Topological potential, 517 pairs

For proteins with more than two domains, each potential duplication is listed separately e.g., a minimum of two duplications would be necessary to produce either a three-domain or a four-domain structure. Members of the pairs in the left-hand column both fall within the same structural subcategory and have fairly similar topologies such pairs are perhaps the result of internal gene duplications. Members of pairs in the right-hand column almost all fall into different major categories of tertiary structure (e.g., one all-helical and one antiparallel jS) presumably they could not have been produced by internal gene duplication. 

Fig. 3.6 Left, diagonal SW wave for the N = 200 dual closed graphene at the diffusion step rj = 1 of the pentagon-heptagon pair red-green circles). The swapping hexagons are circled in pale blue. Right. Diagonal dislocations freely flow in the lattice minimizing, with an almost linear dependence from r), the topological potential W of the structure. At r) = 1,W = 115,870...

For current consoHdation, the basic circuits, used at each of the multiple power take-off points, are stacked into a Christmas tree topology to form a single power take-off terminal pair. Scale-up of these devices to commercial sizes is not expected to be a problem, as standard electrical components are available for all sizes considered. A different type of consoHdation scheme developed (117), uses dc to ac converters to connect the individual electrodes to the consoHdation point. The current from each electrode can be individually controUed by the converter, which can either absorb energy from or deHver energy to the path between the electrode and the consoHdation point. This scheme offers the potential capabiHty of controlling the current level of each electrode pair. 

A wide variety of features have been used in bit vectors, including molecular fragments, 3-D potential pharmacophores, atom pairs, 2-D pharmacophores, topological torsions, and variety of topological indices. 

The interband pairing term enhances Tc [93-97,102] by tuning the chemical potential in an energy window around the Van Hove singularities, z =0, associated with a change of the topology of the Fermi surface from ID to 2D (or 2D to 3D) of one of the subbands of the superlattice in the clean limit. 

Figure 1 2 6. The Fermi surface of the second (red) and third subband (black) of a 2D superlattice of quantum wires near the type (III) ETT where the third suhhand changes from the one-dimensional (left panel) to two-dimensional (right panel) topology. Going from the left panel to the right panel the chemical potential EF crosses a vHs singularity at Ec associated with the change of the Fermi topology going from EF>EC to EF

Figure 17. Schematic diagrams of some representative topologically chiral proteins.79 (a) Condensed schematic drawing of the L subunit of the quinoprotein TV-MADH. The looped line represents the polypeptide backbone with N and C terminals. Cysteine (or half-cystine) residues are numbered, and their a-carbons are indicated by filled circles. Intrachain disulfide bonds are shown as dashed lines joining a pair of filled circles. The heavy line symbolizes an intrachain cofactor link, (b) Chromatium high potential iron protein (HiPIP), one of several Fe4S4 cluster-containing proteins, (c) Toxin II from the scorpion Androctonus australis Hector. Reprinted with permission from C. Liang and K. Mislow, J. Math. Chem. 1994,15,245. Copyright 1994, Baltzer Science Publishers.

Moreover, geometric atom pairs and geometric binding property pairs were proposed, substituting the topological distance between two atom types with the - geometric distance [Sheridan et a/., 1996]. PPP-pairs are a particular case of geometric atom pairs where only pairs of the five potential pharmacophore points are considered [Brown and Martin, 1996]. 

Fig. 11 Representation of lowest adiabatic potential of singlet (S = 0) and triplet (S = 1) Fe(CO)4 around T Jahn-Teller conical intersection at tetrahedral (7 ) geometry. There are three equivalent two-dimensional troughs in the space spanned by each pair-wise selection of equal L-M-L angles (boxed vs unboxed). The topological connectivity where the troughs intersect is indicated. There are two non-equivalent epikemel distortion directions E[ 2(Td,h) leading to 6 equivalent C2v minima ( ), and 12 equivalent Cs(x) saddle-points respectively. The non-Berry pseudo-rotation barrier is very small ( 5kcal mol ). CASSCF optimised geometrical parameters for singlet and triplet states are shown at the top left...

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