Page 1

Computation of Octanol-Water Partition Coefficients by Guiding an Additive Model

with Knowledge

Tiejun Cheng, Yuan Zhao, Xun Li, Fu Lin, Yong Xu, Xinglong Zhang, Yan Li, and

Renxiao Wang*

State Key Laboratory of Bioorganic Chemistry, Shanghai Institute of Organic Chemistry,

Chinese Academy of Sciences, Shanghai, P. R. China

Luhua Lai

State Key Laboratory of Structural Chemistry of Stable and Unstable Species, College of Chemistry,

Peking University, Beijing, P. R. China

Received July 18, 2007

We have developed a new method, i.e., XLOGP3, for logP computation. XLOGP3 predicts the logP value

of a query compound by using the known logP value of a reference compound as a starting point. The

difference in the logP values of the query compound and the reference compound is then estimated by an

additive model. The additive model implemented in XLOGP3 uses a total of 87 atom/group types and two

correction factors as descriptors. It is calibrated on a training set of 8199 organic compounds with reliable

logP data through a multivariate linear regression analysis. For a given query compound, the compound

showing the highest structural similarity in the training set will be selected as the reference compound.

Structural similarity is quantified based on topological torsion descriptors. XLOGP3 has been tested along

with its predecessor, i.e., XLOGP2, as well as several popular logP methods on two independent test sets:

one contains 406 small-molecule drugs approved by the FDA and the other contains 219 oligopeptides. On

both test sets, XLOGP3 produces more accurate predictions than most of the other methods with average

unsigned errors of 0.24-0.51 units. Compared to conventional additive methods, XLOGP3 does not rely

on an extensive classification of fragments and correction factors in order to improve accuracy. It is also

able to utilize the ever-increasing experimentally measured logP data more effectively.

INTRODUCTION

Since the pioneering work of Hansch et al.,1-3the

logarithm of the partition coefficient between n-octanol and

water (logP) has been widely used in quantitative structure-

activity relationship (QSAR) studies as a parameter for

characterizing lipophilicity. These QSAR studies cover a

wide range of themes, including ligand-protein interaction,

transportation process, cellular uptake, and so on.4,5In recent

years, the role of logP has been “rediscovered” in modeling

ADMET properties. Some surveys have revealed that ap-

proximately half of the drug candidates which eventually

fail to reach market are due to unsatisfactory pharmacokinetic

properties or toxicity.6Therefore, it will help to reduce the

overall cost of drug discovery if such compounds can be

identified as early as possible. Many approaches have been

developed for evaluating ADMET properties or “druglike-

ness” based merely on the chemical structures of organic

compounds,7-9in which logP often acts as a key descriptor.

For example, among the descriptors used in Lipinski’s “rule

of five”,10only logP cannot be deduced directly from

chemical structure. Reliable computation of logP is thus

much desired especially by the high-throughput studies in

this field.

Since the 1970s, various methods for logP computation

have been proposed, which have been reviewed from time

to time.11-13Those methods can be roughly divided into two

major categories. (i) Property-based methods: They compute

logP as a function of molecular physicochemical properties,

such as molecular surfaces, volumes, dipoles, partial charges,

HOMO/LUMO energies, and others. Various topological and

electrostatic indices may also be used as descriptors. While

early methods normally employ linear equations to combine

these descriptors, more recent methods tend to employ

sophisticated statistical models, such as the associative neural

network in ALOGPS.14,15The major shortcoming of such

methods is perhaps their theoretical basis. Although it is

intuitively acceptable to assume correlation between logP

and molecular physicochemical properties, the rationale of

mixing some molecular properties in a certain combination

to compute logP is often unclear. Besides, many of these

methods are validated on relatively small sets of organic

compounds. It is unclear if they are applicable in a larger

chemical space. (ii) Additive methods: Since the physico-

chemical properties of a molecule are in principle determined

by its chemical structure, these methods use basic structural

building blocks directly as descriptors. They compute the

logP value of a given molecule by summing up the con-

tributions from all building blocks of its structure. In addition,

so-called correction factors are introduced when the results

produced by the above approach deviate significantly from

* Corresponding author phone: 86-21-54925128; e-mail: wangrx@

mail.sioc.ac.cn. Corresponding author address: Shanghai Institute of Organic

Chemistry, 354 Fenglin Road, Shanghai 200032, P. R. China.

2140

J. Chem. Inf. Model. 2007, 47, 2140-2148

10.1021/ci700257y CCC: $37.00© 2007 American Chemical Society

Published on Web 11/07/2007

Page 2

experimental values. Popular additive methods include

CLOGP,11,16ALOGP,17-19ACD/LogP,20,21KOWWIN,22,23

and KLOGP.24,25Additive methods are normally calibrated

on large data sets. They also produce more accurate results

than property-based methods according to some comparative

evaluations.26,27At present, additive methods are dominant

in practice.

We developed an additive method, called XLOGP,28about

a decade ago. The current release of this method is

XLOGP2,29which uses 90 basic atom types and 10 correc-

tions as descriptors. Along the way of developing and

applying additive methods, we have learned that such

methods have their own problems. We believe that their

fundamental problem lies in the assumption of additivity.

Additivity in logP is certainly observed on a wide range of

organic compounds, which in fact accounts for the success

of additive methods. However, additivity may fail even in

very simple cases. In order to illustrate this issue, we plot in

Figure 1 the correlation between the logP values of a series

of n-carboxylic acids and the lengths of their hydrocarbon

chains. One can see that although a unit contribution of the

methylene group can be derived from region A and B,

respectively, it is not quite possible to derive a unit

contribution of the methylene group across the entire series

of compounds. One would expect that the additivity assump-

tion is more likely to fail on more complicated structures.

