Additivity in the analysis and design of HIV protease inhibitors

Article abstract of DOI:10.1021/jm8009525

We explore the applicability of an additive treatment of substituent effects to the analysis and design of HIV protease inhibitors. Affinity data for a set of inhibitors with a common chemical framework were analyzed to provide estimates of the free energy contribution of each chemical substituent. These estimates were then used to design new inhibitors whose high affinities were confirmed by synthesis and experimental testing. Derivations of additive models by least-squares and ridge-regression methods were found to yield statistically similar results. The additivity approach was also compared with standard molecular descriptor-based QSAR; the latter was not found to provide superior predictions. Crystallographic studies of HIV protease-inhibitor complexes help explain the perhaps surprisingly high degree of substituent additivity in this system, and allow some of the additivity coefficients to be rationalized on a structural basis.

Full text of DOI:10.1021/jm8009525

J. Med. Chem. 2009, 52, 737–754
737
Additivity in the Analysis and Design of HIV Protease Inhibitors
Robert N. Jorissen,‡, G. S. Kiran Kumar Reddy,†,§,¶ Akbar Ali,†,§ Michael D. Altman,|,O Sripriya Chellappan,‡,[
Saima G. Anjum,§ Bruce Tidor, Celia A. Schiffer,# Tariq M. Rana,§,+ and Michael K. Gilson*,‡
Center for AdVanced Research in Biotechnology, UMBI, 9600 Gudelsky DriVe, RockVille, Maryland 20850,
Chemical Biology Program, Department of Biochemistry and Molecular Pharmacology, UniVersity of Massachusetts Medical School,
Worcester, Massachusetts 01605, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts,
Department of Biological Engineering and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology,
Cambridge, Massachusetts, Department of Biochemistry and Molecular Pharmacology, UniVersity of Massachusetts Medical School,
Worcester, Massachusetts 01605
ReceiVed July 28, 2008
We explore the applicability of an additive treatment of substituent effects to the analysis and design of
HIV protease inhibitors. Affinity data for a set of inhibitors with a common chemical framework were
analyzed to provide estimates of the free energy contribution of each chemical substituent. These estimates
were then used to design new inhibitors whose high affinities were confirmed by synthesis and experimental
testing. Derivations of additive models by least-squares and ridge-regression methods were found to yield
statistically similar results. The additivity approach was also compared with standard molecular descriptor-
based QSAR; the latter was not found to provide superior predictions. Crystallographic studies of HIV
protease-inhibitor complexes help explain the perhaps surprisingly high degree of substituent additivity in
this system, and allow some of the additivity coefficients to be rationalized on a structural basis.
1. Introduction
The human immunodeficiency virus (HIV), the cause of
AIDS, currently infects more 30 million people around the
world,1 and approximately 2 million people died of AIDS in
2007 alone. Current treatments include inhibiting the reverse
transcriptase and protease of HIV with small molecule drugs,
but their effectiveness can be diminished by the occurrence of
resistance mutations in the virus.2 New inhibitors of the HIV
Figure 1. Framework of HIV protease inhibitors studied in this work,
showing the three points of substitution.
reverse transcriptase and protease are thus needed that will
inhibit not only wild-type but also mutated forms of the virus’s
proteins.3,4
common chemical scaffold with three variable substituent
We have therefore sought to develop compounds that can
positions (Figure 1). These compounds form an incomplete
inhibit both wild-type and mutated forms of the HIV protease.5-8
combinatorial library, and the question arose as to whether any
The design approach is based in part upon the hypothesis that
of the unsynthesized compounds within the full library should
inhibitors that bind within a consensus envelope of bound
be expected to bind HIV protease with high affinity and might
substrate peptides are more likely to retain affinity for clinically
thus be worth synthesizing and testing.
relevant mutants.9-13 Many of the HIV protease inhibitors
In approaching this problem, it is natural to ask which are
synthesized and tested in the course of this effort possess a
the best substituents and to make sure that all combinations of
the best substituents have been tested. Such an approach
* To whom correspondence should be addressed. Phone: 240-314-6217.
implicitly relies upon an assumption of independence, i.e., that
Fax: 240-314-6255. E-mail: gilson@umbi.umd.edu.
