Minimal topological difference method

The molecular size and shape descriptors may indicate if a ligand molecule, L, does not fit the active site. Unfortunately, in many cases the receptor site cannot be described in simple terms of large , width , and depth . The MTD (minimal topologic difference) method allows a receptor site mapping in the frame of a series of bioactive compounds. The MVD (minimal volume difference) method is an improved variant of the MTD method, which takes into account the 3D extension of a molecule. These two methods are described here in some detail. The results obtained in the study of anti-carcinogenic activity of some retinoids and in the inhibition of carbonic-anhydrase (CA) by a series of sulfonamides are also presented in this chapter. 

The importance of molecular stereochemistry for biological activity was recognized 100 years ago, by Emil Fisher, with his lock and key theory for enzymatic reactions (Motoc 1983). The steric fit of dmg molecule (L-ligand) with its target (usually, receptor, R) depends upon both the shape of the biological receptor and the shape of ligand molecule. MTD (minimal topological difference) method takes into... 

Other approaches to expressing topological differences include treating the problem of directionality of steric effects by the direct expedient of modeling a substituent and calculating its extension in five orthogonal directions (e.g., the minimal steric difference method, [289]). Other approaches [111-115,290-295]... 

The Minimal Topological Difference (abbreviated as MTD) method denotes 16<0 a hypermolecule optimization procedure based on the MSD parameter. Actually, MTD is the MSD parameter calculated 17 19) against a hypermolecule as standard. 

Methods for evaluating the steric misfit are minimal topological difference and -+ molecular shape analysis. 

Results from CoMFA studies have been compared with those from Hansch analyses [38, 1019 — 1023] and the minimal topological difference (MTD) method [1024]. Examples for the comparison of Hansch equations with CoMFA studies are e.g. the papain hydrolysis of N-(X-benzoyl)glycine pyridyl esters (60) (eqs. 204, 205 Zn = PLS component n of the corresponding field compare chapter 7.1) [1019, 1020], the emulsin-catalyzed hydrolysis of phenyl-P-D-glucosides [1020], the mutagenic activities of substituted (o-phenylenediamine)platinum dichlorides [1020], dihydrofolate reductase (DHFR) inhibition [1020], and some other biological activities [38, 1021—1023]. 

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). 

FIGURE2.21 Generic worldofthequantitativestrocture-activity/property relationships-QSA(P)R - through classical, 3D, decisional and orthogonal methods of multivariate analysis of the chemical-biological interactions. In scheme, MSD-MTD, CoMFA, and PCA stand for the minimal steric difference-minimal topological difference , comparative molecular field analysis and principal component analysis , respectively after (Putz Lacrama, 2007). 

The three versions of the minimal steric difference method for evaluation of steric effects are described in Chapters 4,5 and 6. Topological indices derived in the framework of chemical graph theory are discussed in Chapter 3, Good results obtained in the study of octane numbers for alkanes justify the attentive investigation of the possibilities of topological indices for QSAR-studies, Up to now, only the Randici index was studied in this respect (see refs, quoted in Chap.3),... 

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. 

The Monte Carlo version of minimal steric difference (denoted as MCD) improves the computation of non-overlapping volumes in the standard-ligand superposition, translating thus the topological MSD parameter into the (3D) metric context (Mojoc et al. 1975 Ciubotariu et al. 1983). In order to calculate the MCD, the molecules are described by the Cartesian coordinates and vdW radii of their atoms. The atomic coordinates implicitly specify the way one achieves the superposition all molecules of the series are represented in the same Cartesian coordinate system. The mathematical method used in the MCD-technique for computation of nonoverlapping volumes is the Monte Carlo method (Demidovich and Maron 1987). 

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]. 

---