Indeed, additive methods are observed to produce larger

errors on them.26,30

The second problem with conventional additive methods

is that it is unclear how they can be further improved. An

additive method relies on an extensive classification of

molecular fragments, assuming that a properly defined

fragment will have a unit contribution to logP. One possible

approach for improving additive methods is to pursue an even

more extensive classification scheme. As a matter of fact,

some current additive methods already use a large number

of fragments and correction factors, ranging from several

hundred (such as CLOGP) to several thousand (such as ACD/

LogP). An even more extensive classification of fragments,

for example, by considering remote atoms in addition to

neighboring atoms, will certainly increase the total number

of possible fragments to the next level. This will cause

technical problems since calibration of an additive method

requires a sufficient number of logP data. Available logP

data are probably not going to increase fast enough to support

this approach. In addition, given the problem in additivity

assumption mentioned above, we doubt that it will be helpful

even if this approach is practical.

In this article, we will describe a new method for logP

computation by combining a knowledge-based approach with

a conventional additive model. Our basic assumption is that

compounds with similar chemical structures have similar

properties, a strategy that has been successfully applied in

many areas.31Thus, the logP value of a given compound

can be computed more reliably from the known logP value

of an appropriate reference compound. Our method addresses

the problems in conventional additive methods and produces

more accurate results than them. Detailed descriptions of our

method will be given in the following sessions.

METHODS

Data Set Preparation. The training set used in our study

is based on Hansch’s compilation.32It provides experimen-

tally measured logP values of over 16 700 organic com-

pounds, about half of which are identified by Hansch et al.

as reliable (indicated by * or ? in their compilation). Only

those compounds with reliable logP values are considered

in our study. The chemical structure of each compound is

sketched according to its name and formula given in

Hansch’s compilation. If a compound has possible stereoi-

somers (Z/E or R/S), it is carefully sketched in the correct

isomer if such information is specified; otherwise it is

sketched in an arbitrary isomer. A number of compounds

are discarded during this process because they are either

inorganic compounds or contain undesired elements, such

as metal atoms. Three-dimensional structural models of the

remaining 8418 compounds are constructed with the Sybyl

software.33Each compound is constructed in its most

extended conformation and then optimized with the MMFF94

force field. Note that we do not attempt to obtain the lowest-

energy conformation of each compound through extensive

conformational sampling since our method actually does not

rely on three-dimensional structures in computation. All final

models are saved in Tripos Mol2 format for the convenience

of automatic processing.

Two independent test sets are also compiled. Since a

method for computing logP would better be tested on a

variety of organic compounds of pharmaceutical interests,

small-molecule organic drugs approved by the Food and

Drug Administration (FDA) of the United States are con-

sidered in our study. We download a list of such compounds

from DrugBank34and then search for their experimentally

measured logP values in Hansch’s compilation or the online

PHYSPROP database at http://www.syrres.com/esc/phys-

demo.htm. Finally, experimentally measured logP values of

a total of 406 compounds are collected, and they are

assembled as the first test set. The other test set used in our

study is designed to consist of a specific category of organic

compounds. For this purpose, we retrieve all of the oli-

gopeptides out of the 8418 compounds selected from

Hansch’s compilation, 219 in total, as the second test set.

The remaining 8418 - 219 ) 8199 compounds are used

as the training set for calibrating the atom-additive model

in our method. It also serves as the knowledge set for finding

Figure 1. Experimentally measured logP values of n-carboxylic

acids. Additivity of methylene groups is observed in region A and

B but not globally.

COMPUTATION OF OCTANOL-WATER PARTITION COEFFICIENTS

J. Chem. Inf. Model., Vol. 47, No. 6, 2007 2141

Page 3

reference compounds through similarity search (see the

descriptions below). Some additional information on the

training set and test sets used in our study is summarized in

Table 1.

Overall Strategy. The key idea of our method, called

XLOGP3, is to compute the logP of a given compound from

the known logP of a structural analog, i.e., the reference com-

pound. A conventional additive model computes logP as

where aiand Aiare the contribution and the occurrence of

the ith atom/group type in the given compound, respectively,

while cjand Cjare the contribution and the occurrence of

the jth correction factor in the given compound, respectively.

LogP of the reference compound can be computed with the

same additive model as

By subtracting eq 2 from eq 1, one gets

Equation 3 indicates how XLOGP3 computes the logP value

of a given compound by using a reference compound as a

starting point. A real example of this process is given in

Figure 2.

The compound showing the highest structural similarity

with the given compound in a knowledge set will be selected

as the reference compound. In order to avoid using an

irrelevant compound as reference, a similarity threshold of

50% is currently applied in XLOGP3. If a qualified reference

compound cannot be found in the knowledge set, the given

compound will be computed with the pure additive model

(eq 1) for instead.

Additive Model. In our study, we prefer an atom-additive

model to a group-additive model for its simplicity. An atom-

additive model is certainly easier to implement since a

molecule can be dissected into atoms without any ambiguity.

In addition, an atom-additive model, if using a properly

designed atom typing scheme, will not have the “missing

fragment” problem that a group-additive model may have.

A total of 83 basic atom types are implemented in

XLOGP3 to classify carbon, nitrogen, oxygen, sulfur,

phosphorus, and halogen atoms. The classification of a given

atom is made by considering (i) its element type, (ii) its

hybridization state, (iii) its accessibility to solvent, character-

ized by the number of attached hydrogen atoms on this atom,

(iv) the nature its direct neighboring atoms, (v) whether it is

connected to a conjugated system with π electrons, and (vi)

whether it is in a ring. Compared to what is in XLOGP2,29

this atom typing scheme has been redesigned and optimized

considerably. In addition to atom types, four terminal groups

are also included in our classification scheme. Details of this

classification scheme are summarized in the Supporting

Information.

