Hyperstructure approaches

Remark 3 For (ii)-(iv), the hyperstructure approach presented in the section of simultaneous matches-network optimization will be utilized. 

Simon, Z. (1993). MTD and Hyperstructure Approaches. In 3D QSAR in Drug Design. Theory, Methods and Applications. (Kubinyi, H., ed.), ESCOM, Leiden (The Netherlands), pp. 307-319. 

The hyperstructure approaches MSD and MTD (minimal steric difference and minimal topological difference) and molecular shape analysis (MSA) are discussed in chapter 4.6, the use of similarity indices is discussed in chapter 9.4. 

Remark 3 In the Ph.D. thesis of Ciric (1990), the full hyperstmcture was derived and formulated as an MINLP problem. However, since the part of hyperstructure which corresponds to cold stream Cl involves five matches, then the mathematical model will be complex for presentation purposes. For this reason we will postulate the part of the hyperstmcture of Cl by making the following simplification which eliminates a number of the interconnecting streams. This is only made for simplicity of the presentation, while the synthesis approach of Ciric and Floudas (1991) is for the general case. 

The Positional Analysis approach proposed by P. Magee aims to detect the structural features responsible for the ligand-biotarget interaction by constructing the simplest common hyperstructure for a series of compounds and analyzing the presence and interaction parameters for each hyperstructure position by means of the multiple linear regression. 

The DARC-PELCO approach [418—423] is a simple application of a hyperstructure concept to the Free Wilson method while the approach may be appropriate for extremely large data sets, e.g. for the derivation of lipophilicity contributions from partition coefficients, it is usdess for most structure-activity analyses, due to the much too large number of variables (compare eqs. 199 and 200, chapter 8) [390, 391]. The results from Hansch, Free Wilson, and DARC-PELCO analyses have been compared with each other [421, 422, 424] no advantages of the latter approach could be seen. 

Magee [544, 545] combined the hyperstructure concept with the strategies of Hansch analysis and the mixed approach (chapter 4.3). As only several atoms or groups of a molecule modulate biological activity, each position of the hypermolecule... 

Magee s approach to active-site binding analysis [544, 545] may be considered as a combination of the hyperstructure concept (chapter 4.6) with the mixed approach (chapter 4.3), as can e.g. be seen from eq. 202 [545] first a hyperstructure (55) was formulated for a series of / ara-substituted phenyl-N-methylcarbamates and then... 

Papalexandri er al. (1994) proposed an MINLP model for the simultaneous generation of a network and the determination of the TAG without resorting to any pinch decomposition concepts. The reported total annual costs of most of the problems solved by Papalexandri et al. (1994) were poor when compared to those obtained by Hallale (1998) using a pinch approach, yet the MINLP framework itself was versatile enough to contain even those solutions proposed by Hallale. It would then seem plausible that a transfer of some techniques from pinch technology to MINLP optimisation would expose the actual optimum solutions embedded in the MINLP hyperstructure. 

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