Helical fraction

Dried with molecular sieves for 2days, then distd under reduced pressure through a column packed with glass helices. Fractionally crystd by partial freezing and the solid portion was vac distd. 

For an a-helical fraction fH = 0,5 30% methanol, 20% ethanol, 15% i-propanol or 10% trifluoroethanol are necessary. Trifluoroethanol like perfluorinated alcohols, e.g. hexafluoroisopropanol is characterised on the hand by a strong acidic proton at the OG-group due to the —1-effect of the fluor atoms. On the other hand fluorocarbons are more hydrophobic than the hydrocarbons which is mainly due to the larger surface of the F compared with H. For this reason the critical micelle concentration of perfluorinated detergents is much lower than that of the corresponding hydrocarbon compounds. It was found that C4F7-derivatives act as detergents... 

Statistical averages of various physical quantities characterizing the conformation of a polypeptide chain under given environmental conditions can be calculated with the help of Eq. (B-6). For example, the average helical fraction fN (in what follows, this is simply called helical fraction) is given by... 

The helical fraction has here been defined as the number of helix units present in the chain under consideration relative to the total number of residues in the same chain that can assume a-helical conformation, i.e. N — 2. It should be noted that this way of defining fN differs from that of Zimm and Bragg (4), who adopted the number of hydrogen bonds formed in the chain. The difference, however, becomes important only for short chains. 

In the limit of N- oo, Eq. (B-8) reduces to fN = f(2t). Hence /(2t) represents the helical fraction of an infinitely long polypeptide chain. In the ensuing presentation, this is simply designated by /, i.e. 

Fig. 1. Helical fraction fK versus z as a function of fi, computed according to Eq. (B-13).

From the above discussion it is clear that the average conformation of a polypeptide in solution depends on both the chain length N and the co-operativity parameter a, even if the helical fraction is fixed. In particular, it has been shown that, when compared at the same fN and N, the average number of helical sequences, gN, becomes smaller as a is lowered. Thus for fixed fN and N there exist a variety of different interrupted helical conformations, depending on the magnitude of a. Figure 4 illustrates two typical examples of such conformations. This theoretical prediction makes a study of the conformation-dependent properties of synthetic polypeptides rather inviting. 

Methods of Data Analysis a) Measurement of Helical Fraction... 

In most experimental studies, the environmental conditions of a given polypeptide sample are varied by changing either the temperature of the system or the composition of a solvent mixture consisting of a helix-supporting solvent and a helix-breaking solvent. A curve of helical fraction fN versus temperature at fixed solvent composition is called the thermally induced or thermal transition curve, while a curve of fN versus solvent composition at fixed temperature is called the solvent-induced transition curve. The former is classified into two types normal and inverse (or reverse), depending on whether fN decreases or increases with the rise in temperature. 

Helical fraction is the only quantity that can be estimated experimentally among the various quantities characterizing the conformation of polypeptides. There are several means of estimating helical fraction (15,16). The most commonly used is based on the assumption that the Moffitt-Yang parameter b0 derived from optical rotatory dispersion measurement is a linear function of fN. Thus... 

Whatever optical methods are used to evaluate fN, the results are always attended with uncertainty, especially in the regions near zero and unity. This feet unhappily prevents us from entering into a detailed exploration of the transition behavior in these regions of helical fraction. 

Fig. 10. Variations of helical fraction fN with temperature for PBLA in DCA-l,l,2,2-tetra-chloroethane mixtures containing mole per cent DCA as shown (55)...

Fig. 11. Dependence of the mean-square radius of gyration on helical fraction for chains with various N, a = 2 x 10-4, a0 = 22.4 A, and a, = 1.5 A...

Figure 12 has been prepared to illustrate the effect of a on the relation between /0 and fN. These curves correspond to a fixed N of 1200 and the same values of a0 and a, as in Fig. 11. For this relatively large N they all exhibit a minimum. It is seen that the minima shift to a lower helical fraction...

Fig. 14. Plots of /(np/p) versus helical fraction / (43). Methods A and B represent the calculations based respectively on the 2 x 2 matrix and on the 8x8 matrix (see text)...

The data of Fig. 17 are replotted against the helical fraction in Fig. 18. The trend of the curves does not conform very well to the theoretical curves shown in Fig. 11. Figure 19 displays the corresponding plots for PHPG in aqueous methanol (50). Here the plotted points for each sample contain data not only... 

Fig. 18. Variation of 1/2 with helical fraction for PBLG in a DCA-CHL mixture (83 wt.-9o CHL) derived from the data in Fig. 17 (49)...

Fig. 19. Variation of 1/2 with helical fraction for a PHPG sample (Nv = 1970) in mixtures of methanol and water (50). (C) pure methanol, (O) 60 wt - % methanol, ( ) 30wt.-%...

