Rings and Helices

Among open-framework metal phosphates, zincophosphates exhibit diverse compositions and fascinating structural topologies.[212] Notable examples are zincophosphates with extra-large pores bound by 16-, 20-, and 24-rings, and helical channels. 

Compared to scroll rings and helices, the geometry of even the simplest knotted filament (the trefoil) is quite complex. Knotted scroll waves are unknown (or unrecognized) in the BZ reaction, and there have been few thorough studies of knotted scroll wave solutions to reaction-diffusion equations modeling excitable media [26,28]. The analytical theory [32] of invariant knotted solutions to the filament equations (15) is not only difficult but also (probably) inapplicable to the invariant knots that have been computed numerically, because the latter are compact structures whose dynamics seem to be dominated by interactions between the closely spaced segments of the knotted filament. 

FIGURE 17. 33 A model of the flagellar motor assembly of Escherichia coli. The M ring carries an array of about 100 motB proteins at its periphery. These juxtapose with motA proteins in the protein complex that snrronnds the ring assembly. Motion of protons throngh the motA/motB complexes drives the rotation of the rings and the associated rod and helical filament. 

These studies conducted in solution and in the solid state revealed a common 3i4-helical fold stabilized by H-bonds closing 14-membered rings formed between NH and C=0 +2 (see Fig. 2.12A and C). It is noteworthy that the 3i4-helix of j -peptides with L-amino acid-derived chirality centers (Fig. 2.12 A) and the a-helix have opposite polarity and helicity. 

Interestingly, 8-aminoxy acids which are homologs of y-amino acids have also been found to promote the formation of turns and helices. In apolar solvent and in the solid state, model diamides consisting of /9 -aminoxy add residues adopt a novel N-O turn stabilized by both a nine-membered H-bonded ring between C=0 and NHj+2, and a six-membered ring formed between N-O and NH +1. The X-ray crystal structure of a corresponding triamide revealed two consecutive C9 N-O turns suggesting a novel 1.79-helical fold [279]. 

In order to further experimentally probe the hard-core model of polysilane aggregate chirality, a series of poly-[(alkyl)alkylphenylsilylene]s, differing in phenyl ring-substituent position and chain length were synthesized, designed such that the polymer chain diameter, d, and helical pitch, p, in the hard-core model were varied.343... 

Taylor, W.H. and Hagerman, P.J. (1990) Application of the method of phage T4 DNA ligase-catalyzed ring-closure to the study of DNA structure I.NaCl-dependence of DNA flexibility and helical repeat. J. Mol. Biol. 212, 363-376. 

The same test method, although not standardized, can be used to characterize the laminate in-plane shear behavior. This is accomplished by winding a multiorientation (hoop/helical and/or helical only) tube. Other test methods that can be used to measure in-plane shear stiffhess/strength of filament wound composites are discussed by Tamopol skii and Kinds [45]. These methods include schemes for torsion of intact rings and split rings. Both of these ring test methods are used to evaluate the in-plane shear modulii G0r and G0z for a filament-wound laminate. 

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