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.     

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.     

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.     

Carbon-13 and proton NMR studies of helix-coil transition of poly(gamma-benzyl-L-glutamate).

The helix–coil conformational transition undergone by poly(γ-benzyl-L -glutamate) in solutions of trifluoroacetic acid and deuterated chloroform was studied by proton and carbon-13 nmr. The results indicate that in the case of the solvent-induced helix–coil transition, the side chain assumes a helical conformation before the backbone. In the thermally induced helix–coil transition, the results indicate the existence of an intermediate state, which is between the α-helix and random coil and is free from intramolecular hydrogen bonding.     

Comparison of several calculations of helix-coil transitions in heterogeneous polymers

Random number methods are used to calculate helix—coil transition curves for the model of a heterogeneous polypeptide of random sequence. These curves are compared with several other calculations. The random number computations confirm the exact calculation of Lehman; among the several approximate calculations examined only that of Fixman and Zeroka agrees closely with results of the random number method over the whole range of conditions considered. Calculations are also reported of the average length of helix and coil sections in a heterogeneous molecule of random sequence which is undergoing the helix-coil transition.     

PMR chemical shifts of TFA in poly(gamma-bzyl L-glutamate) solutions

The present communication describes a new way of studying helix–random coil transformations of polypeptide, poly-(γ-benzyl L -glutamate), in benzene–trifluoracetic acid (TFA) and chloroform–TFA systems. The difference between the PMR chemical shift of TFA with and without the polypeptide, measured as Δ, may be used to follow the conformational transition. This technique is particularly useful for concentrated solutions, where the PMR peaks of the polymer are so broad that no valuable information may be derived. As the TFA content increases in the system (at constant polymer concentration), Δ decreases normally whether the polymer is helical or random. However, Δ changes in a different way in the helix–random coil transition region, and actually increases with increasing TFA content. This peculiar behavior is explained in terms of the solvation of the helix and random coil structures.     

Nuclear magnetic resonance investigation of the helix in random coil transformation in poly-alpha-amino acids. I

High-resolution nuclear magnetic resonance spectra at 100 MHz and 220 MHz have been obtained on two samples of poly-L -alanine of differing molecular weights (2500 and 42 500) in the chloroform–trifluoroacetic acid system under various conditions of solvent composition, temperature, and polypeptide concentration. Separate helix and random coil peaks are observed for the α-CH and peptide NH backbone proton resonances, thereby permitting the determination of helix content. This observation of separate peaks demonstrates that the lifetimes of the helix and random coil portions of poly-L -alanine have lower limits of about 10^?1 sec. It is suggested that solvent–peptide versus peptide–peptide hydrogen bond competition, coupled with a destabilizing effect of the trifluoroacetic acid on the helix, is responsible for the helix–random coil transformation.     

A ratiometric expressible FRET sensor for phosphoinositides displays a signal change in highly dynamic membrane structures in fibroblasts

Phosphoinositides are important signal transduction intermediates in cell growth, survival, and motility. We have invented a fluorescence sensor for polyphosphorylated phosphoinositides based on a peptide derived from the Listeria protein ActA that undergoes a random coil to helix transition upon lipid binding. The sensor, termed CAY, is a fusion protein of cyan and yellow fluorescent proteins flanking the peptide at its N- and C-termini, respectively. CAY displays fluorescence resonance energy transfer in vitro in the absence of phosphorylated phosphoinositides, and this energy transfer is lost upon interaction with these phospholipids. These results demonstrate that a short peptide undergoing a coil to helix transition can be sufficient for the engineering of a FRET-based biosensor. CAY is predominantly localized to the cytoplasm in fibroblasts expressing the sensor but shows loss of fluorescence resonance energy transfer in regions of active actin dynamics such as ruffles that have previously been demonstrated to contain high levels of phosphoinositides.     

