Parameters STERIMOL

The Kd(X) values thus obtained (Table 3) were analyzed by the multivariant technique using such parameters as n, a0, Bt, Ibmch, and Ihb, where Bj is a STERIMOL parameter showing the minimum width of substituents from an axis connecting the a-atom of the substituents and the rest of molecule, and Ibrnch, an indicator variable representing the number of branches in a substituent. 

In these equations, Dmax is the larger of the summed values of STERIMOL parameters, Bj, for the opposite pair 68). It expresses the maximum total width of substituents. The coefficients of the ct° terms in Eqs. 37 to 39 were virtually equal to that in Eq. 40. This means that the a° terms essentially represent the hydrolytic reactivity of an ester itself and are virtually independent of cyclodextrin catalysis. The catalytic effect of cyclodextrin is only involved in the Dmax term. Interestingly, the coefficient of Draax was negative in Eq. 37 and positive in Eq. 38. This fact indicates that bulky substituents at the meta position are favorable, while those at the para position unfavorable, for the rate acceleration in the (S-cyclodextrin catalysis. Similar results have been obtained for a-cyclodextrin catalysis, but not for (S-cyclodextrin catalysis, by Silipo and Hansch described above. Equation 39 suggests the existence of an optimum diameter for the proper fit of m-substituents in the cavity of a-cyclodextrin. The optimum Dmax value was estimated from Eq. 39 as 4.4 A, which is approximately equivalent to the diameter of the a-cyclodextrin cavity. The situation is shown in Fig. 8. A similar parabolic relationship would be obtained for (5-cyclodextrin catalysis, too, if the correlation analysis involved phenyl acetates with such bulky substituents that they cannot be included within the (5-cyclodextrin cavity. 

In this chapter, an attempt has been made to present a total number of 20 QSAR models (12 QSAR models for topo I inhibitors and eight QSAR models for topo II inhibitors) on 11 different heterocyclic compound series (an-thrapyrazoles, benzimidazoles, benzonaphthofurandiones, camptothecins, desoxypodophyllotoxins, isoaurostatins, naphthyridinones, phenanthridines, quinolines, quinolones, and terpenes) as well as on some miscellaneous heterocyclic compounds for their inhibition against topo I and II. They have been found to be well-correlated with a number of physicochemical and structural parameters. The conclusion, from the analysis of these 20 QSAR, has been drawn that the inhibition of topo I is largely dependent on the hydrophobicity of the compounds/substituents. On the other hand, steric parameters (molar refractivity, molar volume, and Verloop s sterimol parameters) are important for topo II inhibition. 

Table I. Comparison of Vw, MSD, MTD, MTD and STERIMOL parameters in a series of 21 DDT analogs with activity against Culex fatigans. ...

These results give some insight in the scope and limitations of the MTD, MTD and STERIMOL parameters. Let us first compare the MTD and MTD methods. In the example of the benzyl chrysanthemates the regression equations have only steric terms, sothat there is no difference between the two methods in principle. In the case of the benzoylphenyl ureas the intercorrelation between the MTD values and the other parameters is very low, so it is understandable that there is hardly any difference. But in the four other studies there was much more intercorrelation between the MTD values on the one hand and the electronic and/or hydrophobic parameters on the other hand, and in these cases the MTD method gives slightly better results. Our preliminary conclusion from the examples discussed, is that the MTD is the preferable one, both from fundamental and... 

Free-Energy-Related Background of STERIMOL Parameters.137... 

In the following years, various steric parameters have been applied to the analysis besides the Taft Es value. For instance, the Hancock corrected steric E , the Bondi molecular volume Vw, and the Verloop STERIMOL parameters have been used to rationalize various steric effects depending upon the interactions involved. At every addition of such parameters, the versatility of the approach has been expanded remarkably. The number of successful applications has been growing enormously leading to the present state of development. 

