Topological coupling

Fig. 3. Topological coupling of DNA translocation and chromatin remodeling. (A) Alternative models for remodeling of a single nucleosome driven by the translocating complexes are compared with passive remodeling driven by the SP6 RNA polymerase or RNA polymerase III [109]. Note that no superhelicity would be constrained unless rotation of the translocase and DNA ends is impeded or prevented. It is also assumed that translocation occurs in steps of less than 5bp. CRA, chromatin remodelling assembly. The arrows indicate the direction of translocation of the DNA. (B) Model for remodeling of a nucleosome array within a topologically defined domain. Adapted with permission from Ref [119].

Considering nature s exploitation of branched topologies coupled with the extensive research on dendritic stmctures, it is apparent that they have a potential to find use in specialized applications, that is, in targeted drug delivery, maaomolecular carrier systems, enzyme-like catalysis, sensors, light harvesting, surface engineering, and biomimetic applications. ... 

An alternative method that can be used to characterize the topology of PES is the line integral technique developed by Baer [53,54], which uses properties of the non-adiabatic coupling between states to identify and locate different types of intersections. The method has been applied to study the complex PES topologies in a number of small molecules such as H3 [55,56] and C2H [57]. 

In this section, the adiabatic picture will be extended to include the non-adiabatic terais that couple the states. After this has been done, a diabatic picture will be developed that enables the basic topology of the coupled surfaces to be investigated. Of particular interest are the intersection regions, which may form what are called conical intersections. These are a multimode phenomena, that is, they do not occur in ID systems, and the name comes from their shape— in a special 2D space it has the fomi of a double cone. Finally, a model Flamiltonian will be introduced that can describe the coupled surfaces. This enables a global description of the surfaces, and gives both insight and predictive power to the fomration of conical intersections. More detailed review on conical intersections and their properties can be found in [1,14,65,176-178]. 

For states of different symmetry, to first order the terms AW and W[2 are independent. When they both go to zero, there is a conical intersection. To connect this to Section III.C, take Qq to be at the conical intersection. The gradient difference vector in Eq. f75) is then a linear combination of the symmetric modes, while the non-adiabatic coupling vector inEq. (76) is a linear combination of the appropriate nonsymmetric modes. States of the same symmetry may also foiiti a conical intersection. In this case it is, however, not possible to say a priori which modes are responsible for the coupling. All totally symmetric modes may couple on- or off-diagonal, and the magnitudes of the coupling determine the topology. 

One of the main outcomes of the analysis so far is that the topological matrix D, presented in Eq. (38), is identical to an adiabatic-to-diabatic transformation matrix calculated at the end point of a closed contour. From Eq. (38), it is noticed that D does not depend on any particular point along the contour but on the contour itself. Since the integration is carried out over the non-adiabatic coupling matrix, x, and since D has to be a diagonal matrix with numbers of norm 1 for any contour in configuration space, these two facts impose severe restrictions on the non-adiabatic coupling terms. 

The three matrices of interest were already derived and presented in Section V.A. There they were termed the D (topological) matrices (not related to the above mentioned Wigner matrix) and were used to show the kind of quantization one should expect for the relevant non-adiabatic coupling terms. The only difference between these topological mauices and the... 

In Section IV, we introduced the topological matrix D [see Eq. (38)] and showed that for a sub-Hilbert space this matrix is diagonal with (-1-1) and (—1) terms a feature that was defined as quantization of the non-adiabatic coupling matrix. If the present three-state system forms a sub-Hilbert space the resulting D matrix has to be a diagonal matrix as just mentioned. From Eq. (38) it is noticed that the D matrix is calculated along contours, F, that surround conical intersections. Our task in this section is to calculate the D matrix and we do this, again, for circular contours. 

Figure 3-61 The ground arrangements for the major converter topologies (a) the nonisolated dc/dc converter (b) the nonisolated, transformer-coupled converter (c) the isolated, transformer-coupled converter.

Kaplunovsky and Weinstein [kaplu85j develop a field-theoretic formalism that treats the topology and dimension of the spacetime continuum as dynamically generated variables. Dimensionality is introduced out of the characteristic behavior of the energy spectrum of a system of a large number of coupled oscillators. 

Transmembrane Signaling. Figure 2 Membrane topology of receptors that are associated with effector proteins. Upon binding to their cognate ligands (cyan), receptor proteins without intramolecularly linked effector domain couple via transducer proteins (yellow) to or directly recruit and activate effector proteins (red). Notch receptors release their transducer domains upon proteolytic cleavage, a, p and y stand for G-protein a-, p- and y-subunits, respectively. 

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]. 

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