†
a substituent which appears in a high affinity compound will
also tend to impart high affinity when combined with other
substituents to form a different compound. The present study
makes this assumption explicit through an implementation of
the Free and Wilson additivity model14 and evaluates the
accuracy of the additivity model not only retrospectively but
also prospectively by using it to select additional compounds
from within the virtual combinatorial library for synthesis and
testing. The results bear on the reliability of the additivity
approximation in the present system. In addition, methodological
variations are assessed, and the additivity approach is further-
more compared with a traditional quantitative structure-activity
relationship (QSAR) evaluation of the same data sets. The results
of the additivity analysis are also considered in the light of
existing and new crystallographic complexes of bound inhibitors
from the present series.
These authors contributed equally to this study.
Center for Advanced Research in Biotechnology, UMBI.
Chemical Biology Program, Department of Biochemistry and Molecular
‡
§
Pharmacology, University of Massachusetts Medical School.
|
Department of Chemistry, Massachusetts Institute of Technology.
Department of Biological Engineering and Department of Electrical
Engineering and Computer Science, Massachusetts Institute of Technology.
#
Department of Biochemistry and Molecular Pharmacology, University
of Massachusetts Medical School.
Current Address: Ludwig Institute for Cancer Research, P.O Royal
Melbourne Hospital, Parkville, Victoria 3050, Australia.
O
Current address: Merck Research Laboratories, Boston, 33 Avenue
Louis Pasteur, Boston, Massachusetts.
[
Current address: 6304 Summitview Avenue, Yakima, Washington
98908.
¶
Current address: Prime Organics, Inc. 25-R Olympia Avenue, Woburn,
Massachusetts 01801.
+
Current address: Sanford Children’s Health Research Center, Burnham
Institute for Medical Research, 10901 North Torrey Pines Road, La Jolla,
California 92037.
10.1021/jm8009525 CCC: $40.75
2009 American Chemical Society
Published on Web 01/07/2009

738 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
limit in the fit, use of the lower limit, and exclusion of the pKi
value from the fit. The combination that yielded the lowest sum-
squared error was chosen. Empirically, the fitted values never
came close to the arbitrary lower limit of 2, so the precise value
of this quantity is not an important parameter of the models.
The same method was used to establish pKi ranges of 11-13
for tight-binding inhibitors, as detailed in Results.
Confidence limits at the 95% level for the fitted parameters
and pKi predictions were obtained by the bootstrap sampling
procedure.15,17 This procedure consists of random selection of
molecules from the training set with replacement, such that the
total number sampled is equal to the number of molecules in
the training set. For each of 500 such bootstrap samples, a set
of substituent parameters was obtained from fitting and pKi
predictions made where applicable. Confidence limits for each
parameter and pKi prediction were obtained by determining the
range containing the middle 95% of predictions. Note that some
bootstrap samples lack data to enable fitting for some parameters
and therefore do not yield parameter values needed for some
of the pKi predictions, so there may be fewer than 500
parameters/predictions from which to calculate the relevant
confidence interval.
2. Two Methods
2.1. Data Modeling. 2.1.1. Additive Model for Affinity.
The additive model assumes that the free energy contributions
of the substituents of a given compound are independent and
additive.14 Two formulations are considered. In the first, one
compound is chosen to be the reference compound and its
substituents are the reference substituents for each of the three
positions of substitution. The additivity model is then given by:
pKi(a, b, c) ≡ -log10 Ki(a, b, c) ≈ pKi(1, 1, 1) +
S1a + S2b + S3c (1)
where pKi(a, b, c) is the predicted pKi of a compound in the
series with substituents a, b, and c at the R1, R2, and R3
positions, respectively; S1a approximates the change in pKi upon
replacing the reference substituent at R1 (a ) 1) with substituent
a, while leaving R2 and R3 unchanged, and S2b and S3c have
analogous interpretations for the R2 and R3 positions, respec-
tively. The values of S1a, S2b, and S3c are obtained by least-
squares fitting, as described below. In the second formulation,
similar to that of Free and Wilson,14 the observed pKi values
are mean-centered and scaled, i.e., linearly transformed to yield
a mean of zero and a standard deviation of one. This procedure
removes the need to specify a reference molecule or reference
substituents.
Two methods of parametrizing the additive models of affinity
were tested, ordinary least-squares regression and ridge regres-
sion (RRa). The next two subsections describe these procedures.
