Simulation of α-helix–coil transitions in simplified polyvaline: Equilibrium properties and brownian dynamics

A quantitative understanding of helix–coil dynamics will help explain their role in protein folding and in folded proteins. As a contribution to the understanding, the equilibrium and dynamical aspects of the helix–coil transition in polyvaline have been studied by computer simulation using a simplified model of the polypeptide chain. Each amino acid residue is treated as a single quasiparticle in an effective potential that approximates the potential of mean force in solution. The equilibrium properties examined include the helix–coil transition and its dependence on chain position and well depth at the coil–helix interface. A stochastic simulation of the Brownian motion of the chain in its solvent surroundings has been used to investigate dynamical properties. Time histories of the dihedral angles have been used to study the behavior of the helical structure. Auto and cross-correlation functions have been calculated from the time histories and from the state (helix or coil) functions of the residues with relaxation times of tens to hundreds of picoseconds. Helix–coil rate constants of tens of ns^?1 were found for both directions of the transition. © 1993 John Wiley & Sons, Inc.     

Helix–coil transition for poly(L-glutamic acid) in water–ethanol solutions

Potentiometric titrations and some complementary optical rotation data are presented for solutions of poly(L - glutamic acid) (PGA) in several H₂O–ethanol mixtures. The data allow the determination of the intrinsic pK (pK₀), slope of the apparent. pK (pK_app), versus degree of ionization curves and of the enthalpy of ionization as a function of ethanol concentration. The variation of the degree of ionization at which the helix–coil transformation occurs with ethanol and temperature is also determined. Finally free energy, enthalpy, and intropy changes associated with the helix–coil transformation for the uncharged conformers are determined from the titration curves. The effect of the ethanol is to increase the stability of the helical conformation of PGA for both the charged and the uncharged forms of the polymer. The stabilization of the uncharged helix is essentially an entropic effect.     

Helix–coil transitions of compositionally heterogeneous DNA

Fragmented and mitomycin C cross-linked E. coli DNA was fractionated according to base composition by means of hydroxylapatite chromatography and density-gradient centrifugation in order to determine the effect of compositional heterogeneity on the breadth of the helix–coil transition. The transitions of some of the fractions are broader than that of the unfractionated DNA, due, presumably, to nonrandom sequences in molecules of 5 × 10⁵ daltons. Analysis of the transition breadths in terms of the known heterogeneity leads to reconsideration of current DNA helix–coil transition theory. We propose that partially denatured states include those for which the chains do not remain in strict register. Denaturation profiles are comprehensible only if this multitude of entropically favorable, degenerate states is included in the theory.     

The effect of simple shear flow on the helix–coil transition of poly‐L‐lysine

Studies of the helix‐to‐coil transition in dilute solutions of poly‐L ‐lysine, dissolved in mixtures of water and methanol (MeOH), have been carried under shear flow using flow birefringence and modulated polarimetry. The fraction of helical conformations in a given solution remains independent of shear rate for MeOH concentrations above and below the critical value for the helix‐coil transition (i.e., 87.5% MeOH). For the 87.5% MeOH solutions, a shear‐induced helix‐to‐“stretched” coil transition occurs above a critical shear rate. Induction times for the transition show a temperature and shear rate dependence that can be described in terms of an activated jump process. Measurements of circular birefringence on cessation of flow also show that the transition is reversible, with the stretched coil reverting to the helical state on a time scale of several seconds. The activation energy for the jump process is found to be 16.2 kJ/mole. © 1999 John Wiley & Sons, Inc. Biopoly 50: 589–594, 1999     

Helix–coil transition of poly(α,L-glutamic acid) at an interface: Correlation with static and dynamic membrane properties

When adsorbed from an aqueous dilute solution at high pH into the pores of an inert cellulose acetate filter, poly(α,L -glutamic acid) remains strongly anchored to the pore walls. The existence of the helix–coil transition for the adsorbed polypeptide in a certain pH range is evidenced by static and dynamic membrane properties displayed by the “activated” filter, such as excess cation uptake, membrane potential, and hyraulic permeability. In particular, the variations of the hydrodynamic thickeness present a sigmoidal shape characteristic of the helix–coil transition at the interface, a transition apparently less sharp than in solution.     