For years, we have been studying QSAR (quantitative structure-activity relationship) analyses of pesticides and other bioactive compounds. In many examples, we have found a decisive role of the steric effect in determining the activity variation. In this chapter, applications of various steric constants such as E E°, Vw and STERIMOL parameters to QSAR studies mostly from our own laboratory are reviewed. 

Fig. 6. Definition of STERIMOL parameters as for the 2-pentyl group having fully extended staggered conformation...

Fig. 8. Definition of modified STERIMOL parameters the upper is for perillartine and related oximes and the lower is for substituted anilines 521 (reproduced with permission from the American Chemical Society)...

Irrmost correlations in this review, the steric parameters are supposed to be best among others. In deriving Eq. 43 for N-phenyl tetrahydrophthalimide herbicides, STERIMOL parameters are the best ones 42). In Eq. 53 for lindane analogs, Vw works much better than MR 70). However, this does not necessarily mean that the correlations mentioned here are always finalized. Further improvement may be possible using other steric parameters. 

Verloop, A. et al. Applications of STERIMOL Parameters to Drug Design, in Steric Effects in Drug Design (eds. Motoc, I., Charton, M.) Springer, Berlin, Heidelberg, New York, 1983, p. 137... 

While the development of the Taft parameter is similar to that of Hammett and Hansch, / )-val ucs are based on rate constants instead of equilibrium constants. The Taft parameter is a measure of changes in activation energy, not standard free energy. Of the Hammett, Hansch, and Taft parameters, the Taft parameter is utilized the least in QSAR studies. Other steric parameters have been developed over time, and like the Taft parameter, all have shortcomings. One alternative steric parameter was developed by Marvin Charton of Pratt Institute in New York. Charton s parameter is based on the van der Waal radius of a substituent.6 Another alternative steric model is the STERIMOL parameter set developed by Arie Verloop of Philips-Duphar in Holland.7 Unlike Taft and Charton, Verloop... 

To characterize the substituents (the X block) a set common substituent parameters were compiled from the literature. These parameters were as (Taft inductive parameter), trp (Hammett parameter for para substituents), F and R (Swain-Lupton dual substituent parameters), Es and Esc (Taft steric parameters), van der Waals radius, L, Bv B2, B3, (Verloop sterimol parameters), MR (molar refractivity), and n (Hansch lipophilicity parameter). Data are given in Refs. [1,19] and are not reproduced here. 

The most significant term in Eq. 11 is the molar refractivity of the m-substituent at the phenyl ring. Since MR-Ri is primarily a measure of bulk and of polarizabihty of the substituent, the positive coefficients with both terms MR-Ri and CMR suggest that size of Ri-substituent as well as of the whole molecule will be conducive to the activity. The parameter Bs-r is the Sterimol parameter for the maximum-width of the first atom of the group R at the N-heterocyclic ring. This points out a favorable role of the first atom through some steric interaction. 

The major electronic factor influencing the activity has been Hammett s constant a. In some cases, the steric factors were also found to be important, e.g., Bs the Sterimol parameter for the largest width of substituents and L the Sterimol parameter for the length of the substituents. The positive coef-Acients of these parameters give an important positive contribution of width and length of substituents to the inhibition. The values of Taft steric param-... 

Equation 45 contains only molar refractivity terms for Ri and R3 substituents and the Verloop Sterimol parameters L for the length of substituent R4. The negative sign with MR-Ri suggests a steric hindrance directly or through a conformational change. MR-R2 is the most significant parameter. 

Molecular descriptors related to the dimensions of the molecule and often calculated from the - molecular geometry. Combined with molecular shape information, they are closely related to - steric descriptors. The simplest size descriptors are atom count, -> bond count, -> molecular weight, and some among the -> volume descriptors such as van der Waals volume. Other size descriptors are - Sterimol parameters and - WHIM size descriptors. 

Sterimol parameters ( Verloop Sterimol parameters Verloop parameters)... 

Verloop et al. determined the Sterimol parameters for over 1000 substituent groups. 

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