Unit tangles

There is a close relationship between knots and catenanes. Figure 8 a illustrates a transformation that interconverts these two topological species. One can consider each strand of a unit tangle to have an arbitrary polarity, and then one can cleave each strand in two, so that there are two first parts and two second parts. Switch-... 

At one time or another, all of us have tangled with problems of units, but generally these decrease in severity and frequency with experience. Advanced students juggle kilograms and grams, centimeters and angstroms, joules and calories, and rarely fumble in the process. Electrical units are sometimes more troublesome. 

Glycogen is the major storage polysaccharide in animals. This tiny portion of a tangled glycogen granule shows the highly branched polymer, made of glucose units. 

Linear polymer chains arise where the monomers join together in long chains with few or a limited number of side chains. These chains may, however, be in a twisted and tangled formation giving an amorphous type polymer or in a more orderly layout to give a crystalline structure. When the chains are made from a single (identical) repeating unit, a homopolymer is... 

What about the tau protein, the chief component of the tangles, the other pathological trait of Alzheimer s disease In a 1995 study, Olaf Schweers and his colleagues at the Max Planck Unit for Structural Molecular Biology in Hamburg showed that the tau protein only coagulates when... 

Natural rubber is a polymer of 2-methyl-l,3-butadiene (isoprene Section 26.6). On average, a molecule of mbber contains 5000 isoprene units. All the double bonds in natural rubber are cis. Rubber is a waterproof material because it consists of a tangle of hydrocarbon chains that have no affinity for water. Charles Macintosh, a Scotsman, was the first to use mbber as a waterproof coating for raincoats. 

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