XLOGP3 also uses two correction factors, both of which

have clear physical meanings and are found to have

significant impacts on certain classes of compounds. The first

correction factor accounts for internal hydrogen bonds, which

makes a molecule less hydrophilic than what is indicated

by its chemical structure. The second correction factor is

used on organic compounds with amino acid moieties. Under

a neutral pH condition, such a compound exists primarily in

zwitterionic form instead of neutral form and thus exhibits

a much lower apparent partition coefficient. Details of these

two correction factors are also given in the Supporting

Information.

With our new classification scheme of atom/group types

and correction factors, the total number of descriptors has

been reduced from 100 in XLOGP2 (90 atom types plus 10

correction factors) to 89 in XLOGP3 (87 atom/group types

plus 2 correction factors). For the sake of convenience, the

additive model described above will be referred to as

XLOGP3-AA throughout the rest of this article.

Similarity Search Algorithm. In our method, the refer-

ence compound is required to be a structural analog to the

given compound. The similarity between any two organic

molecules is quantified by the number of common fragments

found on their chemical structures. We adopt the so-called

topological torsion descriptor (TTD) proposed by Nilakantan

et al.35for this purpose. The topological torsion descriptor

was originally defined as a set of four consecutively

bonded non-hydrogen atoms (Figure 3), and each atom was

characterized by its type, the number of non-hydrogen

Table 1. Some Properties of the Data Sets Used in This Study

propertya

training set

N ) 8199

222.7 ((89.2)

15.0 ((5.9)

3.8 ((2.3)

test set 1

N ) 406

306.1 ((119.7) 365.0 ((86.4)

21.2 ((8.5)

5.1 ((2.8)

test set 2

N ) 219

molecular weight

no. of heavy atoms

no. of oxygen and

nitrogen atoms

logP

25.9 ((6.3)

7.9 ((1.8)

1.84 ((1.63) 1.85 ((1.99)

-0.86 ((1.18)

aNumbers outside brackets are mean values; numbers inside brackets

are standard deviations.

logP )∑

i)1

M

aiAi+∑

j)1

N

cjCj

(1)

logP0)∑

i)1

M

aiAi

0+∑

j)1

N

cjCj

0

(2)

logP ) logP0+∑

i)1

M

ai(Ai- Ai

0) +∑

j)1

N

cj(Cj- Cj

0) (3)

Figure 2. The basic computational procedure of XLOGP3.

Figure 3. Topological torsion descriptors in 3-ethylfuran.

2142 J. Chem. Inf. Model., Vol. 47, No. 6, 2007

CHENG ET AL.

Page 4

branches attached to it, and its number of π electron pairs.

In our study, we have extended the concept of topological

torsion descriptor by characterizing each component atom

with its XLOGP3 atom type so that more structural details

are encoded implicitly. All possible topological torsion

descriptors in a given structure are generated and recorded.

The similarity score SimABbetween two molecules A and B

is then calculated as a Tanimoto coefficient36

∑

i

where TTDi

TTDj

Dk

and B. SimABranges from 0 to 1. A score of 1 indicates the

highest structural similarity between A and B.

In our method, the contribution of each topological torsion

descriptor is also regulated by an adjustable weight factor

w. By using weight factors, different topological torsion

descriptors may have different contributions to the final

similarity score, which is a popular option for computing

structural similarity.36Our past experience suggests that large

errors in computed logP values are often associated with

chemical moieties containing heteroatoms. This is under-

standable since heteroatoms are generally more electrone-

gative and polar than carbon atoms and thus play a more

important role in the interactions with solvent molecules.

Thus, it will be helpful for finding the right reference

compound in logP computation if similarity score is biased

somewhat toward heteroatom-containing moieties. In our

algorithm, the weight factor of each topological torsion

descriptor is computed as (H+4)/N, where H is the total

number of heteroatoms in its contents, and N is the total

occurrence of this descriptor in the given molecule. The

weight factor is divided by N so that repeating topological

torsion descriptors will not have exaggerated contributions.

Other logP Methods under Evaluation. Two methods

which were originally developed by us are evaluated in this

study, including XLOGP2 (the previous release of XLOGP)29

and PLOGP (a method particularly developed for computing

logP/logD values of peptides).37Other methods also evalu-

ated in this study include CLOGP,11,16HINTLOGP,38TOP-

KAT,39AlogP98,30ALOGPS,14,15and KOWWIN.22,23Among

them, CLOGP and HINTLOGP are implemented in the

Sybyl software (version 7.2); AlogP98 is implemented in

the Discovery Studio software (version 1.7); TOPKAT is

from the standalone TOPKAT package (version 6.2);

ALOGPS (version 2.1) is acquired directly from its authors;

while KOWWIN is available online for testing at http://

www.syrres.com/esc/est_kowdemo.htm. One should be aware

that different implementations of the same method may

produce somewhat different results. Therefore, the results

reported in this study are valid strictly on the implementations

indicated above.

Program Description. The XLOGP3 program is written

in the C++ language and has been tested on Unix/Linux

and Windows platforms. Besides logP, it also computes some

other basic properties required by druglikeness rules, such

Ais the ith topological torsion descriptor in A;

Bis the jth topological torsion descriptor in B; and TT

ABis the kth topological torsion descriptor common in A

as molecular weight and the number of hydrogen bond

donors and acceptors. The XLOGP3 program is available

online for testing at http://www.sioc-ccbg.ac.cn/software/

xlogp3/. The standalone release of XLOGP3 is available by

contacting the authors.

RESULTS

The Additive Model. A total of 89 descriptors are used

in XLOGP3-AA, including 87 atom/group types and two

correction factors. The contributions of all descriptors are

obtained through a multivariate linear regression analysis on

the 8199 compounds in the training set (see the Supporting

Information). The regression analysis produces a correlation

coefficient between experimental and fitted values (R2) of

0.913, a standard deviation between experimental and fitted

values (SD) of 0.48, and a Fisher value (F) of 970 (Figure

4).

