Topology of interaction

Peptides may bind to a membrane either by association to its surface or by insertion into its interior. The latter class comprises the integral membrane proteins whose structures are largely a-helical or / -barrel type (see Chap. 12 in Ref. [32]). The topology of interaction of helices with membranes is displayed in Fig. 5.1. 

An important pair of terms is suprafadal and antarafacial. These describe the topology of interaction of a given system in a pericyclic transition state, and they are best defined with reference to Figure 15.9. Here, lines which appear as "loops" or "arcs" show where interactions occur on the orbitals. These lines define a geometry for interaction of the orbitals shown with other orbitals. This should become clearer below with examples. 

A complex system must be understood not just in terms of the set of components out of which it is constructed, but the topology of the interconnections and interactions among those components. Any measure of complexity must likewise respect both the structure and dynamics of a complex system. 

As discussed in connection with the facial selectivities of 7-methylidenenorbom-ane 46 and bicyclo[2.2.2]octene 48, the components of the molecules, i.e., n functionality and two interacting o orbitals at the two P positions, are the same, but the connectivity of these fragments, i.e., the topology of the n systems, is different (A and B, Fig. 9). A similar situation was found in the case of spiro[cyclopentane-l,9 -fluorene] 68 [96, 97] and 11-isopropylidenedibenzo-norbomadienes 71 (see 3.4.1 and 3.4.2) [123]. In these systems, the n faces of the olefins are subject to unsymmetrization due to the difference of the interacting orbitals at the P positions. In principle, consistent facial selectivities were observed in these systems. 

The examples just presented give initial impressions of how DNA can be utilized as a template in the synthesis of nanometric and mesoscopic aggregates. However, the studies emphasize the importance of fundamental research on the interaction between DNA and the various binders, such as metal and organic cations. Of particular importance are the consequences of binding events on the structure and topology of the nucleic acid components involved. 

Figure 3.4 Transmembrane topology of a 7-TM domain G-protein receptor such as the P-adrenoceptor. Agonist binding is predicted to be within the transmembrane domains. The extracellular structure is stabilised by the disulphide bond joining the first and second extracellular loop. The third intracellular loop is the main site of G-protein interaction while the third intracellular loop and carboxy tail are targets for phosphorylation by kinases responsible for initiating receptor desensitisation...

This simple three-state model of protein folding, shown schematically in Figure 7, ascribes a separate force to shaping the structure of each state. Local steric interactions trap the protein chain in a large ensemble of conformations with the correct topology hydrophobic interactions drive the chain to a smaller, more compact subset of conformations then dispersion forces supply the enthalpy loss required to achieve a relatively fixed and rigid ensemble of native conformations. 

In dendrimers based on metals as branching centers (Fig. 1 d), the electrochemical behavior is even more complex since (i) each unit of the dendrimer is electro active, (ii) the chemical nature of the metal-based units constituting the dendrimer may be different, (iii) chemically equivalent units can be different from the topological viewpoint, and (iv) the degree of interaction among the moieties depends on their chemical nature and distance. 

From (2.70), it follows that the free energy cannot be divided simply into two terms, associated with the interactions of type a and type b. There are also coupling terms, which would vanish only if fluctuations in AUa and AUb were uncorrelated. One might expect that such a decoupling could be accomplished by carrying out the transformations that involve interactions of type a and type 6 separately. In Sect. 2,8.4, we have already discussed such a case for electrostatic and van der Waals interactions in the context of single-topology alchemical transformations. Even then, however, correlations between these two types of interactions are not... 

A cluster framework such as that seen in U has also been observed for its heavier homologues (14). Apparently, the latter topology is the result of a close packing of anionic pnictide moieties with alkali metal ions that maximizes ionic interactions. The topology of the rhombodo-decahedral Li6PeSi2 framework in U has been simply described as a Pe octahedron representing the anionic partial structure, of which the triangular faces are capped by two p.3-RSi moieties and six /t3-Li ions as counterion partial structure (Fig. 3). 

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