (5%). Therefore, the heat-denatured state of a protein, in solutions with acidic pH preventing aggregation, approximates well the completely unfolded state of this macromolecule. The heat capacity change caused by hydration of amino acid residues upon protein unfolding was also determined and it was shown that this is the major contributor to the observed heat capacity effect of unfolding. Its value is different for different proteins and correlates well with the surface area of non-polar groups exposed upon unfolding. The heat capacity effect due to the configurational freedom gain by the polypeptide chain was found to contribute only a small part of the overall heat capacity change on unfolding.     

Conformational motion correlations in the formation of polypeptide secondary structure in a viscous medium

The Langevin dynamics method and statistical correlation analysis were used to study the α-helical structure folding dynamics of the (Ala)₅₀, (AlaGly)₂₅, and (AlaGly)₇₅ polypeptides depending on the viscosity of the medium. Friction forces that arise when the effective viscosity of the medium is similar to the viscosity of water were found to result in strong correlations between the backbone torsion angles. The polypeptides under study folded mainly to produce α-helical structures. A structure of two contacting α-helices that were approximately equal in length and had a loop between them was observed for a longer chain of 150 residues. A method to visualize the correlation matrix of the dihedral angles of a polypeptide chain was developed for analyzing the effects of the dynamic correlation of conformational degrees of freedom. The analysis of the dynamics of the correlation matrix showed that rotations involving angles of the same type (φ–φ and ψ–ψ) occur predominantly in one direction. Rotations invoving different angles (φ–ψ) occur predominantly in opposite directions, so that the total macromolecule does not rotate. A significant reduction in the effective viscosity of the medium disrupts the correlation and makes the rotations stochastic, thus distorting the formation of the regular (helical) structure. The effects of correlated conformational motions are consequences of viscous friction forces. This conclusion agrees with our previous results that outlined the principle of the minimum rate of energy dissipation and the equipartition of energy dissipation rate between conformational degrees of freedom.     

Primary structure of streptococcal proteinase. III. Isolation of cyanogen bromide peptides: complete covalent structure of the polypeptide chain.

The following sequence has been derived for streptococcal proteinase. (See article). The sequence permits the assignment of the single cysteine residue essential for catalytic action at position 47 from the NH2 terminus of the protein. The tryptophan residue at the binding site of the enzyme is at position 214. A histidine residue at position 195 has been assigned as the catalytically important entity in the molecule. Streptococcal proteinase and papain, an enzyme with similar properties, are compared with respect to structure and function.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

A toy model for predicting the rate of amyloid formation from unfolded protein

We develop a toy model for predicting the rate of amyloid formation from an unfolded polypeptide. The model assumes irreversible amyloid growth, employs a collision encounter scheme and uses a Gaussian chain approximation to describe the polypeptide sequence. A principal feature of the model is its dependence on a number of key sequence residues whose correct placement, geometric arrangement and orientation in relation to their interacting partners define the success, or otherwise, of the amyloid formation reaction. Although not realistic at the molecular level, the model captures some essential features of the system and is therefore useful from a heuristic standpoint. For the case of amyloid formation from an unstructured state, the model suggests that the major determinants of the rate of fibril formation are the length of the sequence separating the critical amino acids promoting amyloid formation and the positional placement of the critical residues within the sequence. Our findings suggest also that the sequence distance between the key interacting amino acid residues may play a role in defining the maximum width of a fibril and that the addition of non-interacting segments of long structure-less polypeptide chain to an amyloidogenic peptide may act to inhibit fibril formation. We discuss these findings with reference to the placement of critical sequence residues within the polypeptide chain, the design of polypeptides with lower amyloid formation propensities and the development of aggregation inhibitors as potential therapeutics for protein depositional disorders.     

A vector-based method for drawing RNA secondary structure.