2.1.1.1. Fitting the Additive Model by Ordinary Least-
Squares Regression. Ordinary least-squares regression was used
to optimize the values of the substituent parameters based on
the experimental pKi data. This method fits a vector ꢀ to the
linear equation:
The statistical significance of the fit of modeled (yfit) to
measured (yobs) pKi values was assessed by calculating the
appropriate F-statistic and its corresponding p-value. Molecules
containing unique instances of their R1 substituents and their
associated R1 substituent parameters were omitted from this
analysis because their parameters could be trivially adjusted to
give a perfect fit for that molecule’s pKi value. The F-statistic
was calculated as:
(TSS - RSS)(N - M)
F )
(4)
(RSS)(M - 1)
where TSS is the total sum of squares ) ∑i (yobs,i - yobs)2, RSS
is the residual sum of squares (eq 3), N is the number of
observations (number of molecules included in the calculation
of the F-statistic), and M is the number of parameters (number
of substituent parameters included). The corresponding p-value
was obtained from the look-up table at http://graphpad.com/
quickcalcs/pvalue1.cfm with the associated numerator and
denominator degrees of freedom M and N - M - 1, respec-
tively. The calculated p-values were less than 0.0001 in all cases,
indicating high statistical significance.
The effect of changing the reference molecule was shown to
be modest. The value of any fitted parameter rarely deviated
by more than 0.25 pKi units from the median value of that
parameter obtained from systematically changing the reference
molecule to all of the training molecules in a given set. Similarly,
the values of the pKi predictions for each test set molecule were
always within 0.25 pKi units of the median predictions for that
molecule (results not shown).
y
obs ≈ yfit ) Xꢀ
(2)
such that the residual sum of squares deviations (RSS) is a
minimum.
RSS )
(yobs,i - yfit,I)2)(yobs - Xꢀ)T(yobs - Xꢀ) (3)
∑
i
The values in the column vector ꢀ correspond to all the
substituent parameters S1a, S2b, and S3c in eq 1 other than the
reference substituents; element i in the vector yobs equals the
measured value of pKi(a, b, c) - pKi(1, 1, 1) for compound i
and element i in the vector yfit is the corresponding fitted, and
the rows of the design matrix X contain ones and zeroes,
depending on whether or not a given molecule contains a given
substituent.
Least-squares fitting was performed via singular value de-
composition15 with code implemented by the authors in C and
employing an available singular value decomposition routine.16
Additional code was written to compute predicted values of pKi
from eq 1.
Four of the measured Ki values were reported experimentally
as g10 µM, corresponding to a pKi e 5. For convenience, these
inequalities were converted to ranges by setting the somewhat
arbitrary limit that pKi g 2. The same least-squares fitting
procedure then was carried out for all combinations of three
possibilities for each of these measurements: use of the upper
2.1.1.2. Fitting the Additive Model by Ridge Regres-
18,19
sion. Ridge regression
was evaluated as an alternative to
ordinary least-squares for optimization of the additive substituent
parameters. Ridge regression fits observed data to eq 2 but
operates on mean-centered and scaled data (see above) and
supplements the RSS in the target function with an additional
term that penalizes fits with large substituent parameters:
RSSRR ) (yobs - Xꢀ)T(yobs - Xꢀ) + λꢀTꢀ
(5)
a Nonstandard abbreviations: TSS, total sum of squares; RSS, residual
sum of squares; GA, genetic algorithm; PLS, partial least-squares; GCV,
generalized cross-validation; CC,cyclic carbamate; CI, confidence interval;
add, additivity; RR, ridge regression; GARR, genetic algorithm/ridge
regression; GAPLS, genetic algorithm/partial least-squares.
where λ is the ridge parameter. The value of RSSRR is minimized
by the regression coefficients ꢀ that solve the following linear
equation:

AdditiVity Analysis of HIV Protease Inhibitors
(XTX + λI)ꢀ ) XTy
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 739
For the GA-PLS method, the fitness was a function of the
cross-validated Q2 value, the number of compounds, n, and the
number of PLS factors, c, with an additional term to penalize
models using more than 6 descriptors:
(6)
The ridge parameter λ is a positive number that drives the
coefficients in the ꢀ vector toward zero and drives all values of
yfit toward the average value of the observed data yobs. As λ
goes to zero, ridge regression reduces to linear least-squares
regression with mean-centered and scaled data. Shrinking the
coefficients by using an appropriate value of λ can reduce the
sensitivity of the fitted model to noise in the input data and
thereby improve its predictivity. Even a small value of λ may
be sufficient to avoid problems that can arise if the matrix
product XTX is ill-conditioned, i.e., if it is sensitive to numerical
errors upon matrix inversion or similar operations. However, if
λ is too large, then the shrinkage of the coefficients detracts
from the predictivity of the model.