In order to test the predictive power of this regression

model, an eight-fold cross-validation test is conducted. A

total of 1000 compounds are randomly selected from the

entire data set as a test set; the regression model is trained

on the remaining 7199 compounds and is subsequently

applied to the test set. The above trial is repeated for 1000

times to obtain robust statistical results. The average

outcomes out of 1000 individual trials are as follows: a

correlation coefficient between experimental and predicted

values (R2) of 0.904, a root-mean-squared error (RMSE) of

0.50, and a mean unsigned error (MUE) of 0.39. The results

from this cross-validation test are very close to the ones from

the regression analysis, indicating that XLOGP3-AA is not

an overfitted model.

It is appropriate to make a comparison of XLOGP3-AA

with XLOGP2 since the latter is also a pure additive model.

A multivariate linear regression analysis of XLOGP2 on the

training set used in this study produced the following: R2

) 0.885, SD ) 0.56, and F ) 631. It is clear that XLOGP3-

AA is a better regression model than XLOGP2. Apparently,

the refined atom typing scheme in XLOGP3-AA should

account for its improved performance over XLOGP2.

Considering that XLOGP3-AA uses fewer descriptors than

Figure 4. Experimentally measured logP values versus computed

values by XLOGP3-AA on the training set (N ) 8199, R2) 0.913,

SD ) 0.48, logPexp) 0.993 × logPcalc+ 0.024).

SimAB)

wiTTDi

AB

∑

i

wiTTDi

A+∑

j

wjTTDj

B-∑

k

wkTTDk

AB

(4)

COMPUTATION OF OCTANOL-WATER PARTITION COEFFICIENTS

J. Chem. Inf. Model., Vol. 47, No. 6, 2007 2143

Page 5

XLOGP2 (89 versus 100), its improved performance on a

large diverse set of organic compounds is inspiring.

The Full Model. The full model of XLOGP3 (eq 3) is

also applied to the entire training set. For any given

compound, its reference compound is selected among the

N-1 remaining compounds in the training set. Since a

similarity threshold of 50% is applied in XLOGP3, only 6256

compounds among all 8199 compounds in the training set,

accounting for 76.3% of the entire population, find qualified

reference compounds. Other compounds are still computed

with XLOGP3-AA. Even so, XLOGP3 still demonstrates

improved accuracy as compared to XLOGP3-AA: the

correlation coefficient (R2) between experimental and pre-

dicted values is increased from 0.911 to 0.937, while the

mean unsigned error (MUE) in prediction is reduced from

0.38 to 0.31 (Table 2 and Figure 5).

Several popular methods for logP computation, including

CLOGP, HINTLOGP, AlogP98, and ALOGPS, are also

applied to the entire training set. Their statistical results are

summarized in Table 2. The average error produced by

XLOGP3 is arguably the smallest among all methods under

test. It is encouraging to observe that in this test XLOGP3

is at least comparable to CLOGP, which is perhaps the most

popular logP algorithm. Considering that our training set is

in fact a subset of the data set used by CLOGP, the advantage

of XLOGP3 may be more obvious than what is indicated in

Table 2.

Performance on FDA-Approved Drugs. In order to

evaluate its predictive power, we have applied XLOGP3 to

the 406 FDA approved small-molecule drugs in the first test

set. This test set is challenging because its structural

complexity is greater than that of the training set (see Table

1). The logP values of these compounds also span over nearly

12 units. The scatter plot of experimentally measured logP

values versus predicted values by XLOGP3 is given in Figure

6. XLOGP3 makes reasonable predictions for most com-

pounds in this test set except for about a dozen of significant

outliers.

Statistical results produced by other logP methods in this

test set are summarized in Table 3. One can see that the

performance of XLOGP3 is considerably better than its

predecessor XLOGP2. It also outperforms some other

popular methods, such as CLOGP and TOPKAT. XLOGP3

is only second to ALOGPS with a marginally larger average

error. It should be mentioned that calibration of XLOGP3 is

completely independent of this test set, while ALOGPS uses

the PHYSPROP database40as training set, which in fact

contains all of the compounds in this test set. It is unclear

how well ALOGPS will perform if these compounds are

removed from its training set.

Performance on Oligopeptides. Our second test set

consists of 219 oligopeptides. This test set is used to validate

the predictive power of our method on a series of compounds

sharing the same structural scaffold. The statistical results

Table 2. Results of Some logP Methods on the Training Set (N )

8199)

methoda

XLOGP3

CLOGP

XLOGP3-AAd

ALOGPS

AlogP98

XLOGP2

HINTLOGP

R2

RMSEb

0.41

0.45

0.50

0.54

0.62

0.68

1.88

MUEc

0.31

0.30

0.39

0.34

0.46

0.48

1.22

0.937

0.931

0.904

0.894

0.854

0.831

0.419

aMethods are ranked by the correlation coefficients produced by

them.bRoot-mean-squared error between experimental and predicted

values.cMean unsigned error between experimental and predicted

values.dEight-fold cross-validation results.

Figure 5. Error distributions of XLOGP3 and XLOGP3-AA on

the training set.

Figure 6. Experimentally measured logP values versus predicted

values by XLOGP3 for 406 small-molecule drugs approved by the

FDA (R2) 0.872, RMSE ) 0.72, MUE ) 0.51).

Table 3. Results of Some logP Methods on 406 FDA Approved

Small-Molecule Drugs

methoda

ALOGPS

XLOGP3

XLOGP3-AA

CLOGP

TOPKAT

AlogP98

XLOGP2

KOWWIN

HINTLOGP

R2

RMSEb

0.60

0.72

0.80

0.88

0.88

0.90

0.95

1.10

1.93

MUEc

0.42

0.51

0.57

0.51

0.56

0.64

0.68

0.63

1.30

0.908

0.872

0.847

0.838

0.815

0.802

0.777

0.771

0.491

aMethods are ranked by the correlation coefficients produced by

them.bRoot-mean-squared error between experimental and predicted

values.cMean unsigned error between experimental and predicted

values.