Helix–coil stability constants for amino acids in nonaqueous solvents. Studies of random poly(γ-benzyl-L-glutamate-co-L-alanine) and poly(γ-benzyl-L-glutamate-co-L-leucine) in a mixed solvent

The host–guest technique has been applied to the determination of the helix–coil stability constants of two naturally occurring amino acids, L -alanine and L -leucine, in a nonaqueous solvent system. Random copolymers containing L -alanine and L -leucine, respectively, as guest residues and γ-benzyl-L -glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix–coil transition behavior in a dichloroacetic acid (DCA)–1,2-dichloroethane (DCE) mixture. Two types of helix–coil transitions were carried out on the copolymers: solvent-induced transitions in DCA–DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA–DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, σ and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L -alanine residue stabilizes the α-helical conformation more than the L -leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.     

A Study of stepwise conformational changes in poly(β-benzyl-L-aspartate) with the helix–coil transition by means of proton and carbon-13 NMR

The helix–coil transition for poly(β-benzyl-L -aspartate) [poly(Asp[OBzl])] in solvent mixtures of trifluoroacetic acid/deuterated chloroform (F₃AcOH/CDCl₃) was studied by means of proton and carbon-13 nmr. Conformational fixation of the side chain occurs before the coil–helix transition of the backbone, when neighboring phenyl rings face each other. Another type of conformational fixation occurs in the side chain after the coil–helix transition of the backbone. These conformational changes of the side chain are due to the changes of the strength of the interaction between the side-chain ester group and the F₃AcOH molecule. In the absence of F₃AcOH (coil-forming solvent), the polymer has a rather rigid structure in which the side chain may wrap around the backbone. These conformational changes of the polymer are closely related to the changes of the interaction between the polymer and F₃AcOH molecules.     

Helix–coil stability constants for the naturally occurring amino acids in water. XXI. Glutamine parameters from random poly(hydroxypropylglutamine-co-L-glutamine) and poly(hydroxybutylglutamine-co-L-glutamine)

Water-soluble, random copolymers containing L -glutamine and either N⁵-(3-hydroxypropyl)-L -glutamine or N⁵-(4-hydroxybutyl)-L -glutamine were synthesized, fractionated, and characterized. The thermally induced helix–coil transitions of these copolymers were studied in water. A short-range interaction theory was used to deduce the Zimm-Bragg parameters σ and s for the helix–coil transition in poly(L -glutamine) in water from an analysis of the melting curves of the copolymers in the manner described in earlier papers. The computed values of s indicate that L -glutamine is helix-indifferent at low temperature and a helix-destabilizing residue at high temperature in water. At all temperatures in the range of 0–70°C, the glutamine residue promotes helix–coil boundaries since the computed value of σ is large.     

Single-residue substitution in homopolypeptides: Perturbative helix–coil theory at a single site

Based on Lifson–Roig's helix–coil transition theory, substitution of a single heteroresidue into a homopolymer host is studied. This study models recent experiments that substitute a single amino acid into a small peptide in water [A. Chakrabartty, J. A. Schellman, and R. L. Baldwin (1991), Nature, Vol. 351, pp. 586–688]. Our formalism, which is based on a perturbation method, differs from the existing theory for sequenced polymers and is naturally analogous, hence likely to be useful, to substitution experiments in the laboratory. It is shown that the intrinsic helix propensity w is directly proportional to the equilibrium constant for the helix–coil equilibrium of a single residue in a host peptide. This intuitive new result will simplify experimental data interpretations for measurements of the helical conformation on the single amino acid level. It is also shown that substitution affects the total helicity of the host peptide according to two considerations: the helicity of the replaced residue prior to the substitution, and the sensitivity of the site, a measure of neighboring interactions. The relationship between substitution stability and thermal stability is explored. © 1993 John Wiley & Sons, Inc.     