Fitness ) 1 - (n - 1)(1-Q2) ⁄ (n - c) - m62
(7)
Here m6 equals the larger of zero and the number of
descriptors selected minus six. It was added to the fitness
function because we have observed that GA-PLS calculations
without such a term can find a highly fit descriptor set even
when the descriptors are merely random numbers arbitrarily
assigned to each compound. Penalizing models with a larger
number of selected descriptors ameliorates this problem (un-
published results).
For ridge regression without GA, the value of λ that
corresponded to the highest value of the leave-one-out statistic,
Q2, was found using the golden section search.15 For ridge
regression with GA, the value of λ was chosen to optimize a
rapidly computable approximation to Q2, the generalized cross-
validation statistic (GCV). The GCV approximates leave-one-
out cross validation without actually performing repeated
calculations leaving out each molecule in turn.23 To rapidly find
the GCV-optimized value of λ, the following formula was
iterated to convergence,24 starting from an initial guess of 0.1:
The code to perform ridge regression calculations was written
in C by the authors. Fitting was carried out with λ set to 10-12
,
1, 3, 10, and 100 in order to assess the tradeoff between the
increasing RSS and the decreasing size of the sum-of-squared
coefficients in the ꢀ vector. The optimal value of λ will shrink
the coefficients while producing only a small increase in RSS.
Although methods exist to find λ through cross-validation, they
were not used in this case because some of the molecules in
the training set contain unique instances of some of the R1
substituents and predictions for these molecules made within
the context of cross-validation (in which these molecules would
be omitted from the training) would be meaningless. The λ value
of 10-12 amounts to ordinary linear regression with mean-
centered and scaled data. The present ridge regression code was
not outfitted with the ability to handle data ranges, so compounds
for which only inequality data are available were omitted. Also,
so that the ridge regression results could be compared with the
traditional QSAR results on an equal footing, compounds with
substituents 5 or 6 at R2 were omitted. These substituents are
not distinguished from each other by the global QSAR descrip-
tors because they are stereoisomers of each other, and so we
wished to exclude them from the QSAR analysis. This proved
to remove most of the compounds containing R1 substituents
17, 18, and 19, and so the remaining four of these compounds
were also removed. The resulting set of compounds used for
the ridge regression and regular QSAR tests comprises com-
pounds 1-55 and 71-106 from Table 1.
2.1.2. Modeling Affinity by QSAR with Global Molecu-
lar Descriptors. The additivity approximation was compared
with traditional QSAR methods in which the molecules are
represented by global molecular descriptors, which quantify
aspects of the chemical structure as a whole. Parameters were
fit by partial least-squares (PLS)19,20 and ridge regression.18,19
Molecular descriptors were calculated with version 2.1 of the
DRAGON program.21 Here, 511 descriptors were calculated
from descriptor categories 1-6 (constitutional descriptors,
topological descriptors, molecular walk counts, BCUT descrip-
tors, Galvez topological charge indices, and 2D autocorrela-
tions). Principal components from each descriptor class were
calculated with DRAGON, which generated 39 principal
component-derived descriptors for the set of molecules. One
set of calculations used all 39 transformed descriptors for both
PLS and ridge regression. A second set of calculations used a
genetic algorithm (GA) to select a subset of the 39 descriptors.
The genetic algorithm used is very similar to that used by
Hoffman et al.22 for selecting molecular descriptors for PLS
regression. For both GA-PLS and GA-ridge regression methods,
five GA runs were performed, each with 100 generations of
100 chromosomes apiece. The descriptors chosen were those
encoded by the most fit chromosome.
yoTbsP2yobstrace(A-1 - λ
A )
-2
GCV
λGCV
)
(8)
ꢀTA-1ꢀtrace(P)
where n is the number of data points (pKi values), m is the
number of variables (descriptors), A ) XTX + λIm, the
projection matrix P ) In - XA-1XT, and Ix is an identity matrix
with x rows and columns. The term yTobs P2 yobs is the residual
sum-of-squares.24 In the rare instance when this iterative
procedure failed to converge, the value of λ was left at 0.1.
