Topology-adapted representation

Here, a topology-adapted representation [55] was chosen, where (Xi,X2) lift the degeneracy at the intersection and thus span the branching plane [74], These modes are obtained by orthogonalizing the modes (X, Xa) of Eq. (10). The third mode Xg is in turn orthogonal to (Xi, ) and carries information on the intersection space, i.e., the X+ component of Eqs. (9)-(10). Alternative construction schemes are possible in particular, the bilinear coupling terms can be eliminated within the three-mode subspace [54,72]. 

Figure 7.9 Topological structures of a-amylase A. Two-dimensional representation of the secondary and domain structures of porcine pancreatic a-amylase. Alpha helices are represented as circles and (3-strands in the up-direction as squares, and in the down direction as double squares. The (a/(3)g—TIM barrel comprises domain A. Hydrogen bonds between (3-strands are shown by dashed lines. The a-helices and (3-strands are identified in the various domains by A, B and C. (Reprinted by permission ofthe authors M. Qian et al.120) Two-dimensional representation ofthe secondary and domain structures of barley malt a-amylase (AMY2-2). Alpha helices are represented as cylinders and (3-strands as arrows. The (a/(3)g—TIM barrel comprises domain A, with eight (3-strands and an equivalent of eight a-helices. The active-site is composed ofthe loops that connect the C-termini ofthe (3-strands to the N-termini ofthe peripheral a-helices. (Adapted from A. Kadziola et al.121)...

Fig. 3 Schematic representation of the predicted topology of the monoamine transporters based on the crystalhzation of LeuTAa (Yamashita et al., 2005). The representation demonstrates how extracellular Na, Cl, and substrate are exchanged for intracellular K. The putative phosphoiy-lation sites on the N-terminus and C-terminus are shown along with predicted glycosylation sites between TMH III and TMH IV. This figure was adapted from Yamashita et td. (2005)...

There are three general classes of descriptors topological, geometrical, and physicochemical. Topological descriptors are derived from the topological representation of the structure, the connection table. The geometrical descriptors are derived from the three dimensional model of the molecule. Physicochemical descriptors may be measured experimentally, calculated using a mathematical model, or represented by linearly correlated calculated descriptors. The descriptors that are currently available in ADAPT are as follows ... 

We provided a novel multi-resolution approach to surface reconstruction from point clouds. Our method automatically adapts to the underlying surface topology and provides a fully-connected hybrid-mesh representation. In the context of reverse engineering it is able to provide accurate reconstructions assumed that the input data shows a sufficient point density. However, in case the point distribution is not continuous the generated reconstruction may... 

Fig. 2 Schematic representation of the spatial inhomogeneities, (I) spatial inhomogeneities, (II) topological inhomogeneities, (III) connectivity inhomogeneities, and (IV) mobility inhomogeneities. (Adapted with permission from Shibayama and Norisuye 2002)...

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