Helicity topology linked

Figure 4.1 Alpha/beta domains are found in many proteins. They occur in different classes, two of which are shown here (a) a closed barrel exemplified by schematic and topological diagrams of the enzyme trlosephosphate isomerase and (b) an open twisted sheet with helices on both sides, as in the coenzymebinding domain of some dehydrogenases. Both classes are built up from p-a-p motifs that are linked such that the p strands are parallel. Rectangles represent a helices, and arrows represent p strands in the topological diagrams, [(a) Adapted from J. Richardson, (b) Adapted from B. Furugren.j...

Like other hormones in this class of cytokines, GH has a four-helix bundle structure as described in Chapter 3 (see Figures 3.7 and 13.18). Two of the a helices, A and D, are long (around 30 residues) and the other two are about 10 residues shorter. Similar to other four-helix bundle structures, the internal core of the bundle is made up almost exclusively of hydrophobic residues. The topology of the bundle is up-up-down-down with two cross-over connections from one end of the bundle to the other, linking helix A with B and helix C with D (see Figure 13.18). Two short additional helices are in the first cross-over connection and a further one in the loop connecting helices C and D. 

It is only on this level that the link between helicity and topological quantization [103] can be understood properly. The 0(3) group, like the U(l) group, is multiply connected. The group space of U(l) is a circle [6, p. 105]. As explained earlier in this review, this is not simply connected because a path that goes twice... 

Helicity is defined as a qualitative measurement of how a topological configuration is linked, knotted, or twisted. If A is the vector potential of electromagnetism, the quantity then defines magnetic helicity. In order to obtain a nonnull value for K, the condition A (V A) /- 0 must be verified in the volume... 

Most cellular DNAs are supercoiled. Underwinding decreases the total number of helical turns in the DNA relative to the relaxed, B form. To maintain an underwound state, DNA must be either a closed circle or bound to protein. Underwinding is quantified by a topological parameter called linking number, Lk. 

Figure 8-23 Predicted topology of the human glucose transporter GLUT1. The 12 predicted helices are numbered and the single external N-linked oligosaccharide is marked CHO. The sequence RXGRR (marked) is found in many 12-helix transporters. Its occurrence in these two positions suggests that the transporters may have evolved by duplication of a 6-helix motif. However, the human glucose transporters otherwise show no sequence similarity to other 12-helix transporters. After Bell et al.398...

This equation shows a close relation between the wave and particle aspects of the helicity. On the left side, the wave helicity is the semisum of the electric and magnetic helicities that characterizes the topology of the force lines as a function of the linking number of the pairs of electric lines and of the magnetic lines. On... 

One of these topological constants of the motion is the electromagnetic helicity, defined as the semisum of the magnetic and electric helicities, which is equal to the linking number of the force lines... 

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