The resultant GA fitness function for ridge regression was
the leave-one-out cross-validation statistic Q2 minus the quantity
m26 described earlier. Note that the GCV method was not used
to calculate the leave-one-out cross-validation statistic Q2 itself
but only used to find reasonable values for λ during the cross-
validation.
2.2. Compounds Studied as HIV-1 Protease Inhibitors.
Table 1 lists all 106 compounds studied here, and Table 2
provides the chemical structures of their substituents. The R1
substituents are separated into those that contain a cyclic
carbamate group and those that do not, and the inhibitors are
similarly divided into those that contain a cyclic carbamate group
at R1 (CC compounds) and those that do not (non-CC
compounds). Some of the CC compounds achieve high affinities,
but the CC substituents tend to be larger than the non-CC
substituents and thus tend to protrude from the substrate
envelope more than the non-CC substituents. Therefore, the
substrate envelope hypothesis would suggest that inhibitors
containing non-CC R1 inhibitors should better inhibit mutant
forms of the HIV protease.9-13 The design methodologies for
most of the training set compounds discussed in this work have
been reported elsewhere,5-7 as have the chemical synthesis and
inhibition assays.5-7,25-27 The synthesis of new compounds is
described in the next section.
2.3. Experimental Methods. 2.3.1. Chemistry. The general
synthetic route applied for the preparation of the inhibitors is
illustrated in Scheme 1. The Boc-protected intermediates (R)-
(hydroxyethylamino)sulfonamides 110-112 were prepared ac-
cording to the procedures described earlier.5 Briefly, ring
opening of commercially available chiral epoxide, (1S,2S)-(1-

740 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
Table 1. Substituent Indices and Observed and Fitted pKi Values of the Molecules Used in This Studya
observed
Ki(obs)
model 1
model 2
model 3
dev
molecule
R1
R2
R3
pKi
fitb
dev
fit
dev
fit
1
2
3
4
5
6
7
8
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
5
5
5
5
6
6
6
6
6
1
1
1
2
2
3
1
1
1
1
2
2
3
4
1
1
1
1
1
2
2
4
1
1
1
1
4
1
1
1
1
1
1
1
8
8
1
2
4
2
3
2
1
4
5
6
2
3
2
1
1
2
4
5
6
2
3
1
1
4
5
6
1
1
4
5
6
1
4
6
1
9
0.10
3.80
0.530
238.7
170.2
42.0
10.00
8.42
9.28
6.62
6.77
7.38
10.08
9.77
10.15
9.97
6.72
6.80
6.82
9.59
11.40
9.08
10.00
8.38
9.21
6.60
6.42
6.93
10.35
9.56
9.71
10.11
6.94
6.77
7.27
9.20
10.74
9.12
0.00
0.04
0.07
0.02
0.35
0.45
-0.27
0.21
10.00
8.42
9.26
6.75
6.64
6.97
10.26
9.52
9.69
10.09
7.02
6.91
7.23
9.19
10.66
9.08
0.00
0.00
0.02
-0.13
0.13
0.41
-0.18
0.25
10.00
8.56
9.61
7.03
6.85
7.08
10.03
9.64
9.73
10.23
7.06
6.89
7.12
9.21
0.00
-0.14
-0.33
-0.41
-0.09
0.29
0.05
0.13
0.43
-0.26
-0.34
-0.09
-0.29
0.38
0.63
0.14
-0.25
0.03
0.083
0.170
0.070
0.107
188.8
160.2
150.0
0.257
0.004
0.84
0.184
0.080
0.016
29.5
167.7
0.80
0.066
0.230
0.343
0.085
0.58
0.006
0.042