The curve drawn in Fig. 19 looks somewhat more like the theoretical curves in Fig. 11, but still exhibits no detectable minimum. It can be observed that the curve shows a strikingly steep rise in the region of high helical fractions, but the highest point reached is still far below the value which would be obtained if the sample assumed intact and rigid a-helical conformation. This fact indicates what great difficulty we encounter in experimental investigations of the dimensions of polypeptides in the vicinity of perfect helix. Furthermore, it indicates how sensitively the presence of even a small fraction of random-coil portions affects the overall shape of helical polypeptide molecules. 

With the help of a relation between [m ]578 and the helical fraction fN established for PBLG in mixtures of EDC and DCA the data of Fig. 29 can be converted to a plot of [fj] versus fN. The result is shown in Fig. 30, together with the data of Teramoto et al. 102) for another sample and those from recent work... 

Fig. 30. Variation of [>/] with helical fraction for high-molecular-weight PBLG in DCA-EDC mixtures (83,102). The data points at fN = 1 are for DMF. The Nw are from top to bottom...

Another interesting contribution to the study of viscosity behavior in the helix-coil Jransition region is the one due to Hayashi et al. (22) on a PBLA sample (Mw = 23.2 x 104) in m-cresol and a mixture of chloroform and DCA (5.7 voL-% DCA). As mentioned in Chapter B, PBLA undergoes an inverse transition in the chloroform-DCA mixture, while it undergoes a normal transition in m-cresol. Furthermore, its cooperativity parameter is distinctly smaller in the former solvent than in the latter. Thus we may expect that, when compared at the same helical fraction and chain length, the PBLA molecule in the chloroform-DCA mixture assumes a more extended shape and hence a larger intrinsic viscosity than in m-cresol, provided these two solvents have comparable solvent powers for the polymer. The experimental results shown in Fig. 32 are taken to substantiate this prediction, because the approximate agreement of the data points atfN=0 indicates that the two solvents have nearly equal solvent powers for the solute. 

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... 

Fig. 33. Functional relation between reduced sedimentation coefficient and helical fraction fN for PHPG in aqueous methanol at different compositions and temperatures (13). Weight fractions of methanol in the solvent mixtures are ( ) 1.0, J) 0.6, (0) 0.3, ( ) 0.1, (O) 0.0...

It is seen that

characteristic behavior suggests that the molecular shape of PBLG in the mixed solvent studied does not differ very much from swollen spheres of randomly coiled polymers at stages where the helical fraction is less than about 0.6. In this connection, it is worth recalling from Chapter C, Section 2.b that the dimensional features of a polypeptide remain close to Gaussian at such stages of helix-coil transition, provided the chain is sufficiently long. 

More recently, Ohta et al. (51) have obtained a similar relation between and / from measurements on PHEG in mixtures of water and isopropanol. It is hazardous, however, to generalize from these limited results. The helical fraction at which

limiting value for intact helix may vary with polypeptide species, chain length, and environmental conditions. 

The gradual declines of x T/t]0 observed in Fig. 41 may be accounted for in part by departures of the actual polymer from the all-or-none model, and in part by the increase in the population of partially broken helical rods with the increase in helical fraction. At any rate, these experimental results on the system PCBL-ro-cresol are of great interest as the first affirmation of a system that exhibits a helix-coil transition close to the all-or-none type. 

At thermal equilibrium, the helical fraction and all other quantities characterizing the conformation of a helix-forming polypeptide are fluctuating from time to time about certain mean values which are uniquely determined by three basic parameters s, a, and N. The rates of these fluctuations depend on how fast helix units are created or disappear at various positions in the molecular chain. Recently, there has been great interest in estimating the mean relaxation times of these local helix-coil interconversion processes, and several methods have been proposed and tested. In what follows, we outline the theory underlying the dielectric method due to Schwarz (122, 123) as reformulated by Teramoto and Fujita (124). 

Here k is the Boltzmann constant, T is the absolute temperature, C is the number of peptide residues per cubic centimeter of solution, / and s are the helical fraction and the Zimm-Bragg parameter for the polypeptide molecule in the absence of external field, and ft is a parameter which represents the average correlation between the helix unit at the end of a helical sequence and the random-coil unit next to it. Though a detailed account of this parameter is left for Ref. (124), we note here that / = 0 corresponds to the complete absence of correlation between these two units, while ft — 1 corresponds to the case in which the dipole moment of a random coil unit points in the same direction as the axis of the preceding helix unit. 

Fig. 43. Frequency dependence of chemically induced dielectric constant (e )ch and dielectric loss (s%h for PBLG in a DCA-EDC mixture (73.5 vol.-% DCA) at various equilibrium helical fractions Jas indicated (123)...

A-Methyl formamide [123-39-7] M 59.1, m -3.5 , b 100.5°/25mm, d 1.005., n 1.4306 Dried with molecular sieves for 2days, then distd under reduced pressure through a column packed with glass helices. Fractionally crystd by partial freezing and the solid portion was vac distd. 

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