MOTIVATION: To produce a polygonal display of RNA secondary structure with minimal overlap and distortion of structural elements, with minimal search for positioning them, and with minimal user intervention. RESULTS: A new algorithm for automatically drawing RNA secondary structure has been developed. The algorithm represents the direction and space for a structural element using vector and vector space. Two heuristics are used. The first heuristic is concerned with ordering structural elements to be positioned and the second with positioning them in space. The algorithm and a graphical user interface have been implemented in a working program called VizQFolder on IBM PC compatibles. Experimental results demonstrate that VizQFolder is capable of automatically generating nearly overlap-free polygonal displays for long RNA molecules. The only distortion performed to avoid overlap is the rotation of helices, leading to efficient generation of a polygonal display without sacrificing its readability. VizQFolder is not coupled to a specific prediction program of RNA secondary structure, and thus can be used for visualizing secondary structure models obtained by any means. AVAILABILITY: The executable code of VizQFolder is available at http://automation.inha.ac.kr/khan. It can also be obtained from the authors upon request.     

Accurate general method for lattice approximation of three-dimensional structure of a chain molecule

An algorithm based on dynamic programming gives the lattice models having the minimal RMS deviations from the actual folds of protein (RNA, etc.) chains for a given lattice and a given orientation of the macromolecule relative to the lattice. The algorithm is applicable for 3-D lattices of any kind. The accuracy of the lattice approximation increases when the distance between neighbor chain links is not rigidly fixed. Special repulsive potentials facilitate generation of self-avoiding lattice chains. The results of model building show the efficiency and precisionof this proposed general method when compared with others. © 1995 Wiley-Liss, Inc.     

Identification of formation of initial native structure in onconase from an unfolded state

In the oxidative folding of onconase, the stabilization of intermediates early in the folding process gives rise to efficient formation of its biologically active form. To identify the residues responsible for the initial formation of structured intermediates, the transition from an ensemble of unstructured three-disulfide species, 3S(U), to a single structured three-disulfide intermediate species, des-[30-75] or 3S(F), at pH 8.0 and 25 °C was examined. This transition was first monitored by far-UV circular dichroism spectroscopy at pH 8.0 and 25 °C, showing that it occurs with the formation of secondary structure, presumably because of native interactions. The time dependence of formation of nativelike structure was then followed by nuclear magnetic resonance spectroscopy after we had arrested the transition at different times by lowering the pH to 3 and then acquiring (1)H-(15)N heteronuclear single-quantum coherence spectra at pH 3 and 16 °C to identify amide hydrogens that become part of nativelike structure. H/D exchange was utilized to reduce the intensity of resonances from backbone amide hydrogens not involved in structure, without allowing exchange of backbone amide hydrogens involved in initial structure. Six hydrogen-bonding residues, namely, Tyr38, Lys49, Ser82, Cys90, Glu91, and Ala94, were identified as being involved in the earliest detectable nativelike structure before complete formation of des-[30-75] and are further stabilized later in the formation of this intermediate through S-S/SH interchange. By observing the stabilization of the structures of these residues by their neighboring residues, we have identified the initial, nativelike structural elements formed in this transition, providing details of the initial events in the oxidative folding of onconase.     

A method of calculating the discrete secondary structures of globular proteins

The model of formation of alpha-helices and beta-structures determined by joint action of the three elements: N-terminal, internal and C-terminal fragments are presented. Algorithm for calculation of their localization in a given amino acid sequence was constructed on the base of this model. The preference of the fragments of the amino acid sequence to a definite type of the secondary structure was estimated on the base of corresponding average values of linear discriminant functions dsk (s = alpha, beta, k = N, in, C). The latter were constructed in the previous paper on the base of the revealed significant characteristics. These integral characteristics are used for calculating the localisation of discrete secondary structures. The total prediction for 3 states (alpha, beta, c) given 71% correctly predicted residues (for 4 states alpha, beta, c, t) 62% for the training set, consisting of 72 proteins. For the control set (15 proteins) the accuracy of prediction is about 65%. The essential advantages of this method are: 1) the possibility to localize the discrete secondary structures; 2) the high accuracy of prediction of long secondary structures (for alpha-helices approximately 90%, for beta-structures approximately 80%), which is important for the determination of the protein folding. The influence of mutation on the secondary structure of proteins was investigated. The anormally high stability of the secondary structures of immunoglobulins to mutations was revealed. This probably results from the selection during evolution of such variants of amino acid sequences, which are able to provide the functional variability of antigenic determinants, but keep invariant the tertially structure of protein.