Model calculations on the kinetics of oligonucleotide double helix coil transitions. Evidence for a fast chain sliding reaction

Relaxation data obtained previously for the double helix coil transition of oligoriboadenylates and oligoribouridylates are compared to the results of numerical calculations according to various models. In these models the helix coil transition is described by individual rate constants for the first steps of helix formation, whereas the rate constants of the following steps of helix chain growth are assumed to be uniform. The existence of various helix intermediates containing the same number of base pairs is accounted for by statistical factors. First a quasistationary treatment of a zipper model is used for an analysis of the influence of various model parameters. Then relaxation spectra are calculated including helix coil intermediates explicitly without any assumption of quasistationarity. The relaxation spectrum calculated for any chain length N comprises N—1 fast processes with time constants in the range of 0.1 to 0.5 μs and one slow process with a time constant τ depending upon the nucleotide concentration (τ is usually in the ms time range). The fast processes are associated mainly with the unzippering at helix ends and are usually characterized by relatively small amplitudes, whereas the slow process represents the overall helix coil transition usually characterized by a very large amplitude.Consideration of staggered helix series (where the different helix scries are coupled to each other by the single stranded state) leads to a spectrum of slow relaxation processes with one separate relaxation process for each helix series. It is shown that this “non-sliding” staggering zipper model is not consistent with the experimental results. The measured relaxation curves can be represented by single exponentials for nucleotide chain lengths 8 to 11 (within experimental accuracy). This is also true for conditions where several, clearly separated time constants should be expected according to the theoretical model. The experimental data suggest the existence of a direct coupling between different series of staggered helices by a chain sliding mechanism with a time constant < 1ms. Chain sliding may be explained by diffusion of helix defects along the double helix such as diffusion of small loops. A simple model calculation for the diffusion of a bulge loop assuming quasistationarity suggests a sliding time constant around 100 μs for a helix comprising 10 base pairs.Finally some thermodynamic and kinetic parameters are evaluated according to the “sliding” staggering zipper model: The negative activation enthalpy observed for helix recombination can he described using a series of nucleation parameters indicating reduced stability constants for the first three base pairs. Nucleation may usually be achieved with the formation of the third or fourth base pair depending upon the magnitude of the chain growth parameter. The rate constant of helix chain growth is around 10⁶ s^?1 at 0.05 M [Na⁺] and increases to about 4 × 10⁶ s^?1 at 0.17 M [Na⁺].     

The strand-separation transition of T2 bacteriophage DNA

Strand separation of T2 DNA has been investigated in a helix-destabilizing solvent. Temperature-shift experiments in which the conformation of the DNA is monitored by its viscosity, sedimentation behavior, and kinetics of helix formation show that a well-defined strand-separation transition follows the helix–coil transition usually observed by changes in absorbance. For T2 DNA, this strand-separation transition is 70% as broad as the helix–coil transition, and is characterized by extremely slow kinetics of conformational change in the population. Strand separation requires the expansion of the two-stranded coil observed at the end of the helix–coil transition. This expansion is apparently coupled with the disurption of the last remaining base pairs in the molecule. The expansion process increases the viscosity, and can be readily followed as a function of time and/or temperature. Subsequent separation of the expanded form into complementary strands results in a viscosity decrease, the net result of a reduction in hydrodynamic volume and the halving of the molecular weight. Only under conditions where the driving force for strand separation is large are these events at all synchronous in the population. When the kinetics of conformational change are complete in the strand-separation transition, a mixture of expanded forms and separate strands is observed; the breadth of the transition reflects differences in stability with respect to strand separation among the molecules in the population. The transition exhibits hysteresis and is not a reversible equilibrium between double-stranded and single-stranded forms. It appears that renucleation is kinetically forbidden within the strand-separation region.     