2144 J. Chem. Inf. Model., Vol. 47, No. 6, 2007

CHENG ET AL.

Page 6

produced by XLOGP3 as well as other logP methods are

summarized in Table 4.

The correlation between experimentally measured logP

values versus predicted values by XLOGP3 on this test set

produces R2) 0.758 and MUE ) 0.55. An interesting

observation is that this performance is even worse than that

of XLOGP3-AA (R2) 0.824 and MUE ) 0.59). It should

be mentioned that there are no peptides in our training set

since we remove all of them intentionally. This result

indicates that if an irrelevant reference compound is used in

logP computation, it will not necessarily lead to an improved

prediction as compared to a pure additive model. We conduct

another test by incorporating the oligopeptides in this test

set into the training set so that XLOGP3 is able to use an

appropriate reference compound in computation. After this

treatment, XLOGP3 indeed demonstrates much improved

accuracy with R2) 0.932 and MUE ) 0.24 (Figure 7 and

Table 4). This level of accuracy is very promising and clearly

better than all of the other logP methods under our test. In

particular, XLOGP3 also outperforms PLOGP,37a method

especially developed for computing logP or logD values of

oligopeptides. The power of XLOGP3 in handling congeneric

compounds based on known knowledge is clearly demon-

strated in this test.

DISCUSSION

On the Advantages over Conventional Additive Meth-

ods. The new strategy for logP computation implemented

in XLOGP3 has some obvious advantages over conventional

additive methods. The first advantage is that it relies less on

the additivity assumption. XLOGP3 computes the logP value

of a given compound by using the known logP value of a

reference compound as a starting point. Nonadditive features,

which are presumably the primary origin of errors in logP

computation, will cancel out at least on the common

substructures between the query compound and the reference

compound (Figure 2), which will result in a reduced error.

One would expect that the assumption of additivity tends to

fail on complex molecules. In Figure 8, we plot the average

errors of XLOGP3, XLOGP3-AA, and CLOGP on our

training set as a function of molecular size. One can see that

additive methods, i.e., XLOGP3-AA and CLOGP, generally

produce larger errors on larger molecules. In contrast, the

accuracy of XLOGP3 is not very sensitive to molecular size,

which justifies our statement above.

The improved performance of our strategy can also be

explained conceptually as the following. According to

XLOGP3

where X and Y denote the query compound and the reference

compound, respectively, and AA represents a pure additive

model, e.g., XLOGP3-AA. The above equation can be

rewritten as

Thus, the absolute error of XLOGP3 on X is

Table 4. Results of Some logP Methods on 219 Oligopeptides

methoda

XLOGP3d

PLOGP

XLOGP3-AA

ALOGPS

XLOGP3e

TOPKAT

CLOGP

AlogP98

XLOGP2

KOWWIN

HINTLOGP

R2

RMSEb

0.32

0.46

0.72

0.73

0.71

0.74

0.97

2.07

2.24

2.18

2.92

MUEc

0.24

0.28

0.59

0.54

0.55

0.43

0.75

1.62

1.78

1.70

2.34

0.932

0.832

0.824

0.765

0.758

0.706

0.536

0.086

0.078

0.075

0.007

aMethods are ranked by the correlation coefficients produced by

them.bRoot-mean-squared error between experimental and predicted

values.cMean unsigned error between experimental and predicted

values.dWhen peptides are included in the knowledge set.eWhen

peptides are not included in the knowledge set.

Figure 7. Experimentally measured logP values versus predicted

values by XLOGP3 for 219 oligopeptides (R2) 0.932, RMSE )

0.32, MUE ) 0.24).

Figure 8. Average errors as a function of molecular size observed

on the training set.

logPcalc

X(XLOGP3) )

logPexp

Y

+ logPcalc

X(AA) - logPcalc

Y(AA) (5)

logPcalc

X(XLOGP3) )

logPexp

Y

+ [logPexp

X

+ ∆Ecalc-exp

[logPexp

X

(AA)] -

+ ∆Ecalc-exp

YY

(AA)] )

logPexp

X

+ ∆Ecalc-exp

X

(AA) - ∆Ecalc-exp

Y

(AA) (6)

logPcalc

X(XLOGP3) -

logPexp

X

) ∆Ecalc-exp

X

(AA) - ∆Ecalc-exp

Y

(AA) (7)

COMPUTATION OF OCTANOL-WATER PARTITION COEFFICIENTS

J. Chem. Inf. Model., Vol. 47, No. 6, 2007 2145

Page 7

In comparison, the absolute error of a conventional additive

model on X is

Thus, if the absolute errors produced by an additive model

on X and Y have the same sign and are also at the same

range, the absolute error of XLOGP3 (eq 7) will be smaller

than the one produced by an additive model (eq 8). It is

reasonable to expect that the above assumption is more likely

to be valid if the reference compound resembles the query

compound more closely. Currently, a similarity threshold of

50% is applied in XLOGP3. This similarity threshold

certainly can be raised once a more comprehensive knowl-

edge set is available. We expect that this will help XLOGP3

make even more accurate predictions.

The second advantage of our strategy is that it does not

rely on an extensive classification of fragments and correction

factors in order to improve accuracy. The additive model in

XLOGP3 uses only 89 descriptors, a very modest number

as compared to hundreds to thousands of descriptors used

in some other additive methods. In particular, it seems to be

critical for conventional additive methods to use corrections

factors to achieve an acceptable level of accuracy. Some

correction factors have relatively clear physical meanings,

while others simply serve as “patches” when computed

values deviate significantly from experimental values. In fact,

a correction factor is always associated with a special pattern

in molecular structure. In our method, if a query compound

has such a pattern, the reference compound selected by

similarity search, ideally, should have the same pattern. If

so, the contribution of this pattern to logP will cancel out

between the query compound and the reference compound

and thus does not need to be considered explicitly using a

correction factor. This explains why our method does not

need many correction factors. Furthermore, in a conventional

additive method, a special structural pattern will draw

attention and be handled with a correction factor only if it

is observed on a good number of compounds. Otherwise,

its impact on logP will not be statistically significant in

regression analysis and thus will be neglected. In contrast,

the impact of a special structural pattern on the query

compound may be taken into account by our method even

if only one compound in the knowledge set contains this

particular pattern. From this point of view, using the known

logP value of a structural analog as reference is in principle

more effective than using correction factors.

