Ординатура / Офтальмология / Английские материалы / Carbonic Anhydrase Its Inhibitors and Activators_Supuran, Scozzafava, Conway_2004

TABLE 5.3

Activity Data Used by Carotti et al.a to Derive QSAR for Benzenesulfonamides

a Carotti, A. et al. (1989) QSAR 8, 1–10.

TABLE 5.4

Activities of the Group of Benzenesulfonamides Studied by DeBenedetti et al.a

a DeBenedetti et al. (1985) QSAR 4, 23–28.

Copyright © 2004 CRC Press, LLC

TABLE 5.5

Sulfanilamide Schiff’s Bases Studied by Supuran and Clarea

a Supuran, C.T., and Clare, B.W. (1998) European Journal of Medicinal Chemistry 33, 489–500.

Copyright © 2004 CRC Press, LLC

Values of pKa for the sulfonamide group calculated by the Pallas software were also included. They derived the following equation for CA II:

− log Kii = 0.0651(±0.0212)Dx + 9916(±3917)QH − 6614(±(2408)QH2

+ 113.6(±21.1)(Qm + Qp ) − 4007.0(±1592.5)

(n = 35, R2 = 0.854, s = 0.274, F = 27.5)

where Dx is the component of the dipole moment in the direction of the benzene carbon–sulfur bond, QH the charge on the sulfonamide protons, Ip an indicator variable related to lipophilicity, (SpE – SmE/2) the difference in electrophilic superdelocalizability between the p- and the average of the two m-atoms of the sulfanilamide benzene ring and (Qm + Qp) the sum of the ESP-determined charges on those three atoms.

For CA I, their best equation was:

− log Ki = 11.74(±3.65)QS − 1.713(±0.621)D1 − 0.1956(±0.0457) log P

(5.8)

− 1.0062(±0.1571)pKa − 172.8(±62.0)SpE − 59.07(±13.0)

(n = 35, R2 = 0.762, s = 0.218)

where QS is the charge on the sulfonamide S, Dl the local dipole index (a measure of separation of charge), log P the lipophilicity calculated by the program ClogP, pKa the dissociation constant of the sulfonamide protons and SpE the electrophilic superdelocalizability of the p-carbon of the sulfanilamide benzene ring.

Clare and Supuran (1999) reported in an AM1 study of a series of 1,3- and 1,4- benzenedisulfonamides (Table 5.6) of the forms RSO2NHC6H4SO2NH2 (m and p), RSO2NHCH2C6H4SO2NH2 and RSO2NHCH2CH2C6H4SO2NH2 (both p) with one primary sulfonamide the QSARs for the inhibition of CA I, CA II and CA IV. For CA I, they obtained:

− 0.299(±0.108)EH − 0.600(±0.145)EL + 2.12 ∞10−3 (−1.14 ∞10−3 )Πyy

+ 0.0209(±0.0088) HS − 3.13(±0.96)QC + 10.30(±5.58)

(n = 72, R2 = 0.619, s = 0.22)

where QS is the charge on the primary sulfonamide S; QH the charge on the secondary sulfonamide H; EH and EL are the energies of the HOMO and LUMO, respectively;

Copyright © 2004 CRC Press, LLC

TABLE 5.6

Benzenedisulfonamides Studied by Clare and Supurana

Copyright © 2004 CRC Press, LLC

TABLE 5.6 (continued)

Benzenedisulfonamides Studied by Clare and Supurana

SO2NH2 SO2NH2 SO2NH2 SO2NH2

Copyright © 2004 CRC Press, LLC

TABLE 5.6 (continued)

Benzenedisulfonamides Studied by Clare and Supurana

SO2NH2 SO2NH2 SO2NH2 SO2NH2

a Clare, B.W., and Supuran, C.T. (1999) European Journal of Medicinal Chemistry 34, 463–474. With permission from Elsevier.

Πyy is the intermediate diagonal component of the polarization tensor; HS the calculated solvation energy; and QC the charge on the carbon atom bound to the primary sulfonamide S.