Influence of local and residual structures on the scaling behavior and dimensions of unfolded proteins

Although recent spectroscopic studies of chemically denatured proteins hint at significant nonrandom residual structure, the results of extensive small angle X-ray scattering studies suggest random coil behavior, calling for a coherent understanding of these seemingly contradicting observations. Here, we report the results of a Monte Carlo study of the effects of two types of local structures, alpha helix and Polyproline II (PPII) helix, on the dimensions of random coil polyalanine chains viewed as a model of highly denatured proteins. We find that although Flory's power law scaling, long regarded as a signature of random coil behavior, holds for chains containing up to 90% alpha or PPII helix, the absolute magnitude of the chain dimensions is sensitive to helix content. As residual alpha helix content increases, the chain contracts until it reaches a minimum radius at approximately 70% helix, after which the chain dimensions expand rapidly. With an alpha helix content of approximately 20%, corresponding to the Ramachandran probability of being in the helical basin, experimentally observed radii of gyration are recovered. Experimental radii are similarly recovered at an alpha helix content of approximately 87%, providing an explanation for the previously puzzling experimental finding that the dimensions of the highly helical methanol-induced unfolded state are experimentally indistinguishable from those of the helix-poor urea-unfolded state. In contrast, the radius of gyration increases monotonically with increasing PPII content, and is always more expanded than the dimensions observed experimentally. These results suggest that PPII is unlikely the sole, dominant preferred conformation for unfolded proteins.     

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.     

Vacuum-ultraviolet circular dichroism of chondroitins and their complexes with poly(L-arginine)

The vacuum-ultraviolet circular dichroism (VUCD) of chondroitin and chontroitin-6-sulfate has been measured to 160 nm for films and to 170 nm for D₂O solutions. The pD-dependent dichroic behavior of these glycosaminoglycans in D₂O is similar above 200 nm and is in agreement with previous studies. Near 190 nm, the CD band sign is also dependent on pD. VUCD spectra were recorded for films and solutions of poly(L -arginine). In trifluoroethanol the polypeptide is α-helical, while in D₂O it exists as a random coil. The well-characterized coil–helix transition of poly(L -arginine) during complexation with chondroitin-6-sulfate was observed by VUCD, including the previously inaccessible entire π → π* band. By construction of difference spectra it was also possible to monitor the VUCD of the polysaccharide component during complexation.     

The strand-separation transition of T7 DNA

The strand-separation transition of T7 DNA has been investigated by temperature shift and viscosity measurements in two formamide–water solvents. The strand-separation region is quite narrow, and follows directly at the end of the denaturation transition observed by absorbance. The kinetics of strand separation of T7 DNA are slow and complex in the strand-separation transition. Similarities and differences in the behavior of T2 and T7 DNA in strand separation are indicated and discussed. Briefly, the time course of strand separation and the conformational changes observed in the population undergoing strand separation are similar for the two molecules. However, the transition breadths and the interval between the helix–coil transition and the strand-separation transition differ markedly. Both DNA molecules exhibit hysteresis in the strand-separation region. For both molecules, it appears that strand separation involves the coupled denaturation and disentanglement of the two-stranded form found at the end of the helix–coil transition.     

Conformational and kinetic studies of synthetic polypeptides by NMR

The α-helix–coil transition of poly-L -leucine, poly-L -alanine and poly-L -methionine in chloroform–trifluoroacetic acid system was studied by nuclear magnetic resonance (NMR) and optical rotatory dispersion (ORD). The kinetics of the hydrogen–deuterium exchange in the peptide was also followed in these polymers by means of NMR. Two types of the NMR spectra and the hydrogen–deuterium exchange reaction were found, corresponding to the high and low molecular weight polypeptides. In high molecular weights, the NH and α-CH resonance lines gave single peaks and the hydrogen–deuterium exchange was expressed as a single first order reaction. In low molecular weights, the NH and α-CH lines were separated into two peaks, corresponding to helical and random-coiled states, respectively, and the exchange react ion was expressed as super-position of a very rapid exchange reaction in the random-coiled part and another slow exchange reaction of the first order in the helical part. These results suggest that the helix–coil interconversion of low molecular weight polypeptides has a longer relaxation time (? 4.5 × 10^?3 sec) than that of high molecular weight polypeptides.     

