Packing of Helices

To pack a helix closely is more involved than the packing of spheres. The density depends on the degree of overlap that can be achieved between neighboring hehces, i.e., the interpenetration that can be achieved by having the turns of the helix intermesh. 

An example of a very close pack is metallic selenium, shown in Fig. 5.20. One can look upon the polymeric chains in the trigonal crystal as being related to a close packing of metaUic atoms with a coordination number CN = 12 that overlap along the 

Waals bonds are offset by the six lateral neighbors. The only other choice of packing would have been to reduce the neighboring chains from six to four, as shown for the organic polymers with more complicated helix geometries. 

The helices of organic macromolecules have their side-groups stick out sufficiently without matching the lattice symmeoy that intermeshing as in Se is not possible. In these cases the coordination number must be reduced to four, as shown in Fig. 5.21. The raised part of the schematic screws, the threads, can only intermesh (approxi- 

Facking of Helices with Large 6ide Groups 

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Strobel, S. A., and Doudna, J. A. (1997). RNA seeing double Close-packing of helices in RNA tertiary structure. Trends Biochem. Sci. 22, 262—266. 

Nolte et al. found that an amphiphilic block copolymer 83 composed of a hydrophobic tail of poly(styrene) and a hydrophilic head group of a charged, right-handed helical poly(isocyanide), which is referred to as a superamphiphile , self-assembles in a hierarchical fashion in water to form left-handed superhelices (Fig. 34) [ 158]. They suggest that this type of copolymer will serve as an experimental model for the theoretical study of the packing of helices due to their versatility and easy accessibility. 

An interesting inclusion compound derived from 2,6-dimethylbicyclo[3.3.1]nonane-exo-2,exo-6-diol, 2, was reported by the group led by Bishop and Dance. " The crystal structure of the alicyclic diol 2 can be ho. construed as packing of helices along the c-axis. The parallel canals that result from the helical tubules have an unobstmcted triangular cross-sectional area of roughly 20 which are H3C ... 

Figure 5.5 Model of the packing of helical rods of cholesterol skeletons according to fire geometry defined by the gyroid. The three rod-directions are parallel to the [lll]-directions, and one set of rods is perpendicular to the plane of the figure.

More complex helical domains incorporate both parallel and perpendicular packing of helices, for example, in the globin fold (Figure 15.10). 

The Cu(ll) complex, [Cu2(L55)2(H20)] H20, 75 derived from L55 crystallizes as a ID helical coordination polymer assembled from the dimeric building blocks similar to 71. But, the major difference is the presence of one more water molecule in the crystal lattice of 75. Interestingly, despite the similar structures and crystal packing of helical coordination polymers in 71 and 75, a stable dehydrated complex from 75 could not be obtained because the anhydrous species rapidly gets rehydrated in the presence of air. This indicates that the formation of new Cu-0 bond by the carboxylate group is restricted in 75. Fmther, in contrast to 71, the reason why the reversible hydration takes place in the case of [Cu2(L55)2(H20)] H20, 75, can be understood by the close examination of the crystal structure of 75. ... 

The a-phase PLLA is most common structure that can be obtained fi om crystallization in melt, solution and fiber spinning with low strain rate and temperature. Santis and Kovacs [213] first determined the conformation of a-phase PLLA and PDLA. PLLA is left handed IO7 helix, and a right handed IO3 helix for the i/-isomer PDLA. Both PLA are orthorhombic crystal systems with unit-cell parameters of a = 1.06 nm 6=0.610 nm and c=2.88 nm. The ratio of a and b is 1.737, which is nearly equal to /3 indicating an almost hexagonal packing of helices. Figure 4.46 shows the crystal structure of a phase PLLA. 

In concentrated solution, DNA fragments can form lyotropic liquid crystal phases. Short fragments behave like rods, and so the formation of liquid crystal phases is possible. On increasing concentration (above 160 mg/ml for 50 nm DNA in physiological salt solutions), cholesteric and hexagonal columnar phases may be observed (see Chapter 5 for a discussion of these structures) Just below the cholesteric phase, a blue phase is sometimes observed. This phase is named for the colour arising from the double twist cylinders that result from the packing of helices onto a cubic lattice. 

Figure 12.6 Packing of helical phosphole 8. Copyright 2012 Wiley-VCH Verlag GmbH Co. KGaA, Weinheim [15].

Figure 5.18. Diagram of the packing of helical chains exhibiting a tetragonal symmetry.

From a structural standpoint, iPP exists in three different crystal modifications that all rest on the same threefold helical chain conformation. Only the packing of helices differs in these three forms [26]. In addition, iPP displays an original self-epitaxy, analyzed later on, which leads to lamellar branching in its stable a phase, and exists as a crystallographic feature in its highly unusual /phase [27]. 

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