On the two kinds of nucleation in the helix–coil transition theory of polypeptide chains

The nucleation of a helical sequence from a random chain of the polypeptide molecule as well as the nucleation of a random-coil sequence from the helical conformation of the molecule are considered simultaneously in evaluating the partition function of the system. This partition function is then used for a comparative analysis of the theories of Zimm and Bragg, Gibbs and DiMarzio, and Lifson and Roig. It is shown that while all three account properly for the essential nature of the nucleation phenomenon the first considers in detail the random-coil nucleation, the second emphasizes the details of the helix nucleation, while the third neglects the fine details of both in a symmetric way.     

Adsorption of polypeptides on the solid surface. II. Effect of secondary chain structure and helix–coil transition

The theory of adsorption of semistiff chains on a planar surface developed by the authors previously has been used to consider the helix–coil transition in single-stranded macromolecule interacting with an adsorbent plane. The cases of nonselective interaction when the adsorption energy is independent of the unit conformation (a) and selective interaction with only helical (b) or coiled (c) sequences active in adsorption were investigated. In case (b) the existence of secondary structure favors chain bonding to the surface. This leads to the increase in the stability of the helical state and complete polypeptide chain spiralization. The profile of the conformational helix–coil transition acquires an asymmetrical shape inherent to the second-order phase transition. In case (c) the bonding of a partially helical chain to the surface is similar to the adsorption of Gaussian coils and is accompanied by the destruction of secondary structure, this destruction being appreciable even if the helical state in space was favorable.     

Interaction of sodium decyl sulfate with poly(L-ornithine) and poly(L-lysine) in aqueous solution

The binding isotherms of sodium decyl sulfate to poly(L -ornithine), poly(D ,L -ornithine), and poly(L -lysine) at neutral pH were determined potentiometrically. The nature of a highly cooperative binding in all three cases suggests a micelle-like clustering of the surfactant ions onto the polypeptide side groups. The hydrophobic interaction between the nonpolar groups overshadows the coulombic interaction between the charged groups. The titration curves can be interpreted well by the Zimm–Bragg theory. The average cluster size of bound surfactant ions is sufficiently large to promote the β-structure of (L -Lys)_n even at a very low binding ratio of surfactant to polypeptide residue, whereas the onset of the helical structure for (L -Orn)_n begins after about 7 surfactant ions are bound to two turns of the helix. The CD results are consistent with this explanation.     

Adsorption of polypeptides on solid surfaces. I. Effect of chain stiffness

The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.     

A molecular thermodynamic approach to predict the secondary structure of homopolypeptides in aqueous systems.

Under physiological conditions, many polypeptide chains spontaneously fold into discrete and tightly packed three-dimensional structures. The folded polypeptide chain conformation is believed to represent a minimum Gibbs energy of the system, governed by the weak interactions that operate between the amino acid residues and between the residues and the solvent. A semiempirical molecular thermodynamic model is proposed to represent the Gibbs energy of folding of aqueous homopolypeptide systems. The model takes into consideration both the entropy contribution and the enthalpy contribution of folding homopolypeptide chains in aqueous solutions. The entropy contribution is derived from the Flory-Huggins expression for the entropy of mixing. It accounts for the entropy loss in folding a random-coiled polypeptide chain into a specific polypeptide conformation. The enthalpy contribution is derived from a molecular segment-based Non-Random Two Liquid (NRTL) local composition model [H. Renon and J. M. Prausnitz (1968) AIChE J., Vol. 14, pp. 135-142; C.-C. Chen and L. B. Evans (1986) AIChE J., Vol. 32, pp. 444-454], which takes into consideration of the residue-residue, residue-solvent, and solvent-solvent binary physical interactions along with the local compositions of amino acid residues in aqueous homopolypeptides. The UNIFAC group contribution method [A. Fredenslund, R. L. Jones, and J. M. Prausnitz (1975) AIChE J., 21, 1086-1099; A. Fredenslund, J. Gmehling, and P. Rasmussen (1977) Vapor-Liquid Equilibrium Using UNIFAC, Elsevier Scientific Publishing Company, Amsterdam], developed originally to estimate the excess Gibbs energy of solutions of small molecules, was used to estimate the NRTL binary interaction parameters. The model yields a hydrophobicity scale for the 20 amino acid side chains, which compares favorably with established scales [Y. Nozaki and C. Tanford (1971) Journal of Biological Chemistry, Vol. 46, pp. 2211-2217; E. B. Leodidis and T. A. Hatton (1990) Journal of Physical Chemistry, Vol. 94, pp. 6411-6420]. In addition, the model generates qualitatively correct thermodynamic constants and it accurately predicts thermodynamically favorable folding of a number of aqueous homopolypeptides from random-coiled states into alpha-helices. The model further facilitates estimation of the Zimm-Bragg helix growth parameter s and the nucleation parameter sigma for amino acid residues [B. H. Zimm and J. K. Bragg (1959) Journal of Chemical Physics, Vol. 31, pp. 526-535]. The calculated values of the two parameters fall into the ranges suggested by Zimm and Bragg.     

