Structure generation mathematical approach

Molecular Shape Analysis. Once a set of shapes or conformations are generated for a chemical or series of analogs, the usual question is which are similar. Similarity in three dimensions of collections of atoms is very difficult and often subjective. Molecular shape analysis is an attempt to provide a similarity index for molecular structures. The basic approach is to compute the maximum overlap volume of the two molecules by superimposing one onto the other. This is done for all pairs of molecules being considered and this measure, in cubic angstroms, can be used as a parameter for mathematical procedures such as correlation analysis. 

Deductive approaches to non-linearity have on the whole been more popular. On the basis of available information on enzymes structure and biological function, plausible physical models have been formulated. These then generate mathematical predictions and experimental data are then tested against the predictions. The risk here, of course, is that information may be overlooked or discarded in the attempt to substantiate a favoured model. 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, that is, their inability to distinguish stereoisomers. Examples of 3D QSAR include molecular shape analysis (MSA) [26], distance geometry,and Voronoi techniques [27]. The MSA method utilizes shape descriptors and MLR analysis, whereas the other two approaches apply atomic refractivity as structural descriptor and the solution of mathematical inequalities to obtain the quantitative relationships. These methods have been applied to study structure-activity relationships of many data sets by Hopfinger and Crippen, respectively. Perhaps the most popular example of the 3D QSAR is the com-... 

There appears to be three fundamental approaches to the synthesis of chemical process flowsheets. The first, systematic generation, builds the flowsheet from smaller, more basic components strung together in such a way that raw materials eventually become transformed into the desired product. The second, evolutionary modification, starts with an existing flowsheet for the same or a similar product and then makes modifications as necessary to adopt the design to meet the objectives of the specific case at hand. The third, superstructure optimization, views synthesis as a mathematical optimization over structure this approach starts with a larger superflowsheet that contains embedded within it many redundant alternatives and interconnections and then systematically strips the less desirable parts of the superstructure away. 

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