For CA II they obtained:

− log IC50 = −2.63 ∞ 10−3(±1.34 ∞10−3 )Πyy − 3.67 ∞10−3(±1.23∞10−3 )Πzz (5.10)

−0.0239(±0.0117)μ − 0.644(±0.173)EL + 0.115(±0.046)log P

+4.16(±1.14)QO + 0.592(±0.095)I3 + 7.50(±2.26)

(n = 72, R2 = 0.682, s = 0.24)

where Πzz is the diagonal component of the polarizability tensor along the axis of highest inertia, μ the magnitude of the dipole moment, log P the lipophilicity calculated by ClogP, QO the sum of the charges on the secondary sulfonamide oxygens and I3 is 1 if there are two carbon atoms between the secondary SO2NH group and the primary benzenesulfonamide ring (rather than 1 or 0) and 0 otherwise.

Copyright © 2004 CRC Press, LLC

+0.921(±0.367)D1 + 0.184(±0.060) log P + 2.885(1.108)QO

+0.35(±0.101)I3 − 0.45(±2.16)

(n = 72, R2 = 0.661, s = 0.25)

where QN is the charge on the secondary sulfonamide N and the other symbols are as defined for Equation 5.9 and Equation 5.10. Equation 5.9 to Equation 5.11 benefit from having a large number of compounds studied.

5.2.2 STERIC EFFECTS, AREA, VOLUME AND POLARIZABILITY

The area and volume of molecules tend to correlate so closely that usually only one can enter a QSAR equation without introducing unacceptable collinearity. Polarizability, either as the tensor components or as their average, also correlates with size but not so strongly so as to preclude the use of both. Equation 5.5 presents a correlation with the Sterimol parameters obtained by Carotti et al. (1989), and Equations 5.9 and 5.10 correlations with components of the polarizability obtained by Clare and Supuran (1999).

5.2.3 LIPOPHILICITY

As with most other groups of drugs, lipophilicity enters the QSAR for CA inhibitors if a sufficiently large variety of drugs is examined. Thus, the results of Kakeya et al. (1969a, 1969b, 1969c, 1970) and Hansch et al. (1985) cited in Equations 5.2 and 5.3 involve lipophilicity, with higher lipophilicity favoring activity, and similarly in the work of Carotti et al. (1989) in Equations 5.4 and 5.5. Lipophilicity also plays a part in the more elaborate equations derived by Clare and Supuran (Clare and Supuran 1999; Supuran and Clare 1998) as shown in Equations 5.8, 5.10 and 5.11. Table 5.7 presents a study of the 4-, 5- and 6-substituted 1,3-benzenedisulfonamide inhibitors of chloroform CA (a mixture of CA I and CA II). Kishida and Manabee (1980) used only the substituent π values to explain activity. They gave the following equation:

–log IC50 = –0.2125π4 – 2.1814π5 + 2.8731(π6 – 0.6193)2 + 0.5674 (5.12)

(R = 0.9486, n = 19, F = 50.9414)

This obviously cannot be valid, as it treats the equivalent 4- and 6-positions differently. Altomare et al. (1991a) determined the lipophilicities of a number of benzene-

sulfonamide inhibitors of BCA B (Table 5.3) and gave the following equation:

Copyright © 2004 CRC Press, LLC

TABLE 5.7

Activities and Structures of Disulfonamides Studied by Kishida and Manabea

SO2NH2

R3

a Kishida, K., and Manabe, R.

(1980) Medical Journal of the Osaka

University 30, 95–100.

log 1/Ki = 0.91(±0.32)σ + 0.72(±0.15)π*ODP – 0.35(±0.11)B5,3 + 6.08(±0.23)

where π*ODP is the new, chromatographically determined hydrophobic substituent constant. This equation is based on the same data as, and is comparable to, that in Equation 5.5.