Derivation of the small-angle x-ray scattering functions for local conformations of polypeptide chains in solution

The small-angle x-ray scattering (SAXS) functions are analytically derived for both the randomly coiled and helical local conformations of a polypeptide chain in solution. The resulting scattering functions for helices of various types are characterized by a maximum in the range of scattering-vector corresponding to Bragg spacings of 3-5 A, whereas the random-coil function has no maximum. This result is compatible with the extant SAXS data for partially neutralized poly(L-glutamic acid) and poly(L-lysine) in aqueous solutions. Comparison of the SAXS data with the calculated scattering functions shows that helical structures in both polypeptide chains are of the 3.6(13)-helix (alpha-helix) rather than 3.0(10)-type.     

Probing the influence of sequence-dependent interactions upon α-helix stability in alanine-based linear peptides

The observation that short, linear alanine-based polypeptides form stable α-helices in aqueous solution has allowed the development of well-defined experimental systems with which to study the influence of amino acid sequence upon the stability of secondary structure. We have performed detailed conformational searches upon six alanine-based peptides in order to rationalize the observed variation in the α-helical stability in terms of side-chain-backbone and side-chain-side-chain interactions. Although a simple, gas-phase, potential model was used to obtain the conformational energies for these peptides, good agreement was obtained with experiment regarding their relative α-helical stabilities. Our calculations clearly indicate that valine, isoleucine, and phenylalanine residues should destabilize the α-helical conformation when included within alanine-based peptides because of energetically unfavorable side-chain-backbone interactions, which tend to result in the formation of regions of 3₁₀-helix. In the case of valine, the destabilization most probably arises from entropic effects as the isopropyl side chain can assume more orientations in the 3₁₀-helical form of the peptide. A detailed examination of very short-range interactions in these peptides has also indicated that an interaction, involving fewer than five consecutive residues, whose stabilizing effect reinforces that of the (i, i + 4) hydrogen bond may be the basis of the requirement for increased nucleation (σ) and propagation parameters (s) required by Zimm–Bragg theory to predict the α-helical content for compounds in this class of short peptides. Our calculations complement recent work using modified Zimm–Bragg and Lifson–Roig theories of the helix–coil transition, and are consistent with molecular dynamics simulations upon linear peptides in aqueous solution. © 1993 John Wiley & Sons, Inc.     

