Helix dimensions

The protein tropomyosin (TM) is composed of two identical chains of a helix (see table 5.1) that are in turn twisted around each other in a helical structure. Consider the average amino acid residue weight to be 105 daltons and use typical a-helix dimensions (fig. 4.4) to calculate the length of each chain in TM. Explain any discrepancy observed between the calculated length and the observed length of 360 A. 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

Because of the double helical nature of DNA molecules, their size can be represented in terms of the numbers of nucleotide base pairs they contain. For example, the E. coli chromosome consists of 4.64 X 10 base pairs (abbreviated bp) or 4.64 X 10 kilobase pairs (kbp). DNA is a threadlike molecule. The diameter of the DNA double helix is only 2 nm, but the length of the DNA molecule forming the E. coli chromosome is over 1.6 X 10 nm (1.6 mm). Because the long dimension of an E. coli cell is only 2000 nm (0.002 mm), its chromosome must be highly folded. Because of their long, threadlike nature, DNA molecules are easily sheared into shorter fragments during isolation procedures, and it is difficult to obtain intact chromosomes even from the simple cells of prokaryotes. 

Angular dimensions that define gears and are used in their specification and design are helix angle, lead angle, shaft angle, and angular pitch. 

Here, ry is the separation between the molecules resolved along the helix axis and is the angle between an appropriate molecular axis in the two chiral molecules. For this system the C axis closest to the symmetry axes of the constituent Gay-Berne molecules is used. In the chiral nematic phase G2(r ) is periodic with a periodicity equal to half the pitch of the helix. For this system, like that with a point chiral centre, the pitch of the helix is approximately twice the dimensions of the simulation box. This clearly shows the influence of the periodic boundary conditions on the structure of the phase formed [74]. As we would expect simulations using the atropisomer with the opposite helicity simply reverses the sense of the helix. 

The information obtained from the experiments described above can be used to construct models for the three-dimensional arrangement of the membrane-spanning helices within the transport proteins. One such model, which takes the diameter of an a-helix as 1.1 nm and seems to fit the measured dimensions of lac permease quite nicely, is illustrated in Fig. 5, although it must be emphasized that this is only one of... 

A typical virus with helical symmetry is the tobacco mosaic virus (TMV). This is an RNA virus in which the 2130 identical protein subunits (each 158 amino acids in length) are arranged in a helix. In TMV, the helix has 16 1/2 subunits per turn and the overall dimensions of the virus particle are 18 X 300 nm. The lengths of helical viruses are determined by the length of the nucleic acid, but the width of the helical virus particle is determined by the size and packing of the protein subunits. 

The unit cell is tetragonal, with a symmetry approximating P2i2 2i. The cell dimensions are a = b= 18.87 A (1.887 nm) and c = 7.99 A (799 pm). The helix diameter is 13.3 A (1.33 nm). One ethylenediamine molecule for every two D-glucose residues is indicated. The location of the ethylenediamine molecule in the lattice was discussed. The structure is almost identical to that of the amy-lose-dimethyl sulfoxide complex. 

Govaerts et al. (2004) proposed a parallel /1-helix model for prion rods that is consistent in overall dimensions with their low-resolution EM studies of two-dimensional PrP 27-30 crystals (Wille et al, 2002). In this model, residues 89-174 form 4 coils, or complete helical turns (Jenkins and Pickersgill, 2001), of a left-handed, parallel /Hielix (Fig. 5B). The coils of one monomer are proposed to stack on the coils of another to form an extended triangular -structure. Three of these triangular units pack together to form the fibril (Fig. 5G and D). The G-terminal a-helices (a2 and a3) of monomeric PrP are proposed to retain their native structure in the fibril and pack around the outside of the trimer (Fig. 5G and D). The presence of these helices in the prion rods is consistent with antibody binding studies (Peretz et al, 1997), the presence of a disulfide bond (Turk et al, 1988), and FTIR measurements (Wille et al, 1996). 

Suppose that one takes an electron micrograph of such a helical molecule at a resolution sufficient to reveal the helix structure. This micrograph will appear as a projection of the helix in two dimensions (Scheme 19a) and will still not allow one to distinguish between a dextro- and levorotatory helix positioned as mirror images as in Scheme 19a. An unequivocal solution to the problem may be achieved, in analogy to the optical solution illustrated in Section II, if a second micrograph is taken with the plane of the sample tilted in a known direction, yielding a new two-dimensional projection (Scheme 19b). 

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