0.072
0.016
0.0008
0.032
0.006
0.232
0.019
9
0.44
0.46
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
-0.14
-0.22
0.03
-0.45
0.39
-0.12
-0.30
-0.11
-0.41
0.40
0.74
0.00
-0.18
0.02
0.32
0.12
-0.52
-0.48
-0.05
0.15
-0.20
0.01
0.08
0.21
0.66
10.37c
8.93
-0.04
-0.21
0.00
0.29
0.19
-0.38
-0.49
-0.10
0.15
-0.18
0.02
0.11
0.17
0.12
-0.27
-0.01
0.49
-0.33
-0.16
9.74
9.95
9.92
9.98
10.10
10.80
7.53
6.78
9.10
10.18
9.64
9.46
10.07
9.24
11.22
10.38
10.14
10.80
12.10
10.49
11.22
9.63
10.10
10.51
7.34
7.16
9.59
10.28
9.49
9.64
10.05
9.13
11.05
10.26
10.41
10.81
11.61
10.82
11.38
10.08
10.48
7.41
7.30
9.58
10.23
9.49
9.66
10.06
9.16
11.01
10.27
10.43
10.83
11.58
10.84
11.40
10.06
10.57
7.40
7.23
9.55
9.98
9.59
9.67
10.18
9.16
0.22
0.13
-0.45
-0.45
0.20
0.05
-0.21
-0.11
0.08
0.30
0.06
-0.25
-0.11
0.46
0.35
0.26
10.70c
10.31
10.40
10.90
10.54c
10.15
10.74c
10.52
10.90
0.11
-0.29
-0.03
0.52
-0.35
-0.18
0.89
0.18
10.72
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
7
7
7
8
9
1
2
8
2
1
2
2
1
2
2
2
2
1
2
8
2
8
2
2
4
4
5
6
6
4
4
5
6
6
4
4
5
6
6
1
1
7
1
3
1
3
1
3
7
1
3
7
3
2
1
2
9
2
1
2
2
2
8
2
2
8
2
8
2
2
8
2
8
2
2
8
1
9
1
0.117
9.93
7.48
10.34
5.97
9.41
7.28
4.88
9.77
6.21
4.58
5.63
6.29
10.03
7.39
10.48
7.30
9.42
5.94
6.23
7.62
7.24
5.93
6.12
6.27
4.84
10.30
7.16
10.29
5.97
9.91
6.76
4.90
9.57
6.43
4.56
5.63
6.29
10.17
7.20
10.53
6.88
9.84
5.94
6.23
6.79
6.89
6.22
6.58
6.69
5.17
5.27
4.60
4.96
5.07
5.58
5.69
5.02
5.38
5.48
9.54
9.92
8.93
0.37
0.32
0.05
0.00
-0.50
0.52
-0.02
0.20
-0.21
0.02
0.00
0.00
-0.14
0.19
-0.05
0.42
-0.42
0.00
0.00
0.83
0.34
-0.29
-0.47
-0.42
-0.33
-0.27
0.31
0.36
-0.07
0.11
33.0
0.046
1064.4
0.39
52.6
13232
0.17
609.6
26318
7.48
5.97
0.00
0.00
7.48
0.00
5.97
10.01
6.66
4.90
9.68
6.32
4.56
5.63
6.29
10.34
7.09
0.00
-0.60
0.62
-0.02
0.09
-0.11
0.02
0.00
9
9
7.09
5.07
0.19
-0.19
10
10
10
11
12
13
13
13
14
14
15
16
17
17
17
17
17
18
18
18
18
18
19
19
19
19
19
20
20
20
6.41
4.39
5.63
6.29
-0.20
0.19
0.00
2360.7
514.6
0.00
0.00
-0.31
0.30
0.093
40.4
0.033
50.2
0.38
1148.0
582.4
23.9
7.39
7.30
0.00
0.00
7.30
0.00
5.94
6.23
6.79
6.89
6.22
6.58
6.69
5.17
5.27
4.60
4.96
5.07
5.58
5.69
5.02
5.38
5.48
0.00
0.00
0.83
5.94
6.23
6.79
6.89
6.22
6.58
6.69
5.17
5.27
4.60
4.96
5.07
5.58
5.69
5.02
5.38
5.48
9.40
9.80
8.92
0.00
0.00
0.83
58.0
1169.90
764.2
0.35
0.35
-0.29
-0.46
-0.42
-0.33
-0.27
0.31
0.36
-0.07
0.11
-0.69
-0.02
-0.51
1.11
-0.29
-0.46
-0.42
-0.33
-0.27
0.31
0.36
-0.07
0.11
-0.69
-0.02
-0.51
1.11
0.22
0.12
542.9
14618
>10000
12182.3
4763.1
>10000
2024.20
>10000
>10000
13586.5
258.8
5-2
4.91
5.32
5-2
5.69
5-2
5-2
4.87
-0.69
-0.02
-0.51
1.10
0.08
0.01
6.59
9.62
9.92
8.38
0.24
0.12
4.17
-0.54
-0.55

AdditiVity Analysis of HIV Protease Inhibitors
Table 1. Continued
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 741
observed
Ki(obs)
model 1
fitb
model 2
model 3
molecule
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
R1
R2
R3
pKi
dev