Beyond the nearest-neighbor Zimm-Bragg model for helix-coil transition in peptides

The nearest-neighbor (micro = 1) variant of the Zimm and Bragg (ZB) model has been extensively used to describe the helix-coil transition in biopolymers. In this work, we investigate the helix-coil transition for a 21-residue alanine peptide (AP) with the ZB model up to fourth nearest neighbor (micro = 1, 2, 3, and 4). We use a matrix approach that takes into account combinations of any number of helical stretches of any length and therefore gives the exact statistical weight of the chain within the assumptions of the ZB model. The parameters of the model are determined by fitting the temperature-dependent circular dichroism and Fourier transform infrared experimental spectra of the AP. All variants of the model fit the experimental data, thus giving similar results in terms of the macroscopic observables, such as temperature-dependent fractional helicity. However, the resulting microscopic parameters, such as distributions of the individual residue helical probabilities and free energy surfaces, vary significantly depending on the variant of the model. Overall, the mean residue enthalpy and entropy (in the absolute value) both increase with micro, but combined yield essentially the same "effective" value of the ZB propagation parameters for all micro. Greater helical probabilities for individual residues are predicted for larger micro, in particular, near the center of the sequence. The ZB nucleation parameters increase with increasing micro, which results in a lower free energy barrier to helix nucleation and lower apparent "cooperativity" of the transition. The significance of the long-range interactions for the predictions of ZB model for helix-coil transition, the calculated model parameters and the limitations of the model are discussed.     

Roles of non‐native hydrogen‐bonding interaction in helix‐coil transition of a single polypeptide as revealed by comparison between Gō‐like and non‐Gō models

To explore the role of non‐native interactions in the helix‐coil transition, a detailed comparison between a Gō‐like model and a non‐Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō‐like model, and the non‐native ones with sequence interval more than 4 is also included into the non‐Gō model. Some significant differences between the results from those two models have been found. The non‐native hydrogen bonds were found most populated at temperature around the helix‐coil transition. The rearrangement of non‐native hydrogen bonds into native ones in the formation of α‐helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non‐Gō model for a non‐short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non‐native hydrogen bonds have complicated the temperature‐dependence of Zimm‐Bragg nucleation constant. The increase of relative probability of non‐native hydrogen bonding for long polypeptide chains leads to non‐monotonous chain length effect on the transition temperature. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Size-exclusion high-performance liquid chromatography in the study of the autoassociating antibiotic gramicidin A in micellar milieu

Gramicidin A (gA) is a polypeptide antibiotic which forms dimeric channels specific for monovalent cations in biological membranes. It is a polymorphic molecule that adopts several different conformations, double-stranded (ds) helical dimers (pore conformation) and single-stranded beta-helical dimers (channel conformation). This study investigated the conformational adaptability of gramicidin A when incorporated into micelles as membrane-mimetic model system. Taking advantage of our reported, versatile, size-exclusion high-performance liquid chromatography (SE-HPLC) strategy that allows the separation of double-stranded dimers and monomers, we have quantitatively characterized the conformational transition undergone by the peptide in the micellar milieu. The importance of both hydrophobic/hydrophilic moieties of the amphipaths in the stabilization of concrete conformational species is demonstrated using detergents with different hydrocarbon chain length and/or polar head. SE-HPLC is a valuable, rapid, accurate technique for the structural characterization of hydrophobic autoassociating peptides that work in lipid environments such as biological membranes.     

Thermal unfolding of helices of a C-peptide analogue of ribonuclease A in sodium dodecyl sulfate solution

The conformation of a 13-residue C-peptide analogue of ribonuclease A, suc-AET-AAAKFLRAHA-CONH2, in NaDodSO4 solutions with respect to temperature was studied with CD. The equilibrium constant of unfolding yielded a straight line in a van't Hoff plot. In 10 mM NaDodSO4, delta G mu = 120 cal/mol, delta H mu = 700 cal/mol, and delta S mu = 2.0 entropy units all on per helical residue. These values compared fairly well with the thermodynamic parameters of the uncharged helix-coil transition of (Glu)n in 0.1 M NaCl based on the theories of Zimm and Bragg and Zimm and Rice. The peptide was not unfolded at 75 degrees C completely. Even in water without surfactant it was not a "random coil."     