The third advantage of our strategy is its ability of utilizing

the ever-increasing logP data more effectively. XLOGP3 can

be considered as an interpolation method. It is well-known

that the predicted values by an interpolation method will be

more accurate if a greater number of known points exist in

the solution space. The knowledge set used by the current

release of XLOGP3 includes all of the compounds in our

training set and two test sets, a total of nearly 9000 organic

compounds with known logP values. It is built as an external

module so that it can be expanded conveniently once more

logP data are available. If this knowledge set is expanded,

XLOGP3 will certainly have a better chance to find an

appropriate reference compound for a query compound, and

it in turn will lead to an improved accuracy. Experimentally

measured logP data are certainly increasing constantly.

XLOGP3 will benefit from this expansion almost in a

proportional manner. In contrast, conventional additive

methods use experimental logP data primarily for deducing

the contribution of each descriptor through regression

analyses. It is a common sense that once the size of the

training set exceeds what is enough, a regression model will

tend to converge, and its quality will not continue to improve

automatically.

Using an external knowledge set brings XLOGP3 another

appealing feature. Some researchers may maintain their in-

house collections of logP data. For understandable reasons,

such data are not always available to public. We provide

auxiliary tools in the XLOGP3 package so that the users

may process their own data sets into the format accepted by

XLOGP3 and then supply them as the knowledge set used

by XLOGP3. The importance of this feature should not be

underestimated since in-house logP data are perhaps many

times more than publicly available data. In contrast, con-

ventional additive methods are normally provided to users

as is and lack the ability of utilizing users’ in-house data.

On Other Approaches with Similar Ideas. Development

of XLOGP3 is inspired by some pioneering studies. For

example, the k-nearest neighbors algorithm (k-NN) is a

popular method for classifying objects based on the closest

training examples in a feature space, which has long been

applied to QSAR studies.41,42In XLOGP3, the so-called

reference compound is in fact the nearest neighbor of a query

compound in the structural space. A standard k-NN approach,

however, predicts the features of a new object by weighing

the corresponding features of its closest training examples,

while XLOGP3 quantifies the difference between a query

compound and its reference compound with a mathematical

model.

In the field of logP computation, some studies have

successfully applied similar ideas as ours. Two of them

should be mentioned in particular. The first one is the

“Experimental Value Adjusted (EVA)” algorithm proposed

by Meylan and Howard with their KOWWIN method.23The

basic idea is to use an analog compound with known logP

as reference, while the difference between the query com-

pound and its reference compound is computed by an

additive model. They reported that EVA produced improved

results over the pure additive KOWWIN method. Neverthe-

less, they did not describe in their publication how to choose

appropriate analog compounds in order to apply EVA. They

mentioned that “our current computer program ... requires

the user to manually select and enter the similar compound

and known logP”. The EVA algorithm is not implemented

in the online demo version of KOWWIN evaluated in our

study. It is not clear to us if the EVA algorithm has been

automated in any other releases of KOWWIN. Recently,

Sedykh and Klopman published a new method for logP

computation.25Their method also adopts the same idea as

the EVA algorithm. A major new development is that they

have provided an automatic approach for selecting an analog

to the query compound based on structural similarity. They

also reported that this new method led to improved perfor-

mance over conventional additive methods.

Our method is conceptually similar to Klopman’s method

although it is conceived independently. Both methods follow

the idea originally proposed by Meylan and Howard; both

logPcalc

X(AA) - logPexp

X

) ∆Ecalc-exp

X

(AA) (8)

2146 J. Chem. Inf. Model., Vol. 47, No. 6, 2007

CHENG ET AL.

Page 8

methods compute the similarity between two organic com-

pounds by counting the common substructures on them; and

both methods search among a large number of compounds

with known logP values for reference compounds. Neverthe-

less, our method is technically different from Klopman’s

method virtually at every aspect. Compared to Klopman’s

method, the most remarkable feature of XLOGP3 is its

simplicity. First, Klopman’s method uses 102 fragments and

36 correction factors in its additive model; while XLOGP3

only uses 87 fragments and two correction factors. As we

have discussed in this article, using a reference compound

in logP computation should make most correction factors

unnecessary. It seems that Klopman’s method has not fully

taken advantage of this feature. Second, although both

Klopman’s method and XLOGP3 decompose chemical

structures into substructures, the size of substructure itself

is an adjustable parameter in Klopman’s method; while in

XLOGP3, each substructure is formed uniformly by four

non-hydrogen atoms, i.e., a topological torsion descriptor.

Third, the training set used in Klopman’s study is carefully

selected so that every compound has at least one structural

analog under certain similarity thresholds. Selection of this

training set seems to be critical for achieving the reported

accuracy in Klopman’s study.25In our study, we emphasize

on XLOGP3’s ability of utilizing external data sets. The

knowledge set used by XLOGP3 is simply an assembly of

diverse organic compounds with known logP data. In

practice, external data sets supplied by users of XLOGP3

do not need any special editing either.

A comparative evaluation of Klopman’s method on our

test sets has not been made in our study since it is not

available to us. According to Klopman’s report, their method

produces standard deviations of 0.50-0.97 units on some

independent test sets, which are smaller than the ones

produced by CLOGP up to 0.20 units. Based on the results

obtained in our own tests (Tables 2-4), we believe that the

overall accuracy of XLOGP3 is at least comparable to that

of Klopman’s method. As for empirical methods, a simpler

method is certainly more appealing if it is able to produce

comparable results as a more sophisticated method. A simpler

method is also easier for other researchers to reproduce.