Nematic polymers: Excluded-volume effects

We present a theoretical model which describes a cooperative helix–coil liquid-crystal phase transition. We show that this model predicts a first-order phase transition where certain types of chainlike macromolecules in solution make a transition from a nearly coiled to a nearly rigid conformation accompanied by a simultaneous development of long-range nematic-type liquid crystalline orientational order. From this model, the phase boundaries between nematic and isotropic phases are obtained as functions of concentration of macromolecules and of other physical parameters.     

Solvent effects on the helix–coil transition in polypeptides

A simple way to incorporate the solvent–peptide interaction in any available theory of the helix–coil transition is developed. The competition between the intramolecular hydrogen bonding and the solvent–polymer hydrogen bonding is considered in multi-component solvents where some of the components have hydrogen-bonding capacity. Molecular averages are computed by using the theory of Lifson and Roig. The experimental data of Yang are analyzed, and the range of acceptable values of the equilibrium constants of hydrogen bond formation is deduced. The enthalpy of the transition in multicomponent solvents is calculated.     

Helix–coil transition in nucleoprotein—theory and applications

A general theory of helix–coil transition of irreversibly complexed nucleoproteins is presented. The equations are tested by experimental results in basic polypeptide–DNA complexes, nucleohistone I and pea bud nucleohistones. They show good agreement between theory and experiments. The theory provides direct measurement of a fraction of DNA base pairs covered by proteins, yielding a value of about 75% histone-covered base pairs in pea bud nucleohistone. It also provides a measurement of an average number of amino acid residues per nucleotide in protein-bound regions. This number varies from 1.0 to 1.4 in DNA–polylysine or DNA–polyarginine and from 2.9 to 3.3 in nucleohistone Ia, Ib, f1, and pea bud nucleohistone.     

DNA sequencing and helix–coil transition. II. Loop entropy and DNA melting

An explicit analytical theory of DNA melting is constructed. It accounts for the loop entropy and the elasticity of DNA strands. Explicit analytical formulas are presented for the melting curves of natural DNA and periodic polymers. The nature of the DNA helix–coil transition is investigated, and it is found to crucially depend on the nucleotide sequence.     

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.     

A nuclear magnetic resonance study of the helix–coil transition of poly(L-glutamic acid)

There have been many reports that the nuclear magnetic resonance (nmr) spectra of a large number of polypeptides exhibit peak doubling of the α-carbon and the α-carbon proton in the helix–coil transition region. One apparent exception to this generalization has been polypeptides with ionizable side chains, where the helix–coil transition is induced by changes in pH in aqueous solution. Because it is important to establish the proper theoretical reason for the peak doubling and its relation to the rate of conformational change of amino acid residues, we have reexamined the proton and carbon-13 nmr spectra, at high field, for two polydisperse samples of poly(L -glutamic acid). Doubling of the α-carbon proton resonance as well as those of the α- and β-carbon, and backbone carbonyl are observed for a low-molecular-weight sample (DP = 54), while a higher molecular weight sample (DP = 309), exhibits only single resonances. Thus, polydispersity by itself is not sufficient to observe peak doubling; low-molecular weight is also required.     

