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     ...Introduction

Definition of Log D Property Data

Log D is the ratio of the equilibrium concentrations of all species (unionized and ionized) of a molecule in octanol to same species in the water phase at a given temperature, normally 25° C. It differs from LogP in that ionized species are considered as well as the neutral form of the molecule.


LogD is defined as:

- where the sum is over all species and  the subscripts oct and aq stand for the octanol and water phase respectively.

Log D Lipophilicity Profile

The lipophilicity profile becomes quite complex, even for diprotic compounds. Here we examine a monoprotic base and acid-base-ampholyte to explain how LogD is computed in these two cases from 14 cases handled in CSLogD.


Simple base:

The basic equilibrium expression is:  HX+  =  Xo + H+ ...which exists in two phases.

The equilibrium dissociation constant, k2 for the octanol phase is commonly known as the ”Scherrer pKa” or “limiting pKa” is not necessary to evaluate.  P3 and P4 are partition coefficients with logP3 = logP and P4 for the protonated base. LogD can be expressed with use of P3, P4, and k1 as:

The rather straight forward form for logD does not take into consideration ion-pairing, which occur with counterions present (1, 2).  Further, partition coefficients for ionized species have to be estimated since they are rarely available in reported logD measurements. In CSLogD the partition coefficients of ionized species are estimated from a fit to a series of observed values for partition coefficients for both anionic and cationic species.


(1). A. Avdeef (1992) Quant.Struct.-Act. Relat. 11, 510; (2).R. Scherrer (2001) “Biolipid pKa Values and the Lipophilicity of Ampholytes and Ion Pairs” in Pharmacokinetic Optimization in Drug Research, Eds. B. Testa, H. van de Waterbeemd, G. Folkers, and R. Guy, Publ. Wily-VCH

Ampholyte:  Acid-Base or Base-Acid

LogD can be expressed in a general form for ampholytes. The largest class covered by CSLogD is for tri-ampholytes containing three (3) ionizable groups per organic compound.


The general expression is:

...where the P terms are partition coefficients of the species with Po having the least number of dissociated hydrogens (e.g., diprotic base, Po goes with the neutral form B, PhX with HB+, Ph2X with H2B++, and Ph3X = 0). Ao, A1, A2, and A3 are various combinations of pKa's with pH whose expressions and number depend upon the type of ampholyte in question (e.g., base-base versus acid-base-base).


Acid-Base or Base-Acid


Here there are four different species (anion, cation, zwitterion, and neutral), as shown schematically below where k1, k2, k3, k4, and kT are the microconstants

Also for the apparent dissociation constants, we have:

Using the expressions for k1, k2, k3, k4, kT, ka1, ka2, and [HX], we have for the expression for logD:

The general expression for D for AB-BA ampholyte is:

Using equations (1) - (10) with equation (12), it can be shown that D takes the form involving only aqueous species and their partition coefficients:

With the assumption that the zwitterion does not enter the octanol phase and ka1 ~ k2, expression (13), becomes:

It is this expression used within CSLogD for the case of acid-base ampholytes where Px- and Ph2x+ are calculated from a multi-linear regression model of observed values for bases and acids.  How well LogD agrees with observed drugs and drug-like compounds, please see the section entitled  CSLogD vs Experimental.

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