Helical turn angle

Below the Neel temperature, the beta phase is in an incommensurate helical antiferromagnetic state in which the helical turn angle varies from 24.0 at the Curie temperature to 42.9° at the Neel temperature (Greenhough et al., 1981). However, various turn angles are commensurate with the basal plane of the hexagonal crystal structure and nine such transitions have been definitely identified and the results are summarized in Part 14.13. Using sensitive calorimetry, Astrbm and Benediktsson (1988) were able to confirm only two of these transitions at 166 and 173 K and measured the enthalpies of transition to be 2 1 J/mol in both cases, but this is cmisidered to be within experimental noise and therefore these transitimis were not considered in the evaluation of the thermodynamic data. 

The beta phase below the Neel temperature at 180 K exists in an incommensurate helical antiferromagnetic state in which the helical turn angle varies from 24.0° at the Curie temperature to 42.9° at the Neel temperature (Green-hough et al., 1981). However, various turn angles are commensurate with the... 

Using the experimental elastic constant data, the helical turn angle and dl N/df the values of dl /d In c = 75 K and dh/d In c = 0 were determined by Bartholin and Bloch (1968a). 

Fig. 8. Temperature dependence of the helical turn angle in terbium. Open circles, ambient pressure open squares, 10.3 kbar open triangles, 19.3 kbar (Kawano et al. 1992).

Fig. 9. Temperature dependence of the helical turn angle in holmium. Open circles, ambient pressure solid triangles, 6kbar open triangles, 7kbar solid circles, 16kbar open squares, 21kbar. The data at ambient pressure (open circles) are from Koehler et al. (1966) and 6kbar (solid triangles) from Umebayashi et al. (1968). The figure is taken from Achiwa et al. (1988).

The spontaneous magnetization (Ts. the magnetization a in a magnetic field and the equilibrium value of the helical turn angle can be derived by minimizing the free energy F, which is considered to be a function of o and (p. With the magnetization found one... 

The distance between two subsequent base pairs along the helical axis is called helical rise (/ ). The pitch (P) is the length of the helix axis for one complete helix turn. The turn angle per nucleotide or twist angle (t) is given by 360°/number of nucleotides per turn. Data describing some properties of A, B, and Z DNA structure are found in Table 2.3 as adapted from Table 1.10 of reference 13 and the Jena image library website address above. 

More recently, Smith et al. have developed another model based on spontaneous curvature.163 Their analysis is motivated by a remarkable experimental study of the elastic properties of individual helical ribbons formed in model biles. As mentioned in Section 5.2, they measure the change in pitch angle and radius for helical ribbons stretched between a rigid rod and a movable cantilever. They find that the results are inconsistent with the following set of three assumptions (a) The helix is in equilibrium, so that the number of helical turns between the contacts is free to relax, (b) The tilt direction is uniform, as will be discussed below in Section 6.3. (c) The free energy is given by the chiral model of Eq. (5). For that reason, they eliminate assumption (c) and consider an alternative model in which the curvature is favored not by a chiral asymmetry but by an asymmetry between the two sides of the bilayer membrane, that is, by a spontaneous curvature of the bilayer. With this assumption, they are able to explain the measurements of elastic properties. 

Molecular models of polynucleotide helices consistent with the observed axial rise per nucleotide (7z) and its turn angle ( ), which are accurately measurable from the fibre... 

Carbon sulfur [7]helicene (M)-(-)-40, which has a relatively low turning angle but possesses two bulky bromine groups at the ends of the inner helix, has a free energy barrier for racemization of 39.0 kcal mol-1 (half-life of 11 h at 199 °C) [85], The relatively small helical turn in-plane (based on the X-ray structures of two racemic polymorphs) is apparently offset by two bulky bromine groups at the ends of the inner helix. 

Huige and Hezemans179 180 have performed extensive molecular mechanics calculations using the consistent force-field method on various oligo- and polyisocyanides. The hexadecamer of ferf-butyl isocyanide was calculated to have a helical middle section and disordered ends. The dihedral angle N=C—C=N in the middle section was found to be 78.6°, and the number of repeat units per helical turn was 3.75. The latter number is in agreement with circular dichroism calculations using Tinoco s exciton theory (3.6—4.6) and De Voe s polarizability theory (3.81). The molecular mechanics calculations further predicted that the less bulky polymers 56 and 57 form helical polymers as well, whereas a disordered structure was calculated for poly(methyl isocyanide) (55). 

When DNA becomes partially dehydrated, it assumes the A form (Figure 17.10 and Table 17.1). In A-DNA, the base pairs are no longer at right angles to the helical axis. Instead, they tilt 20° away from the horizontal. In addition, the distance between adjacent base pairs is slightly reduced, with 11 bp per helical turn instead of the 10.4 bp found in the B form. Each turn of the double helix occurs in 2.5... 

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