Determination of the relaxation time of the helix–coil transition of poly(γ-benzyl-L-glutamate) by the nmr technique

NMR measurements of poly(γ-benzyl-L -glutamate) are reported in several different strengths of magnetic field to determine the relaxation time of the helix–coil transition. Nmr spectra of various samples had line shapes varying from the double to single, depending on the extent of the polydispersity of the sample. This result indicated that the correct line shape of a polypeptide is obscured in the overlapping of multipeaks, which are due to the heterogeneity of the molecular weight in the sample. Thus, the conventional line-shape analysis could not be applied to the kinetic study of the helix–coil transition of polypeptides without consideration of this polydispersity effect on the line shape. To overcome this difficulty, we measured linewidths of nmr spectra for fairly monodisperse samples, using various nmr spectrometers, having field strengths from 60 to 220 MHz. The results were analyzed by a quadratic equation, which involves an additional term proportional to the frequency difference of two sites. The equation differs from the conventional quadratic equation, usually utilized in the case of the fast-exchange limit, only in this additional term. This modification is required to evaluate correctly the unusual broadening of the linewidth resulting from the polydispersity effect and to determine the relaxation time reflected in nmr. Nmr spectra of three samples (DP-35, 85, and 250) were measured by 220-, 100-, and 60-MHz spectrometers in trifluoroacetic acid/chloroform at 28°C and linewidths were analyzed. Relaxation times of the helix–coil transition obtained at the transition midpoint are 2.5 × 10^?4, 7 × 10^?4, and 1.1 × 10^?3 sec, for DP-35, 85, and 250, respectively.     

On the double peak of NMR in the helix—coil transition region

To attempt to resolve the controversy over “fast” and “slow” helix–coil transition rates in polypeptides, nuclear magnetic resonance spectra were measured for monodisperse poly-γ-benzyl-L -glutamate (PBLG). These results were compared with simulated line spectra which were computed by taking the molecular-weight distribution into consideration. Broad but single peaks have been observed in 220 mHz nmr for the α-CH and NH proton resonance spectra in the transition region. The shape of the line changes with the extent of polydispersity. Assuming a fast conversion rate, a molecular model of the helix–coil transition simulates these results. Consequently, the double peak which has been observed in the nmr of polypeptides at the helix–coil transition region is shown to result from the polydispersity in molecular weight.     

Showing up the thermal transconformation of Na–DNA in solution by noise spectrography

Measuring the equivalent noise resistance of Na–DNA solutions in NaCl provides in formation about the free ino atmosphere. In an Arrhenius type diagram, the helix → coil transition is clearly brought Out. A Calculation of the number of free ions in the solution as function of temperature, reveals once more the process of ejection of compensating Na⁺ ions form the macromolecules during the thermal transconformation.     

Studies of the helix–coil transition of poly-L-lysine in film and solution

Water-insoluble films of poly-L -lysine, crosslinked with formaldehyde, were suspended in aqueous media and their relative lengths measured as a function of pH. A sharp transition of the polymer was observed in the pH range which corresponded with that observed in polylysine solutions by optical rotation or dilatometry. In NaBr and NaCl solutions the coiled form of the polylysine film shrinks with increasing salt concentration, but in NaHCO₃ solution the extent of the contraction is larger, and the coil–helix transition of polylysine occurs at lower pH when NaHCO₃ is added to the medium. If one assumes the formation of amino carbamate in this case, this phenomenon can be well explained. Urea does break up the hydrogen bonds in helical polylysine film, but not completely. This result is interesting compared with that obtained for poly(L -glutamic acid). After the coil–helix transition region was found by film experiments, the volume change associated with the coil-to-helix transition was measured and found to be about 1–l.5 ml. per amino residue after taking electrostatic interaction into consideration. This value is nearly same as that obtained for poly(L -glutamic acid). By contrast, the value for poly-γ-benzyl-L -glutamate was reported to be ?0.077 ml./mole of repeating unit. So it is still necessary to determine the magnitude and direction of the volume change for various kinds of polypeptides.     

Helix–coil transition kinetics in aqueous poly(α,L-glutamic acid)

A polarimetric electric-field-jump relaxation apparatus is described and used to determine the relaxation spectrum for the helix–coil transition of poly(α,L -glutamic acid) in water at 24°C. A maximum relaxation time of 1.7 μc occurs at the transition midpoint (pH = 5.9) yielding a rate constant for helical growth of 6 × 10⁷ sec^?1.