Helix-coil transition in heterogeneous DNA.

The broadening of a helix–coil transition due to base pair heterogeneity is calculated on the basis of a cumulant perturbation expansion in the quasi-grand ensemble. In this ensemble the fictitious, homogeneous chain, to which the perturbation is referred, automatically decreases its correlation length as the heterogeneity increases. This “renormalization” seems to stabilize the perturbation expansion, in view of the good agreement between the present results and the exact theory of a heterogeneous polypeptide helix–coil transition. For the DNA model in which ring entropy is included, the transitions is found to be extremely narrow for an infinite random chain with conventional parameters. A tentative reconciliation of this result with contradictory calculations of some other workers is offered on the basis of end effects, coarse graining, or approximation to the ring entropy. An application of the new method to DNA with a non-random base pair distribution requires evaluation of the correlation function between molecular states (helix or coil), at different sites of the reference chain. The evaluation is reduced to quadrature, but numerical calculations have been made only for the random chain.     

Origin of multipeak behavior in the NMR spectra of poly(L-glutamic acid)

The previous report that poly(L -glutamic acid) exhibits doubled resonances in the helix–coil transition region by either proton or carbon-13 nmr resolves the question of whether or not this behavior is limited to uncharged polypeptides in organic solvents, as had been previously thought. In the present work, we show that the underlying principle causing this anomalous double-peak behavior is due to molecular-weight polydispersity of the sample. The molecular-weight range in which this phenomenon is observed is largely dependent on the values of σ, the nucleation or cooperativity factor. The principles developed are shown to encompass all classes of polypeptides in a very natural way and to explain the key experimental data in the literature.     

A carbon-13 magnetic resonance study of the helix-coil transition in polyuridylic acid

The temperature-dependent conformations of poly(U) in 0.5M CsC1 have been studied by carbon-13 nuclear magnetic resonance. The transition from random coil to an ordered structure results in broadening of lines in the ¹³C spectra, due to intramolecular ¹H–¹³C dipolar interactions and restricted motions in the ordered state. Changes in the chemical shifts suggest that the bases are interacting below the transition temperature. The random coil form shows conformation preferences for internal rotation about C4′–C5′, C5′–O5′, and C3′–O 3′ bonds. The statistical randomness of the coil arises mainly because of flexibility about O–P bonds. The results are analyzed in conjunction with theoretical calculations and light-scattering data.     

Effect of sequence-specific interactions on the stability of helical conformations in polypeptides

A modification of the Zimm–Bragg two-state model for the helix–coil transition in polypeptides, which considers the effect of charge–dipole, charge–charge, and other specific interactions on helix stability, is presented. The new model introduces a series of adjustable parameters whose values are estimated by fitting to recent spectroscopic results on medium-sized peptides. This formalism, based on traditional two-state helix–coil transition models, provides a framework in which data on the helix contents of peptides of specific sequence can be rationalized by a statistical mechanical theory.     

Direct computation of long time processes in peptides and proteins: reaction path study of the coil-to-helix transition in polyalanine.

The MaxFlux reaction path algorithm was used to isolate optimal transition pathways for the coil-to-helix transition in polyalanine. Eighteen transition pathways, each connecting one random coil configuration with an ideal alpha-helical configuration, were computed and analyzed. The transition pathway energetics and mechanism were analyzed in terms of the progression of the peptide nonbonded contact formation, helicity, end-to-end distance and energetics. It was found that (1) localized turns characterized by i, i + 3 hydrogen bonds form in the early stages of the coil-to-helix transition, (2) the peptide first collapses and then becomes somewhat more extended in the final stage of helix formation, and (3) 310-helix formation does not appear to be a necessary step in the transition from coil to helix. These conclusions are in agreement with the results of more computationally intensive direct molecular dynamics simulations. Proteins 1999;36:249-261.