Topology-adapted

Crystal Engineering with Soft and Topologically Adaptable Molecular Host Frameworks... 

First, the use of higher dimensional robust networks (such as the two-dimensional GS network) simplifies crystal engineering because is reduces crystal design to the last remaining dimension. The use of two-dimensional supramolecular modules, in particular, provides an easily conceptualized mechanism for topological adaptation (in the case of GS networks the arrangement of the pillars). 

Soft and topologically adaptable supramolecular modules that allow host lattices to achieve dense packing through low-energy deformations, while retaining their inherent dimensionality and supramolecular connectivity, can facilitate the systematic design of molecular inclusion compounds. This is demonstrated by the ability to predict and maintain architectural control in a series of lamellar host frameworks. 

During the study, it was picked up that Cr + influences DNA topology. (Adapted from Plaper et ah, 2002)... 

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]. 

The detailed derivation of iTeff is given in Ref. [53]. Here, two of the six modes (i.e., X and X2) are chosen as topology-adapted modes that span the branching plane for a chosen pair of electronic states (here, states 1 and 2). Each /th-order residual term now also comprises 6 modes,... 

Fig. 8 a, b. a PCA classification of lignocellulose hydrolysates from pine, spruce, aspen and birch using a combination of MOS, MOSFET and CP sensors, b Prediction of the ferment-ability of the same hydrolysates expressed as specific ethanol production rate using ANNs with topologies adapted to the sensor array (from [34] with permission of ACS)... 

Figure 6 The topological disconnectivity graph of alanine hexapeptide. (Adapted from Ref. 67.)...

Figure 2.11 Beta sheets are usuaiiy represented simply by arrows in topology diagrams that show both the direction of each (3 strand and the way the strands are connected to each other along the polypeptide chain. Such topology diagrams are here compared with more elaborate schematic diagrams for different types of (3 sheets, (a) Four strands. Antiparallel (3 sheet in one domain of the enzyme aspartate transcarbamoylase. The structure of this enzyme has been determined to 2.8 A resolution in the laboratory of William Lipscomb, Harvard University, (b) Five strands. Parallel (3 sheet in the redox protein flavodoxin, the structure of which has been determined to 1.8 A resolution in the laboratory of Martha Ludwig, University of Michigan, (c) Eight strands. Antiparallel barrel in the electron carrier plastocyanln. This Is a closed barrel where the sheet is folded such that (3 strands 2 and 8 are adjacent. The structure has been determined to 1.6 A resolution in the laboratory of Hans Freeman in Sydney, Australia. (Adapted from J. Richardson.)...

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...

Where more than one a helix connects two P strands (for example, between strands 4 and S), they are represented as one rectangle in the topology diagram. (Adapted from T.N. Bhat et al., /. Mol. Biol. 1S8 699-709, 1982.)... 

Figure 4.19 Schematic and topological diagrams for the structure of the enzyme carboxypeptidase. The central region of the mixed p sheet contains four adjacent parallel p strands (numbers 8, 5, 3, and 4), where the strand order is reversed between strands 5 and 3. The active-site zinc atom (yellow circle) is bound to side chains in the loop regions outside the carboxy ends of these two p strands. The first part of the polypeptide chain is red, followed by green, blue, and brown. (Adapted from J. Richardson.)...

Figure 4.21 The polypeptide chain of the arabinose-binding protein in E. coli contains two open twisted a/P domains of similar structure. A schematic diagram of one of these domains is shown in (a). The two domains are oriented such that the carboxy ends of the parallel P strands face each other on opposite sides of a crevice in which the sugar molecule binds, as illustrated in the topology diagram (b). [(a) Adapted from J. Richardson.)...