Finally, we would like to point out that the strategy

implemented in XLOGP3 can also be applied to the

computation of other physicochemical properties of organic

compounds. For example, Ralph Ku ¨hne et al. recently

reported a similar approach to the computation of water

solubility.43In fact, this strategy is in principle applicable

wherever a large quantity of experimental data has been

accumulated.

CONCLUSION

We have developed a new method for logP computation,

i.e., XLOGP3. XLOGP3 computes the logP value of a query

compound by using the known logP value of a reference

compound as a starting point. The difference between the

query compound and the reference compound is then

estimated by an additive method. This strategy has several

obvious advantages over conventional additive methods.

First, it relies less on the assumption of additivity. Second,

it in principle does not need a more and more extensive

classification of fragments and correction factors in order to

improve accuracy. Third, it is able to utilize the ever-

increasing logP data effectively. Our tests demonstrate that

XLOGP3 produces more accurate results than its predecessor

as well as some other methods. We believe that XLOGP3

and similar approaches like KOWWIN-EVA and Klopman’s

method collectively represent an inspiring direction for logP

computation.

ACKNOWLEDGMENT

The authors are grateful for the financial support from the

Chinese National Natural Science Foundation (Grant No.

20502031), the Chinese Ministry of Science and Technology

(the 863 high-tech project, Grant No. 2006AA02Z337), and

the Science and Technology Commission of Shanghai

Municipality (the Pu-Jiang Talents program, Grant No.

06PJ14115). Technical aid provided by Chunni Lu and Weiqi

Zhang at the Shanghai Institute of Organic Chemistry is also

appreciated.

Supporting Information Available: Detailed descrip-

tions of the atom/group typing scheme and correction factors

implemented in XLOGP3. This material is available free of

charge via the Internet at http://pubs.acs.org.

REFERENCES AND NOTES

(1) Hansch, C.; Fujita, T. p-σ-π Analysis. A Method for the Correlation

of Biological Activity and Chemical Structure. J. Am. Chem. Soc. 1964,

86, 1616-1626.

(2) Fujita, T.; Iwasa, J.; Hansch, C. A New Substituent Constant, π,

Derived from Partition Coefficients. J. Am. Chem. Soc. 1964, 86,

5175-5180.

(3) Leo, A. J.; Hansch, C.; Elkins, D. Partition Coefficients and their Uses.

Chem. ReV. 1971, 71, 525-616.

(4) Hansch, C.; Leo, A. Exploring QSAR, Fundamentals and Applications

in Chemistry and Biology; American Chemical Society: Washington,

DC, 1995.

(5) Leo, A. J.; Hansch, C. Role of Hydrophobic Effects in Mechanistic

QSAR. Perspect. Drug DiscoVery Des. 1999, 17, 1-25.

(6) van de Waterbeemd, H.; Grifford, E. ADMET In Silico Modelling:

Towards Prediction Paradise? Nat. ReV. Drug DiscoVery 2003, 2, 192-

204.

(7) Clark, D. E.; Grootenhuis, P. D. Progress in Computational Methods

for the Prediction of ADMET Properties. Curr. Opin. Drug DiscoVery

DeV. 2002, 5, 382-390.

(8) Beresford, A. P.; Segall, M.; Tarbit, M. H. In Silico Prediction of

ADME Properties: Are We Making Progress? Curr. Opin. Drug

DiscoVery DeV. 2004, 7, 36-42.

(9) Davis, A. M.; Riley, R. J. Predictive ADMET Studies, the Challenges

and the Opportunities. Curr. Opin. Chem. Biol. 2004, 8, 378-386.

(10) Lipinski, C. A.; Lombardo, F.; Dominy, B. W.; Feeney, P. J.

Experimental and Computational Approaches to Estimate Solubility

and Permeability in Drug Discovery and Development Settings. AdV.

Drug DeliVery ReV. 1997, 23, 3-25.

(11) Leo, A. J. Calculating logPoctfrom Structures. Chem. ReV. 1993, 93,

1281-1306.

(12) Carrupt, P. A.; Testa, B.; Gaillard, P. Computational Approaches to

Lipophilicity: Methods and Applications. In ReViews in Computational

Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; Wiley: New York,

1997; Vol. 11, pp 241-315.

(13) Eros, D.; Kovesdi, I.; Orfi, L.; Takacs-Novak, K.; Acsady, G.; Keri,

G. Reliability of logP Predictions Based on Calculated Molecular

Descriptors: A Critical Review. Curr. Med. Chem. 2002, 9, 1819-

1829.

(14) Tetko, I. V.; Tanchuk, V. Y. Application of Associative Neural

Networks for Prediction of Lipophilicity in ALOGPS 2.1 Program. J.

Chem. Inf. Comput. Sci. 2002, 42, 1136-1145.

(15) Tetko, I. V.; Bruneau, P. Application of ALOGPS to Predict 1-Octanol/

Water Distribution Coefficients, logP, and logD, of AstraZeneca In-

House Database. J. Pharm. Sci. 2004, 93, 3103-3110.

(16) Chou, J. T.; Jurs, P. C. Computer-Assisted Computation of Partition

Coefficients from Molecular Structures Using Fragment Constants.

J. Chem. Inf. Comput. Sci. 1979, 19, 172-178.

(17) Ghose, A. K.; Crippen, G. M. Structure-Directed Quantitative

Structure-Activity Relationships I. Partition Coefficients as a Measure

of Hydrophobicity. J. Comput. Chem. 1986, 7, 565-577.

COMPUTATION OF OCTANOL-WATER PARTITION COEFFICIENTS

J. Chem. Inf. Model., Vol. 47, No. 6, 2007 2147

Page 9

(18) Viswanadhan, V. N.; Ghose, A. K.; Reyankar, G. R.; Robins, R. K.

