Topological framework analysis

Application of this topological framework analysis to ion channel modulators yields access to privileged ion channel chemotypes. Conversion of these frameworks into appropriate scaffolds for synthesis allows subsequent building of ion channel focused libraries. 

It has been recently shown [12] that the ELF topological analysis can also be used in the framework of a distributed moments analysis as was done for Atoms in Molecules (AIM) by Popelier and Bader [32, 33], That way, the Mo( 2) monopole term corresponds to the opposite of the population (denoted N) ... 

Closely related to the approach considered here are the formal frameworks of Feinberg and Clarke, briefly mentioned in Section II. A. Though mainly devised for conventional chemical kinetics, both, Chemical Reaction Network Theory (CRNT), developed by M. Feinberg and co-workers [79,80], as well as Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83], seek to relate aspects of reaction network topology to the possibility of various... 

TABLE 2.1. Geometrical Parameters, Bonding Energies, and Topological Analysis of Electronic Density in the Framework of AIM Theory"... 

A topological analysis of the electron density in the framework of AIM theory, performed for the systems in Figure 6.2, has completely confirmed their formulation as dihydrogen-bonded complexes. In accord with the AIM criteria, the pc and V pc parameters at the bond critical points found in the H- - -H directions are typical of dihydrogen bonds 0.042 and 0.057 au for complex LiH HF and 0.046 and 0.048 au for complex NaH- - -HF, respectively. The presence of the bond critical points can be well illustrated by the molecular graph in Figure 6.3, obtained for the HCCH H-Li complex by Grabowski and co-workers [8]. 

NH4-CH4]+ complex in the gas phase [36]. Topological analysis of the electron density performed in the framework of AIM theory shows the bond critical points on the H- H directions with pc values of 0.013 an. It is interesting that the electron density in this complex is larger than that obtained for the BH4 - CH4 dihydrogen-bonded system (pc = 0.007 an), the CH4 molecule of which acts as a proton donor. In accordance with the electronic density, the H- H distances in the BH4 - H4C complex were remarkably longer than 2.4 A (2.797, 2.929,... 

Relaxation measurements provide a wealth of information both on the extent of the interaction between the resonating nuclei and the unpaired electrons, and on the time dependence of the parameters associated with the interaction. Whereas the dipolar coupling depends on the electron-nucleus distance, and therefore contains structural information, the contact contribution is related to the unpaired spin density on the various resonating nuclei and therefore to the topology (through chemical bonds) and the overall electronic structure of the molecule. The time-dependent phenomena associated with electron-nucleus interactions are related to the molecular system, and to the lifetimes of different chemical situations, for the resonating nucleus. Obtaining either structural or dynamic information, however, is only possible if an in-depth analysis of a series of experimental results provides sufficient data to characterize the system within the theoretical framework discussed in this chapter. 

Table II gives the unit cell composition of the 10 of our as synthesized samples for which an accurate analysis was possible. Also are included and adapted 3 other Nu-10 samples for which an analysis was available in the literature (samples 14, 15, 18). We also included the composition of silica-ZSM-22, another zeolite possessing the same framework topology as Nu-10 (12), that was synthesized in presence of diethylamine (DA) under veiy particular conditions (12).

Papin, J.A. and Palsson, B.O. (2004b). Topological analysis of mass-balanced signaling networks a framework to obtain network properties including crosstalk. J. Theor. Biol. 227, 283-297. 

Molecular topology [155-158,190-199] presents a systematic framework for general shape analysis methods applicable, in principle, to all molecules. The same framework is also the basis for special shape analysis methods designed to exploit the typical features of some special, distinguished molecular families, such as the folding properties of polypeptides, proteins, and other chain biomolecules. Molecular topology and the associated topological shape analysis approaches form the basis of the present book. 

The above example illustrates a general principle of similarity analysis geometrical similarity corresponds to a topological equivalence [108]. In order to formulate the above principle in more precise terms, we have to specify a general framework applicable to most molecular shape similarity problems. The (Pyfysimilarity concept [108] provides such a general framework. 

To sum up this rather technical analysis, it seems indisputable that the fitting of classical "monolayer" zeolites to IPMS is not just an elegant mathematical curiosity. The quantitative analysis that follows from this description allows predictions of framework densities as a function of the network topology. This understanding of structure, which views the (Euclidean) three-dimensional structure in terms of its intrinsic two-dimensional hyperbolic geometry opens up a predictive understanding of structure. 

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