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.     

Calculation of melting curves for DNA

A method is reported for calculating the melting curve of a DNA molecule of random base sequence, including in the formalism the dependence of the free energy of base pair formation on the size of a denatured section. Some explicit results are shown for a “typical” base sequence, in particular the probability of helix formation at individual base pairs in several different regions of the molecule and the amount of melting from the end of the chain. Particular attention is drawn to the variation of local melting behavior from one region of the molecule to another. It is found that sections rich in AT melt at relatively low temperatures with a fairly broad transition curve, whereas regions rich in GC pairs melt at higher temperatures (as expected) with a very abrupt, local transition curve. To account qualitatively for the results one may divide melting into two kinds of processes: (a) the nucleation and growth of denatured regions, and (b) the merging together of two denatured sections at the expense of the intervening helix. The first of these processes dominates in the first stages of melting, and leads to rather broad local melting curves, whereas the second process predominates in the later stages, and occurs, in a particular part of the molecule, over a very narrow temperature range. It is estimated that the average length of a helix plus adjacent coil section at the midpoint of the transition is approximately 600 base pairs. Since transition curves which measure the local melting behavior reflect local compositions fluctuations, these curves contain information about the broad outlines of base sequence in the molecule. Some suggestions are made concerning experiments by which this potential information source could be exploited. In particular, it is pointed out that one might hope to map AT or GC rich regions at particular genetic loci in a biologically active DNA molecule. Values of the relevant parameters found earlier for the transition of homopolymers produce melting curves for a DNA of random base sequence which are in good agreement with the experimental transition curve for T2 phage DNA. Hence the present theoretical picture of the melting of polynucleotides is at least internally self-consistent.     

Nonadditivity in the alpha-helix to coil transition

The Lifson-Roig Model (LRM) and all its variants describe the α-helix to coil transition in terms of additive component-free energies within a free energy decomposition scheme, and these contributions are interpreted through sequence-context dependent nucleation and propagation parameters. Although this phenomenological approach is able to adequately fit experimental data on helix content and heat capacity, the number of required parameters increases dramatically with additional sequence variation. Moreover, due to nonadditive competing microscopic effects that are difficult to disentangle within a LRM, large uncertainties within the parameters emerge. We offer an alternative view that removes the need for sequence-context parameterization by focusing on individual microsopic interactions within a free energy decomposition and explicitly account for nonadditivity in conformational entropy through network rigidity using a Distance Constraint Model (DCM). We apply a LRM and a DCM to previously published experimental heat capacity and helix content data for a series of heterogeneous polypeptides. Both models describe the experimental data well, and the parameters from both models are consistent with prior work. However, the number of DCM parameters is independent of sequence-variability, the parameter values exhibit better transferability, and the helix nucleation is predicted by the DCM explicitly through the nonadditive nature of conformational entropy. The importance of these results is that the DCM offers a system-independent approach for modeling stability within polypeptides and proteins, where the demonstrated accuracy for the α-helix to coil transition over a series of heterogeneous polypeptides described here is one case in point.     

Relationship between helix-coil transition and gene organization of ColE1 plasmid DNA. Differential scanning calorimetric and theoretical studies

Differential scanning calorimetry (DSC) was carried out to analyze the transition of helix to coil state of DNA, using ColE1 DNA molecules digested with EcoRI. The DSC curves showed multimodal transition, consisting of nine to 11 peaks over a temperature range, depending on the ionic strength of the DNA solution. These DSC curves were essentially in good agreement with the optical melting curves of ColE1 DNA. The theoretical melting profiles of ColE1 DNA were predicted from calculations based on the helix-coil transition theory and the nucleotide sequence of the DNA. These profiles resembled the DSC curves and made it possible to assign the peaks seen in the DSC curves to the helix-coil transition of particular regions of the nucleotide sequence of ColE1. The helix-coil transition of each of the small genes gave rise to a single peak in the DSC curve, while the helix-coil transition of large genes contributed to two or more peaks in the DSC curve. This multimodal transition within a single coding region might correspond to the melting of individual segments encoding the different domains of the proteins. The helix-coil transition at the specific sites including ori, the origin of replication of ColE1, was also found to occur in a particular temperature range. DSC, a simple method, is thus useful for analyzing the multimodal helix-coil transition of DNA, and for providing information on the genetic organization of DNA.     

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.     

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.     