Degradation of N5-(2-hydroxyethyl)-L-glutamine and L-glutamic acid homopolymers and copolymers by papain

The rate of degradation of poly[N5-(2-hydroxyethyl)-L-glutamine] (PHEG), poly(L-glutamic acid) (PGA) and poly[HEG-co-GA] random copolymers by papain was measured in the pH range 4.0-7.5, employing the gel permeation chromatography method. The effect of the degree of ionization on the polymer conformation was measured by circular dichroism (c.d.). PHEG, which is uncharged, had a random coil conformation and an almost constant degradation rate within the whole pH interval. The ionization of PGA increased with increasing pH and was accompanied by conformational transition from helix to random coil. The hydrolysis of PGA by papain depended on pH with the optimum at about pH 5, indicating that both the high content of helix (at pH less than 5) and increasing charge density (at pH greater than 5), decreased the degradation rate. Contrary to PGA, pH profiles of the degradation rate of poly[HEG-co-GA] copolymers are monotonous and do not decrease at pH less than 5. In the copolymers the HEG residues act as a helix breaker and limit the formation of helical conformation. The role of structural features of a macromolecular substrate, i.e. the charge, helical conformation and the nature of amino acid residues, in the interaction between enzyme and polymer is discussed.     

Thermodynamics of protein self-association and unfolding. The case of apolipoprotein A-I

Protein self-association and protein unfolding are two temperature-dependent processes whose understanding is of utmost importance for the development of biological pharmaceuticals because protein association may stabilize or destabilize protein structure and function. Here we present new theoretical and experimental methods for analyzing the thermodynamics of self-association and unfolding. We used isothermal dilution calorimetry and analytical ultracentrifugation to measure protein self-association and introduced binding partition functions to analyze the cooperative association equilibria. In a second type of experiment, we monitored thermal protein unfolding with differential scanning calorimetry and circular dichroism spectroscopy and used the Zimm?Bragg theory to analyze the unfolding process. For α-helical proteins, the cooperative Zimm?Bragg theory appears to be a powerful alternative to the classical two-state model. As a model protein, we chose highly purified human recombinant apolipoprotein A-I. Self-association of Apo A-I showed a maximum at 21 °C with an association constant Ka of 5.6 × 10(5) M(?1), a cooperativity parameter σ of 0.003, and a maximal association number n of 8. The association enthalpy was linearly dependent on temperature and changed from endothermic at low temperatures to exothermic above 21 °C with a molar heat capacity ΔC(p)° of ?2.76 kJ mol(?1) K(?1). Above 45 °C, the association could no longer be measured because of the onset of unfolding. Unfolding occurred between 45 and 65 °C and was reversible and independent of protein concentration up to 160 μM. The midpoint of unfolding (T(0)) as measured by DSC was 52?53 °C; the enthalpy of unfolding (ΔH(N)(U)) was 420 kJ/mol. The molar heat capacity (Δ(N)(U)C(p)) increased by 5.0 ± 0.5 kJ mol(?1) K(?1) upon unfolding corresponding to a loss of 80?85 helical segments, which was confirmed by circular dichroism spectroscopy. Unfolding was highly cooperative with a nucleation parameter σ of 4.4 × 10(?5).     

Monte Carlo simulation of the conformational behaviour of a polypeptide chain near a charged surface

The conformational behaviour of a short polypeptide chain in the neighbourhood of a charged plane is simulated using a Monte Carlo method. In this approach, the plane is taken as a model of an interface separating a hydrophobic region from a hydrophilic one. It is shown that in the neighbourhood of the plane, folded molecular conformations are prevailing whilst stretched conformations are preferred far from the interface. When the plane is not charged, the molecule adjusts itself parallel to the interface. For a given position of the molecule with respect to the plane, when the charge density of the plane is increased, the molecule tends to turn perpendicular to the plane. The surface may either attract or repulse the molecule depending on the value of the charge density (the plane is always negatively charged).     

