┞Quantitative Structure-Activity

Relationships : QSAR

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Hammett Equation Hammett Equation ((I)I)

log (kX/kH) ∝ log(KX/KH) = ρσ

log kX = ρσ + log kH

Hammett

m-, p-X-substituted benzoic acids (25o, in water ): KX

O

O H

O

H

H

O

O

O

H

HX

H

X

+

-

+ +

KA

Substituent effect = log(KX/KH) = log KX - log KH = σX

X σX

SubstiSubsti tuent tuent Constant Constant σσ

log kX = ρσ + log kH

Sign of ρ Rate increased by

+−

Electron withdrawalElectron donation

ρ: Reaction constant (slope of a Hammett plot)

Hammett Hammett Equation (II-1) (II-1)

Hydrolysis of ethyl benzoates

COOCH2CH3

X

Physical Organic Chemistry, Ed: Neil Isaacs,John Wiley & Sons, Inc., New York, 1995(Hammett 則), p. 150, Fig. 4.2

Hammett Equation (II-2)Hammett Equation (II-2)Basic hydrolysis of ethyl benzoates COOCH2CH3

X

log k = 2.25 σ - 1.28n = 18 s = 0.11 r2 = 0.99

88% EtOH, 25Υ

Basic hydrolysis of X-C6H5-CONH2

log k = 1.84 σ - 1.54n = 5 s = 0.16 r2 = 0.96

60% EtOH, 82Υ

Basic hydrolysis of X-C6H5-COCl

log k = 1.78 σ - 4.20n = 5 s = 0.11 r2 = 0.98

95% acetone, 25Υ

Hammett Equation (IIIHammett Equation (III))

ratedeterminingstep:k1

ratedeterminingstep:k2

NCHPh

HN

CHPhNH2

Y Y Y

H+

H2O+ PhCHO

k1 k2

+

Change in RateDetermining Step

Physical Organic Chemistry, Ed: Neil Isaacs, John Wiley &Sons, Inc., New York, 1995 (Hammett 則), p. 165, Fig. 4.6

Hammett Equation (IVHammett Equation (IV))Change in Mechanism

N Me

NO

+ H+NH Me

NOY Y

N Me

NOY

N Me

NOY

Physical Organic Chemistry, Ed: Neil Isaacs, John Wiley &Sons, Inc., New York, 1995 (Hammett 則), p. 164, Fig. 4.5

Classical QSARHansch-Fujita

Corwin HanschPomona College

CA, USA

ヽ

log (1/C) =　a (log P)2 + b log P　+ ρσ + δEs + const.

C: etc.)a, b, ρ, δ:

Linear Free Energy Relationships: LFER

log P: σ: 電子的パラメーターEs: 立体パラメーター

QSAR40 オ 2004 Celebrating the 40th anniversary

of the first QSAR article

•“ρ−σ−π Analysis. A Method for theCorrelation of

Biological Activity and Chemical Structure”By Corwin Hansch and Toshio Fujita

J. Am. Chem. Soc., 1964, 86, 1616-1626.

EuroQSAR2004, Istanbul, Turkey

QSARQSAR

log P π

σ Hammett , σ-, σ+, σ0

σI, σR F, R MO (Molecular Orbital)

Es（Taft ） Es

c, Es(AMD) B1, B5, L…（STERIMOL ） MR Molecular RefractivityMolecular connectivity (χ)

Iσp, σm [ Benzoic acid dissociations: 25o, in water]

σp = σI + σR

σ0 [Phenyl acetate ester hydrolysis or Phenylacetic acid dissociations]

σm = σI + α σR

σI : Inductive componentσR: Resonance component

CH2 COOR

X

IIσp, σm [ Benzoic acid dissociations: 25o, in water]

Swain-Lupton の F, RF: Field (+ inductive) effect R: Resonance effect

σp = αF + R

σo = σp（但し，Field effectを考慮する必要がある）

X

Y

IIIσ+ [ Cumyl chlorides solvolysis]σ− [ Phenol or aniline dissociations] Cl

X

OH

NO2 (X)

CH3C CH3

X

O

NO2OO

N

O

X

C(CH3)2

+

solvolysis

cumyl chlorides

+

-

-

+

phenols

-

!+

!-

X: OCH3, NH2, etc.

X: NO2, CN, etc.

