The Helix-Coil Transition

It is known that a large part of the tertiary structure of some proteins consists of packed helical segments. As the temperature increases, these helices unfold and attain a random coil conformation. The transition from the helical to the random coil is similar to the denaturation process. Therefore it is believed that the study of the helix-coil transition is an essential step in the understanding of the denaturation process. It is known, however, that protein denaturation is a far more complex process. It involves the breakdown of an intricate three-dimensional tertiary structure, only part of which is the helix-coil transition. Some proteins do not even contain substantial content of helical structure. Therefore, the study of this particular transition will not give us the answer to the far more complex denaturation process. In the rest of this section we shall focus on the theory of the helix-coil transition only. We shall return to the folding-unfolding process of proteins in Chapter 8. 

We describe here a simplified version of the helix-coil H- C transition theory developed by Lifson and Roig. The main assumptions made in the theory are the following  

Instead of a heteropolypeptide we use a homopolypeptide. The units are treated as being identical. Each unit is identified as a single amino acid residue, the boundaries of which are marked by the dotted vertical lines in Fig. 4.16. 

The state of each unit is determined only by a pair of rotational angles about the single bonds, as indicated in Fig. 4.16. No rotation about the partially double bond (the amide bond) is allowed. We also ignore any changes of state that originate from the side chains, denoted by R in Fig. 4.16. 

The solvent effect is ignored. We note however that the solvent could have a profound effect on the theory. Some aspects of the solvent effects are discussed in Chapter 8. 

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The conformational transitions in the presented model take place accord-itig to the all-or-nothing law, i.e. they occur at the certain r.h. value. The same behaviour has been observed, for example, for the helix-coil transition of the model double-stranded structure A(pA)i7-U(pU)i7 [24]. It is worth noting that this structure is homogeneous, the same is supposed in our model. 

Porschke, D., Eigen, M. Cooperative nonenzymic base recognition. HI. Kinetics of the helix-coil transition of the oligoribouridylic oligoriboadenylic acid system and of oligoriboadenylic acid alone at acidic pH. J. Mol. Biol. 62 (1971) 361-381... 

Teramoto, A. and Fujita, H. Conformation-dependet Properties of Synthetic Polypeptides in the Helix-Coil Transition Region. Vol. 18, pp. 65— 149. 

Typical examples are the conversion of the neutral form of an amino acid into its zwitterionic form, the helix-coil transitions in polypeptides and polynucleotides, and other conformational changes in biopolymers. Reactions of higher molecularity in which reactants and products have different dipole moments are subject to the same effect (association of the carboxylic acids to form hydrogen-bonded dimers). Equilibrium involving ions are often more sensitive to the application of an electric field ... 

The NMR data (James et al., 1997 Liu et al., 1999) show a slight reverse turn in the HI domain, similar to that proposed from X-ray diffraction (Inouye and Kirschner, 1998) however, NMR indicates that the turn is close to Alai 17. A molecular dynamics study of the helix-coil transition of PrP106—126 (Levy et al., 2001) indicates that the turn is near Alai 15, such that Hislll would interact with Vall22 rather than with Alall7. The HI domain, initially modeled as an z-helix. also adopts a /Miairpin fold as shown by molecular dynamics simulation (Daidone et al., 2005). 

Many biological polymers display a cooperative transition from an ordered to disordered state [34] including the helix coil transitions observed for both peptides [35] and nucleic acids [36]. Synthetic systems that are able to undergo a cooperative helix coil transition can complement biopolymer studies and are of potential interest for density-responsive materials. 

The sequential and often cooperative disassembly of double-helical structure, occurring whenever the sample temperature exceeds the so-called melting temperature (Tm) for a given segment of DNA. Because of the low concentrations of intermediate states lying between helix and coil structures, the helix-coil transition can be approximated as a two-state, all-or-nothing process. See DNA Unwinding Kinetic Model for Small DNA... 

The influence of the solvent on chiroptical properties of synthetic polymers is dramatically illustrated in the case of poly (propylene oxide). Price and Osgan had already shown, in their first article, that this polymer presents optical activity of opposite sign when dissolved in CHCI3 or in benzene (78). The hypothesis of a conformational transition similar to the helix-coil transition of polypeptides was rejected because the optical activity varies linearly with the content of the two components in the mixture of solvents. Chiellini observed that the ORD curves in several solvents show a maximum around 235 nm, which should not be attributed to a Cotton effect and which was interpreted by a two-term Drude equation. He emphasized the influence of solvation on the position of the conformational equilibrium (383). In turn, Furakawa, as the result of an investigation in 35 different solvents, focused on the polarizability change of methyl and methylene groups in the polymer due to the formation of a contact complex with aromatic solvents (384). 