Diffuse x-ray wide-angle scattering of polyglutamic acid in solution]

The diffuse wide angle x-ray scattering (WAXS) of polyglutamic acid (PGA) in solution was studied using an x-ray diffractometer with small aperture of the primary beam. The scattering curve was recorded at an angular interval from (article: see text). The experimental scattering intensity of PGA with alpha-helical CD spectrum showed a maximum at 14.4 nm-1. Unordered PGA in solution yielded no maximum at this scattering angle. The studies have proved that the scattering theory can be applied to globular proteins in solution as well as to chain molecules in solution in this angular interval. The differences between the calculated scattering curves and the experimental curves indicate minor movements of the side chains of PGA in solutions and slight structuring of the solvent at the surface of the polypeptide chain.     

Solution properties of synthetic polypeptides. V. Helix–coil transition in poly(β-benzyl L-aspartate)

Simple approximate expressions have been derived from the theory of Zimm and Bragg for use in the analysis of experimental data on the helix-coil transition in polypeptide. On the basis of the resulting expressions practical procedures are proposed to determine two basic parameters characterizing a thermally induced transition, i.e., helix initiation parameter σ and enthalpy change for helix formation, ΔH. They have been applied to the data for poly(β-benzyl L -aspartate) (PBLA) with the result: σ = 1.6 × 10^?4 and ΔH = ?450 cal/mole for PBLA in m-cresol; σ = 0.6 × 10^?4 and ΔH = 260 cal/mole for PBLA in chloroform containing 5.7 vol-% of dichloroacetic acid. This result gives evidence that σ may change not only from one polypeptide to another but also for a given polypeptide in different solvents. The change in limiting viscosity number [η] accompanying the transition was measured in the same solvents. The curve of [η] versus helical content had a relatively monotonic shape for the chloroformdichloroacetic acid solutions as compared with that for the m-cresol solutions, indicating that [η] depended largely on σ. Provided that [η] is a direct measure of the mean-square radius of gyration, 〈S²〉, the results are consistent with the theoretical predictions of Nagai and of Miller and Flory for 〈S²〉.     

Spring mechanics of alpha-helical polypeptide

To design protein- and polymer-based micro-machineries, it is important to understand the mechanical properties of basic structural elements such as the alpha-helix of polypeptides. We employed the force measurement mode of an atomic force microscope (AFM) to investigate the spring mechanics of poly-L-glutamic acid (PGA) in its helical and randomly coiled states. After covalently anchoring the polypeptide between a silicon substrate and an AFM tip, the force required to stretch the polymer was measured. The results indicated that PGA in its helical conformation could be stretched almost fully with a continuous increase in the stretching force, suggesting that it can be used as a reliable coil-spring in the future design of spring-loaded molecular machineries.     

On the flexibility of poly(γ-benzyl L-glutamate) in helicogenic solvents

The molecular-weight dependence of the rms radius of gyration of poly(γ-benzyl L -glutamate) (PBLG) in helicogenic solvents shows negative and positive deviations from expectations for an intact and rigid α-helix in the higher and lower molecular-weight ranges, respectively. In order to study the reason for both deviations, we compare the extant experimental data of with those computed for wormlike chain, freely jointed rod, and a rigid rod having random-coil portions at both ends. The computation for the freely jointed rod and the rigid rod having frayed ends is carried out by a simulation method of Muroga. From the Zimm and Bragg theory and the above comparisons, it is concluded that both deviations can be self-consistently explained if PBLG in helicogenic solvents has an essentially intact α-helical structure with some flexibility arising from random fluctuations in hydrogen bond length. This flexibility explains the negative deviations in the high molecular weight region. The positive deviations in the low molecular weight region result from the tendency of helices to unwind at the ends. © 1998 John Wiley & Sons, Inc. Biopoly 45: 281–288, 1998     

Vibrational spectra and dispersion curves of poly-L-proline II chain

Using Wilson's GF-matrix method as modified by Higgs for infinite helical polymers, dispersion curves and the frequency distribution function have been calculated for poly-L -proline II chain. Infrared spectrum is obtained and a Urey-Bradley force field, which provides best fit with the observed frequencies, is evaluated. The result are discussed from the viewpoint of the conformational characteristics of forms I and II.