CH3H3C

IVMO (Molecular Orbital)

*q: Charge calculated by MO methods on an atomσ of m-, p-substituted benzoic acids

σ = 29.16 [q(=O) + q(-O-) + q(H)] + 12.68n = 27 s = 0.08 r2 = 0.94

C

X

O

OH

(The q values were calculated by AM1)Sotomatsu et al., J. Comp. Chem., 10,94, 1989

∗εHOMO, εLUMO: Energy of HOMO and LUMOHOMO: Highest Occupied Molecular OrbitalLUMO: Lowest Unoccupied Molecular Orbital

Application of Hammett EquationApplication of Hammett EquationSN2 substitution

log k = -2.36 σ - 3.23 n = 31 s = 0.14 r2 = 0.94

N + BrCH2CH=CH2

X

CH3

CH3

N

X

CH2CH=CH2

CH3

CH2

+ Br-

X

+ E+

X+

H EE

X

Electrophilic substitution

log krel = -6.22 σ+ - 0.08 n = 12 s = 0.32 r2 = 0.96X-C6H5 + HNO3 X-C6H4-NO2

I Es: Steric constants by Taft Es = log (kX

A/kHA)

Kutter-Hansch

Es = arv + const.rv: van der Waals

XCH2

O

OR H+

H2O

XCH2 C

OH

OR

O

H H

+

kA

XCH2COOH + ROH

立体パラメーター (II)

E's: Steric constants by Dubois et al.

Esc : Steric constants by Hancock

Esc = Es + 0.306 (nH - 3)

[nH: Number of α-hydrogens]Es(AMD)：Steric constants by Sotomatsu-Fujita

よフ

CONH2

X

B1, B5, L…STERIMOL

MR

III STERIMOL

B1 ㍂L ㍂

B5 ㍂

L

B

L B3 B2

B4

B1

薬物の構造活性相関，ドラッグデザインと作用機作研究への指針，化学の領域，増刊122号，構造活性相関懇話会編集，南江堂，1979年（絶版）. 1, p. 140, 4

IV

MR

MR = πN αn2-1n2+2

Md

43=

n: M: d: N: Avogadro

VMolecular connectivity (χ): Kier

topological ㈻

Kier et al., J. Pharm. Sci., 64, 1971 (1975)薬物の構造活性相関，ドラッグデザインと作用機作研究への指針，化学の領域，増刊122号，構造活性相関懇話会編集，南江堂，1979年（絶版）, p. 151, 6

Subst. Es Es(AMD) B1 B5 L p m p 0 I p

p + F R

H 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Me -1.24 -1.16 0.52 1.04 0.81 -0.17 -0.07 -0.12 -0.01 -0.17 -0.31 0.01 -0.18 Et -1.31 -1.33 0.52 2.17 2.05 -0.15 -0.07 -0.13 -0.01 -0.19 -0.30 0.00 -0.15 n-Pr -1.60 -1.62 0.52 2.49 2.86 -0.13 -0.06 - -0.01 -0.06 -0.29 0.01 -0.14 n-Bu -1.63 -1.64 0.52 3.54 4.11 -0.16 -0.08 - -0.01 - - -0.01 -0.15 i-Bu -2.17 - 0.52 3.45 2.86 -0.12 -0.07 - -0.01 - - -0.01 -0.11 t-Bu -2.78 - 1.60 2.17 2.05 -0.20 -0.10 -0.17 -0.01 -0.13 -0.26 -0.02 -0.18 CH=CH2 -2.84 - 0.60 2.09 2.23 -0.04 0.06 - 0.11 - -0.16 0.13 -0.17 F -0.46 -0.32 0.35 0.35 0.59 0.06 0.34 0.17 0.54 -0.03 -0.07 0.45 -0.39 Cl -0.97 -0.98 0.80 0.80 1.46 0.23 0.37 0.27 0.47 0.19 0.11 0.42 -0.19 Br -1.16 -1.12 0.95 0.95 1.76 0.23 0.39 0.26 0.47 0.25 0.15 0.45 -0.22 I -1.40 -1.44 1.15 1.15 2.17 0.18 0.35 0.27 0.40 0.27 0.14 0.42 -0.24 OH -0.55 - 0.35 0.93 0.68 -0.37 0.12 -0.13 0.24 -0.37 -0.92 0.33 -0.70 NO2 -1.01

-2.52 -1.65 0.70 1.44 1.38 0.78 0.71 0.82 0.67 1.27 0.79 0.65 0.13

NH2 -0.61 - 0.35 0.97 0.72 -0.66 -0.16 -0.38 0.17 -0.15 -1.30 0.08 -0.74 OMe -0.55 -0.40 0.35 2.07 1.92 -0.27 0.12 -0.16 0.30 -0.26 -0.78 0.29 -0.56 CF3 -2.40 -2.46 0.99 1.61 1.24 0.54 0.43 0.53 0.40 0.65 0.61 0.38 0.16

P

πx = log Px - log PH

P = Co/Cw

log P:

Co, Cw:

πx

1. ┞

122 ┞ リ

1979 ∟

2. Exploring QSAR, Fundamentals and Applications inChemistry and Biology, Eds: Corwin Hansch and AlbertLeo, ACS Professional Reference Book, American ChemicalSociety, Washington, DC, 1995

3. Physical Organic Chemistry, Ed: Neil Isaacs, John Wiley &Sons, Inc., New York, 1995 (Hammett )