Conformation-Dependent Properties of Synthetic Polypeptides in the Helix-Coil Transition Region... 

Chapter C deals with molecular dimensions of interrupted helices. Typical theories for mean-square radius of gyration and mean-square end-to-end distance are reviewed. Important predictions from theory are compared with the results of recent light-scattering measurements. Complications attendant upon the analysis of light-scattering data for polypeptides in the helix-coil transition region are discussed. 

Chapter D is concerned with intrinsic viscosity and translational friction coefficient. Published data for the molecular-weight dependence of these quantities of polypeptides in helieogenic solvents and helix-breaking solvents are summarized, and the variations of these quantities during the helix-coil transition are described. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

The shortest helical sequence that can be created in an a-helix-forming polypeptide is hhh, and its statistical weight is as. Since s is of the order of unity in the helix-coil transition region, the probability that such a nucleus for the growth of a helical sequence will be produced is essentially equal to a. For this reason, a is also called the helix-initiation parameter. 

Calorimetric measurements permit the determination of (AH ), the value of AH averaged over the helix-coil transition region (19-21). An approximate... 

Figure 5 illustrates, with the data for poly(/J-benzyl L-aspartate) (PBLA) (22), that there are two types of thermal helix-coil transition, normal and inverse. It should be noted that for a given polypeptide the type of transition depends on the solvent in which the polymer is studied. This suggests that polymer-solvent interactions play a decisive role in the helix-coil transition phenomena of polypeptides. 

Several actual data illustrated in Section 5.a have demonstrated the unmistakable effects of polypeptide-solvent interactions on the helix-coil transition processes of polypeptides. This subsection deals with these effects from a thermodynamic point of view. 

Besides the work by Strazielle et al. cited above, the only available lightscattering determinations of in the helix-coil transition region are limited to the following three studies carried out recently at our laboratory Norisuye et al. 49) for fractions of PBLG in a mixture of cyclohexanol (CHL) and DCA (91.7 wt.-%) Okita et al. (50) for fractions of PHPG in aqueous methanol and Ohta et al. (5/) for fractions of PHEG in aqueous isopropanol. Typical results from these studies are presented below. 

Teramoto et al. (14) have proposed a method of analyzing in the helix-coil transition region. Actually, it is a refinement of Ptitsyn s method (46). In the latter, / in Eq. (C-29) is replaced by fN and the resulting expression is applied to finite chains. Teramoto et al. recast Eq. (C-26) in the form ... 

This chapter summarizes important data for intrinsic viscosity and translational friction coefficient of polypeptides. The first half of the chapter discusses the data obtained in helicogenic solvents and in helix-breaking solvents. It is actually a supplement to the review article by Benoit et al. (61), in which such data published by 1967 were surveyed critically. The second half of the chapter is concerned with the helix-coil transition region. The context here is largely descriptive because of the lack of relevant theory. 

As far as we are aware, only a few experimental results are available for the translational friction coefficient of polypeptides in the helix-coil transition region, and our discussion about it cannot but be very incomplete. Figure 33, taken from the work of Okita et al. (13) on the system PHPG-aqueous methanol, shows the dependence of the reduced sedimentation coefficient [s0] on the helical fraction. Here [s0] is defined as s0ri0/( 1 — i>g0), with and Q0 being the... 

The question arises as to whether or how closely Eq. (D-8) is obeyed by non-randomly coiled macromolecules, especially, by polypeptides in the helix-coil transition region. An answer has been given by a recent work by Norisuye (S3), who measured [fj] and for two high-molecular-weight samples of PBLG... 

Since the mathematical expression for < u2) is equivalent to that for , measurements of should provide information which can be utilized to check the theory of , e.g. Eq. (C-3), for polypeptides in the helix-coil transition region. This idea, however, cannot be developed in straightforward fashion because there is no available theory to estimate of interrupted helical polypeptides from dielectric dispersion curves. Therefore, we are forced to proceed on some yet unproven assumptions, or even drastic approximations. 

The authors group has recently been engaged in more detailed dielectric studies in the helix-coil transition region, using well-fractionated samples of PBLA and PCBL. 

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