Theoretical calculations of the helix–coil transition of DNA in the presence of large,cooperatively binding ligands

Theoretical calculations are conducted on the helix–coil transition of DNA, in the presence of large, cooperatively binding ligands modeled after the DNA-binding proteins of current biological interest. The ligands are allowed to bind both to helx and to coil, to cover up any number of bases or base pairs in the complex, and to interact cooperatively with their nearest neighbors. The DNA is treated in the infinite homogeneous Ising model approximation, and all calculations are done by Lifson's method of sequence-generating functions. DNA melting curves are calculated by computer in order to expolore the effects on the transition of ligand size, binding constant, free activity, and ligand–ligand cooperativity. The calculations indicate that (1) at the same intrinsic free energy change per base pair of the complexes, small ligands, for purely entropic reasons, are more effective than are large ligands in shifting the DNA melting temperature; (2) the response of the DNA melting temperature to increased ligand binding constant K and/or free ligand activity L is adequately represented at high values of KL (but not at low KL) by a simple independent site model; (3) if curves are calculated with the total amount of added ligand remaining constant and the free ligand activity allowed to vary throughout the transition, biphasic melting curves can be obtained in the complete absence of ligand–ligand cooperativity. In an Appendix, the denaturation of poly[d(A-T)] in the presence of the drug, netropsin, is used to verify some features of the theory and to illustrate how the theory can be used to obtain numerical estimates of the ligand binding parameters from the experimental melting curves.     

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 effect of polydispersity on the nuclear magnetic resonance spectra of poly-gamma-benzyl-L-glutamate

The effect of poly dispersity on the nuclear magnetic resonance spectra of samples of poly-γ-benzyl-L -glutamateein the helix–random coil transition is studied. In the transitionregion the α-CH proton resonance shows two peaks whose behavior does not change appreciably upon fractionation by gel permeation chromatography. Theoretical spectra were computed with both a polydispersity model of the transition and a model for slow nucleationof helix from completely random coil molecules. The results suggest that the double peak behavior in the nmr spectra results from a slow rate of helix nucleation rather than polydispersity.     

Theory of melting of the triple helix poly (A + 2U) for a 1 : 2 mixture of Poly A to Poly U

The Zimm-Bragg theory is extended to treat the melting of the triple helix poly (A + 2U) for a solution with a 1 : 2 mole ratio of poly A to poly U. Only the case for long chains is considered. For a given set of parameters the theory predicts the fraction of segments in the triple helix, double helix, and random coil states as a function of temperature. Four nucleation parameters are introduced to describe the two order–disorder transitions (poly (A + 2U) ? poly A + 2 poly U and poly (A + U) ? poly A + poly U) and the single order–order transition (poly (A + 2U) ? poly (A + U) + poly U). A relation between the nucleation parameters is obtained which reduces the number of independent parameters to three. A method for determining these parameters from experiment is presented. From the previously published data of Blake, Massoulié and Fresco⁸ for [Na⁺] = 0.04, we find σ_T = 6.0 × 10^?4, σ_D = 1.0 × 10^?3, and σσ* = 1.5 × 10^?3. σ_T and σ_D are the nucleation parameters for nucleating a triple helix and double helix, respectively, from a random coil region. σσ* is the nucleation parameter for nucleating a triple helix from a double helix and a single strand. Melting curves are generated from the theory and compared with the experimental melting curves.     

Study of helix-coil transition of DNA by dielectric constant measurement

The thermal helix–coil transition of DNA was studied by means of dielectric constant measurements. The dielectric dispersion of native helical DNA is characterized by a large dielectric increment and a large relaxation time, whereas that of denatured coil DNA is characterized by a small dielectric increment and a small relaxation time. The dielectric dispersion of partially denatured DNA is of particular interest. At the intermediate stage of the helix–coil transition, dispersion curves which are different from either that of helix DNA or that of coil DNA appear. This is particularly pronounced for large DNA. This indicates the presence of an intermediate form of DNA. Flow birefringence measurements were carried out simultaneously. The negative birefringence of helical DNA diminishes as the helix–coil transition proceeds. However, the extinction angle remains constant, as long as it can be measured. These results indicate the absence of intermediate forms during the helix–coil transition. The discrepancy between dielectric and birefringence measurements can be resolved by assuming that the intermediate forms are not birefringent. The size distribution of native DNA and of the indicated intermediate form of DNA was studied. It is found that a logarithmic normal distribution function explains the distribution of size of DNA reasonably well.     