Atomic Physicochemical Parameters for Three Dimensional Structure

Directed Quantitative Structure-Activity Relationships. 4. Additional

Parameters for Hydrophobic and Dispersive Interactions and Their

Application for an Automated Superposition of Certain Naturally

Occurring Nucleoside Antibiotics. J. Chem. Inf. Comput. Sci. 1989,

29, 163-172.

(19) Wildman, S. A.; Crippen, G. M. Prediction of Physicochemical

Parameters by Atomic Contributions. J. Chem. Inf. Comput. Sci. 1999,

39, 868-873.

(20) Petrauskas, A. A.; Kolovanov, E. A. ACD/LogP Method Description.

Perspect. Drug DiscoVery Des. 2000, 19, 99-116.

(21) Walker, M. J. Training ACD/LogP with Experimental Data. QSAR

Comb. Sci. 2004, 23, 515-520.

(22) Meylan, W. M.; Howard, P. H. Atom/Fragment Contribution Method

for Estimating Octanol-Water Partition Coefficients. J. Pharm. Sci.

1995, 84, 83-92.

(23) Meylan, W. M.; Howard, P. H. Estimating logP with Atom/Fragments

and Water Solubility with logP. Perspect. Drug DiscoVery Des. 2000,

19, 67-84.

(24) Zhu, H.; Sedykh, A.; Chakravarti, S. K.; Klopman, G. A New Group

Contribution Approach to the Calculation of LogP. Curr. Comput.-

Aided Drug Des. 2005, 1, 3-9.

(25) Sedykn, A. Y.; Klopman, G. A Structural Analogue Approach to the

Prediction of the Octanol-Water Partition Coefficient. J. Chem. Inf.

Model. 2006, 46, 1598-1603.

(26) Viswanadhan, V. N.; Ghose, A. K.; Wendoloski, J. J. Estimating

Aqueous Solvation and Lipophilicity of Small Organic Molecules: A

Comparative Overview of Atom/Group Contribution Methods. Per-

spect. Drug DiscoVery Des. 2000, 19, 85-98.

(27) Mannhold, R.; Petrauskas, A. Substructure versus Whole-molecule

Approaches for Calculating LogP. QSAR Comb. Sci. 2003, 22, 466-

475.

(28) Wang, R.; Fu, Y.; Lai, L. A New Atom-Additive Method for

Calculating Partition Coefficients. J. Chem. Inf. Comput. Sci. 1997,

37, 615-621.

(29) Wang, R.; Gao, Y.; Lai, L. Calculating Partition Coefficient by Atom-

additive Method. Perspect. Drug DiscoVery Des. 2000, 19, 47-66.

(30) Ghose, A. K.; Viswanadhan, V. N.; Wendoloski, J. J. Prediction of

Hydrophobic (Lipophilic) Properties of Small Organic Molecules

Using Fragmental Methods: An Analysis of ALOGP and CLOGP

Methods. J. Phys. Chem. A 1998, 102, 3762-3772.

(31) Johnson, M. A.; Maggiora, G. M. Concepts and Applications of

Molecular Similarity; Wiley: New York, 1990.

(32) Hansch, C.; Leo, A.; Hoekman, D. Exploring QSAR, Hydrophobic

Electronic and Steric Constants; American Chemical Society: Wash-

ington, DC, 1995; Vol. 2, pp 3-193.

(33) The SYBYL software (Version 7.2); Tripos Inc.: St. Louis, MO 63144,

U.S.A.

(34) Wishart, D. S.; Knox, C.; Guo, A. C.; Shrivastava, S.; Hassanali, M.;

Stothard, P.; Chang, Z.; Woolsey, J. DrugBank: A Comprehensive

Resource for In Silico Drug Discovery and Exploration. Nucleic Acids

Res. 2006, 34, D668-D672.

(35) Nilakantan, R.; Bauman, N.; Dixon, J. S.; Venkataraghavan, R.

Topological Torsion: A New Molecular Descriptor for SAR Applica-

tions. Comparison with Other Descriptors. J. Chem. Inf. Comput. Sci.

1987, 27, 82-85.

(36) Willett, P.; Barnard, J. M.; Downs, G. M. Chemical Similarity Search.

J. Chem. Inf. Comput. Sci., 1998, 38, 983-996.

(37) Tao, P.; Wang, R.; Lai, L. Calculating Partition Coefficients of Peptides

by the Addition Method. J. Mol. Model. 1999, 5, 189-195.

(38) Kellogg, G. E.; Semus, S. F.; Abraham, D. J. HINT: A New Method

of Empirical Hydrophobic Field Calculation for CoMFA. J. Comput.-

Aided Mol. Des. 1991, 5, 545-552.

(39) Gombar, V. K.; Enslein, K. Assessment of n-octanol/water Partition

Coefficient: When Is the Assessment Reliable? J. Chem. Inf. Comput.

Sci. 1996, 36, 1127-1134.

(40) Physical/Chemical Property Database (PHYSPROP); SRC Environ-

mental Science Center: Syracuse, NY, 1994.

(41) Itskowitz, P.; Tropsha, A. k Nearest Neighbors QSAR Modeling as a

Variational Problem: Theory and Applications. J. Chem. Inf. Model.

2005, 45, 777-785.

(42) Ajmani, S.; Jadhav, K.; Kulkarni, S. A. Three-Dimensional QSAR

Using the k-Nearest Neighbor Method and Its Interpretation. J. Chem.

Inf. Model. 2006, 46, 24-31.

(43) Ku ¨hne, R.; Ebert, R. U.; Schu ¨u ¨rmann, G. Model Selection Based on

Structural Similarity-Method Description and Application to Water

Solubility Prediction. J. Chem. Inf. Model. 2006, 46, 636-641.

CI700257Y

2148 J. Chem. Inf. Model., Vol. 47, No. 6, 2007

CHENG ET AL.