Figure S.7 The subunit structure of the neuraminidase headpiece (residues 84-469) from influenza virus is built up from six similar, consecutive motifs of four up-and-down antiparallel fi strands (Figure 5.6). Each such motif has been called a propeller blade and the whole subunit stmcture a six-blade propeller. The motifs are connected by loop regions from p strand 4 in one motif to p strand 1 in the next motif. The schematic diagram (a) is viewed down an approximate sixfold axis that relates the centers of the motifs. Four such six-blade propeller subunits are present in each complete neuraminidase molecule (see Figure 5.8). In the topological diagram (b) the yellow loop that connects the N-terminal P strand to the first P strand of motif 1 is not to scale. In the folded structure it is about the same length as the other loops that connect the motifs. (Adapted from J. Varghese et al.. Nature 303 35-40, 1983.)...

Figure S.IS Schematic diagram (a) and topology diagram (b) for the y-crystallin molecule. The two domains of the complete molecule have the same topology each is composed of two Greek key motifs that are joined by a short loop region, [(a) Adapted from T. Blundell et ah. Nature 289 171-777, 1981.]...

Figure 13.4 Schematic diagram (a) and topology diagram (b) of the polypeptide chain of cH-ras p21. The central p sheet of this a/p structure comprises six p strands, five of which are parallel a helices are green, p strands are blue, and the adenine, ribose, and phosphate parts of the GTP analog are blue, green, and ted, respectively. The loop regions that are involved in the activity of this protein are red and labeled Gl-GS. The Gl, G3, and G4 loops have the consensus sequences G-X-X-X-X-G-K-S/T, D-X-X-E, and N-K-X-D, respectively. (Adapted from E.R Pai et al., Nature 341 209-214, 1989.)...

Figure 13.18 Ribbon diagram of the structure of human growth hormone. The fold is a four-helix bundle with up-up-down-down topology, and consequently there are two long cross-connections between helices A and B as well as between helices C and D. (Adapted from J. Wells et al., Annu. Rev. Biochem.

Adapted from Hatefi, Y, 1985. The mitochondrial electron tran.sport chain and oxidative pho.sphorylation. sy.stem. Annual Review of Biochemistry 54 1015-1069 and DePierre, J., and Ern.ster, L., 1977. Enzyme topology of intracellular membrane.s. Annual Review of Biochemistry 46 201-262. 

A Brief Review of the QSAR Technique. Most of the 2D QSAR methods employ graph theoretic indices to characterize molecular structures, which have been extensively studied by Radic, Kier, and Hall [see 23]. Although these structural indices represent different aspects of the molecular structures, their physicochemical meaning is unclear. The successful applications of these topological indices combined with MLR analysis have been summarized recently. Similarly, the ADAPT system employs topological indices as well as other structural parameters (e.g., steric and quantum mechanical parameters) coupled with MLR method for QSAR analysis [24]. It has been extensively applied to QSAR/QSPR studies in analytical chemistry, toxicity analysis, and other biological activity prediction. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least-squares (PLS) analysis has been employed [25]. 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

Fig. 4.1 Topological organization of the vanilloid receptor TRP VI. Highlighted are the molecular determinants of TRPVl regulation, such as recognition (binding) domains for capsaicin and acids, and phosphorylation sites for protein kinases. Numbers designate the key amino acid residues deduced from the rTRPVl primary sequence. Adapted from Ferrer-Montaniel, A. et al. (2004) Fur. J. Biochem. 271, 1820—1826.

Figure 9.29. Three conical intersection surface topologies for electron transfer processes in radical cations (adapted from reference 5).

The growing cell structure algorithm is a variant of a Kohonen network, so the GCS displays several similarities with the SOM. The most distinctive feature of the GCS is that the topology is self-adaptive, adjusting as the algorithm learns about classes in the data. So, unlike the SOM, in which the layout of nodes is regular and predefined, the GCS is not constrained in advance to a particular size of network or a certain lattice geometry. 

Jurs and co-workers have used parameters generated by the ADAPT system [34], The descriptors fall into three categories topological, electronic, and geometric. 

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