Minimal topological difference method structures

In this chapter we presented two structural measures of molecular shape that can be used as predictor variables in MLR (multiple linear regression) analysis of structure-activity studies - cylindrical (8,G) and ovality ( in, i = 1,2,3) molecular descriptors - and two inexpensive overlapping methods useful for quick receptor mapping - MTD (minimal topological difference) and MVD (minimal volume difference). A subsequent statistical analysis of QSAR models developed with these shape molecular descriptors explained well the variance in the observed reactivity data (8 descriptor of cylindrical shape) and biological activity of retinoids (MTD) and sulfonamides (MVD). 

Simon and his coworkers have developed (426) a quantitative 3D-QSAR approach, the minimal steric (topologic) difference (MTD) approach. Oprea et al. (452) compared MTD and CoMFA on affinity of steroids for their binding proteins and found similar results. Snyder and colleagues (453) developed an automated method for pharmacophore extraction that can provide a clear-cut distinction between agonist and antagonist pharmacophores. Klopman (404,454) developed a procedure for the automatic detection of common molecular structural features present in a training set of compounds. This has been used to produce candidate pharmacophores for a set of antiulcer compounds (404). Extensions (454)of this approach allow differentiation between substructures responsible for activity and those that modulate the activity. 

From the computational point of view the Fourier space approach requires less variables to minimize for, but the speed of calculations is significantly decreased by the evaluation of trigonometric function, which is computationally expensive. However, the minimization in the Fourier space does not lead to the structures shown in Figs. 10-12. They have been obtained only in the real-space minimization. Most probably the landscape of the local minima of F as a function of the Fourier amplitudes A,- is completely different from the landscape of F as a function of the field real space. In other words, the basin of attraction of the local minima representing surfaces of complex topology is much larger in the latter case. As far as the minima corresponding to the simple surfaces are concerned (P, D, G etc.), both methods lead to the same results [21-23,119]. 

The surface tension of a liquid is a measure of its tendency to minimize its surface area. The models for surface tension found in the literature are built on thermodynamic approaches, and they relate surface tension to a number of other physical properties, or to combinations of them. However, the literature contains little concerning the effect of specific molecular features on surface tension and provides no method to calculate surface tension from molecular structure. A set of 146 values for surface tension at 30 °C was extracted from a paper by Jasper that reports values for more than 2200 pure compounds with diverse structures, often at several different temperatures and with an experimental error of approximately 0.10 dyn cm . The compounds were encoded using a variety of topological, geometric, and electronic descriptors. A model was developed for a combined set of alkanes, alkyl esters, and alkyl alcohols which utilized 10 descriptors and had s = 0.4 dyn cm (1.8% of the mean). This model was then used to predict the surface tensions for 20 compounds not used in model development. 

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