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.     

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.     

Structure of poly 8-bromoadenylic acid; conformational studies by CPF energy calculations.

Poly 8-bromoadenylic acid [poly(BBrA)] is the only known all-syn polynucleotide. It shows a helix-coil transition with a melting curve centred around 55 degrees C. Energy calculations based on classical potential functions have been used to explore the three-dimensional structure of this polymer in helix and random coil. It is concluded that the ordered state is a helix of two parallel strands with a two-fold rotation axis, and the duplex is stabilised by hydrogen bonds involving N1 and H6. Each strand has a conformation with C3' endo geometry, phi' = 216 degrees, omega' = 280 degrees, omega = 294 degrees, phi = 179 degrees, chi = 243 degrees and psi = 57 degrees. Such a conformation leads to approximately 8 nucleotide units per turn of the helix and an axial rise of 3.9A degrees. The structure of poly(8BrA) has been compared with that of the related polymer poly(A) which forms a double helical structure in acidic conditions with bases in the anti conformation and with interstrand hydrogen-bonds between N7 and H6. This is the first time that a specific geometrical model of a novel polynucleotide structure has been produced initially by potential energy calculations, though such calculations on a number of known structures have been reported previously.     

Dielectric dispersion of the -helix at the transition region to random coil

Dielectric studies have been carried out for the helix–coil transition of poly-β-benzyl-L -aspartate with m-cresol as a solvent. The transition of the solute molecules has been sharply reflected as a characteristic change in the dielectric dispersion curves in changing temperature. Two polarizations, one having a low and the other a high critical frequency, have appeared. According to theoretical considerations of a model of a broken helix, the former is found to come from the orientation. of helical sequences and the latter from the chemical relaxation due to the helix–coil transition. It also seems likely that the unfolded chain may have a polarizability which could not be neglected at the high-temperature side of the transition.     

Statistical-mechanical treatment of violations of the double helix in supercoiled DNA.

We consider the problem of making allowance for superhelicity in the statistical-mechanical calculations of fluctuational violations of the DNA double helix. A simple model is discussed, making it possible in the calculations to use an approach based on the theory of helix–coil transition in DNA. The proposed algorithms allow calculating the effect of superhelicity on the base-pair fluctuational opening for any given sequence of nucleotides. An algorithm is also proposed allowing for the hairpin and cruciform structures in the palindromic regions of a sequence, as well as the open and helical states. The theory is used to calculate the melting curve for superhelical DNA at temperatures well below the melting point of the linear or nicked forms. The maps of opening probability are calculated for SV40 and ?X174 DNA using their recently published complete nucleotide sequences. The data explain well the experimental results of probing the secondary structure of these DNA by single strand-specific endonucleases.     

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.     

Comparison of alpha-helix stability in peptides having a negatively or positively charged residue block attached either to the N- or C-terminus of an alpha-helix: the electrostatic contribution and anisotropic stability of the alpha-helix

An estimation of the thermodynamic effects of a charged random coil, which is attached either to the N- or C-terminus of polyalanine, upon alpha-helix stability is attempted. A temperature-induced helix-coil transition of Ala20Lys20Phe and Lys20Ala20Phe was studied under various conditions of salt concentration and pH. By combining the results with previous ones for Ala20Glu20Phe and Glu20Ala20Phe, which have opposite electric charges to the present system [S. Ihara et al. (1982) Biopolymers 21, 131-145], the free energy of the coil to helix transition of the polyalanine block could be separated into two terms--one term for the electrostatic interaction of electric charges in the random-coil block with the alpha-helix dipole, and a second term for the intrinsic stability of the helix. The first term indicates the significance of the helix dipole-charge interactions, which affects the helix stability depending on the attaching side of the charged block and on the sign of the charges. This clearly shows the anisotropic stability of the alpha-helix. Furthermore, analysis of the dependence of these thermodynamic quantities on salt concentrations showed, assuming that the effect of the attached electric charges was symmetric (in other words, the absolute values of the electrostatic interaction terms were independent of the sign of electric charges), that the intrinsic stability of the alpha-helix was dependent on which side of the helix was attached to the random coil: a random coil attached to the N-terminus of the alpha-helix had little effect while that attached to a C-terminal significantly destabilized the helix.     

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.