Copyright © 2004 CRC Press, LLC

Altomare et al. (1991b) used chromatographic octanol–water and chloro-

form–water distribution coefficients to obtain the difference, log Poct–chf, which is a measure of hydrogen bond donor capacity of the substance. They derived for the

series of benzenesulfonamide inhibitors of BCA B, of a subset given in Table 5.3, the following equation:

(n = 19, R = 0.89, s = 0.305)

5.2.4 QUANTUM MEASURES OTHER THAN CHARGE

Frontier orbital energies were recognized early as predictors of CA inhibitory activity. The energies of the HOMO and LUMO are always to be considered as potential candidates for descriptors in QSAR, especially with aromatic compounds, and have been found to correlate with CA inhibitory activity in benzenesulfonamide derivatives. Thus, DeBenedetti and Menziani (1985) studied the series of 25 substituted benzenesulfonamide inhibitors of human CA II (Table 5.4), using the CNDO/2 semiempirical method and found for the neutral form the following relationship:

(n = 23, r = 0.907, s = 0.278, F = 96.95)

and for the anion:

(n = 23, r = 0.928, s = 0.244, F = 131.0)

A novel correlate of CA inhibitory activity in benzene derivatives, only recently detected, is the direction of the nodes in certain near-frontier, π-like orbitals (Clare and Supuran 2001). These orbitals can be regarded as arising from the degenerate HOMO and LUMO of benzene, and the resultant splitting of energy is also implicated in the nonbonded interaction between the ligand and some aromatic residue in the enzyme. It is clear that if two π-like orbitals, one on the ligand and one on the enzyme, are to interact, a requirement is that nodes in the orbitals largely coincide. We have a procedure to approximately quantify this coincidence. For human CA II:

− log KI = −18.75(±17.44)QN − 3.252(±1.381)D1 + 0.2485(±0.1854) cos 2ΦH

Copyright © 2004 CRC Press, LLC

where QN is the charge on the sulfonamide N, Dl the local dipole index and ΦH the angle the node in the HOMO makes with the sulfonamide group at the center of the benzene ring. The numbers in parentheses are the 95% confidence limits.

A quantum measure that attempts a comprehensive description of molecules is quantum similarity. This generates between each pair of compounds numbers analogous to correlation coefficients. Thus, for property P(x,y,z) of drugs i and j, which are functions of the spatial coordinates x, y and z, a similarity measure can be defined, for example:

ρi,j = Pi Pjdr Pi2 dr Pj2 dr

where the integration is over all space and the two molecules are aligned to maximize ρ2. The property P can be any spatial property of the molecule, such as electron density, an orbital magnitude or electrostatic potential, and the similarity measure is analogous to a Pearson correlation coefficient. The electron density is a property of special interest. It is tedious to compute any of these quantities as it requires optimization of both conformation and alignment.

Amat and Carbo-Dorca (1999) have applied the concept of self-similarity, defined as ZAA = ρA (r) 2 dr, where ρA is the electron density, which avoids this problem, to CA inhibitors. Self-similarities can be substituted for classical descriptors such as Hansch π or Hammett σ. They treated the data of Hansch et al. (1985) and obtained the interesting equation, free from indicator variables, for inhibition of human CA C (now designated CA II):

(n = 29, R2 = 0.984, Q2 = 0.976)

Note that Equation 24 in Amat and Carbo-Dorca (1999) appears to have been misprinted. Here, the scaled self-similarity θAA splits into contributions from fragments. The correlation indicates the splitting of SO2NH2 into two subfragments SO2 and NH2, suggesting that the SO2NH2 binds at two points: the SO2 oxygen and the NH2 hydrogen. Such calculations can throw light on the details of the mechanism of drug activity.

5.2.5 TOPOLOGICAL INDICES

Although topological and graph theoretical indices are very difficult to interpret physically they can be good predictors of activity, and compared to quantum theoretical indices they are very quick and easy to calculate. These two kinds of descriptors should not be regarded as mutually exclusive, but the topological indices can be applied on large data sets, perhaps derived from combinatorial synthesis and high throughput screening, to select data sets for more laborious methods, which give fits of comparable quality but those that are much more interpretable.

Copyright © 2004 CRC Press, LLC