fit
dev
fit
dev
20
20
20
21
21
21
21
21
21
22
22
22
22
22
22
23
23
23
23
23
23
24
24
24
24
24
24
25
25
25
25
25
25
7
8
8
1
1
7
7
8
8
1
1
7
7
8
8
1
1
7
7
8
8
1
1
7
7
8
8
1
1
7
7
8
8
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1.62
8.79
10.21
10.20
9.85
9.32
9.64
10.04
9.74
10.14
9.26
9.66
9.98
10.38
10.23
10.63
9.74
10.14
10.46
10.86
9.11
9.51
8.63
9.03
9.35
9.75
9.56
9.96
9.07
9.47
9.79
10.19
9.41
9.81
8.93
9.33
9.65
10.05
-0.53
0.57
0.16
0.11
0.43
-0.42
-0.15
-0.05
0.06
-0.15
-0.63
0.68
0.71
0.02
-0.62
-0.38
0.03
-0.02
0.06
-0.14
0.45
0.20
9.31
9.53
9.90
9.88
10.25
9.27
9.64
9.86
10.24
10.37
10.74
9.76
10.13
10.35
10.73
9.25
9.62
8.64
9.01
9.23
9.61
9.69
10.07
9.08
9.46
9.68
10.05
9.55
9.92
8.94
9.31
9.53
9.91
-0.51
0.68
0.30
-0.02
0.32
-0.43
-0.13
0.07
0.062
0.063
0.14
0.027
1.45
10.57
8.84
0.309
0.117
0.036
0.084
0.099
0.038
0.014
0.033
0.057
1.88
9.51
9.93
10.44
10.08
10.00
10.42
10.85
10.48
10.24
8.73
0.20
-0.29
-0.74
0.66
0.72
0.13
-0.48
-0.52
-0.09
-0.03
0.07
-0.02
0.59
0.07
-0.13
0.02
0.22
0.00
-0.17
-0.12
-0.05
0.13
-0.16
-0.07
0.27
0.29
2.48
0.82
9.54
8.61
9.09
9.21
0.617
0.063
0.173
0.115
0.79
10.20
9.76
9.94
9.10
9.68
9.68
9.88
9.43
9.87
9.07
-0.02
0.03
0.21
-0.11
-0.31
0.02
0.06
0.14
98
99
0.21
0.21
0.132
0.37
0.134
0.86
100
101
102
103
104
105
106
0.70
0.34
9.15
9.47
-0.18
-0.18
0.12
0.067
10.17
rms deviation
0.35
0.97
55
<0.0001
0.35
0.97
55
0.35
0.96
49
R2
F
p-value
<0.0001
<0.0001
a The chemical structures of the substituents are shown in Table 2. The solid line separates the compounds whose R1 substituents are the larger cyclic
carbamate-containing (CC) substituents from the non-CC compounds, whose R1 substituents are smaller (see Table 2). The Ki values are in nM. Statistics
associated with the three least-squares regressions are also shown. b fit: fitted pKi value; dev: deviation of fitted pKi from the corresponding observed value.
c The observed pKi value used in the regression was changed to a range of 11-13, for reasons explained in the text.
oxiranyl-2-phenylethyl)carbamic acid tert-butyl ester 107 with
selected R2 primary amines provided the amino alcohols 108
and 109. Reactions of selected R3 sulfonyl chlorides with 108
and/or 109 gave the sulfonamide intermediates, (R)-(hydroxy-
ethylamino)sulfonamides 110-112. After removing the Boc
protection, the free amine fragments were coupled with selected
R1 carboxylic acids using two different coupling methods: The
cyclic carbamate-based acid fragment was first converted to the
corresponding acyl chloride and then reacted with amine to
provide the target compounds 35 and 36 (method A);5 the
selected carboxylic acids were reacted with free amines using
EDCI/HOBt in H2O-CH2Cl2 (1:1) mixture to afford the designed
inhibitors 37, 39, 41, 44, 49, 51, and 53 (method B).25
2.3.2. HIV-1 Protease Inhibition Assays. The HIV-1 pro-
tease inhibitory activities of all newly designed inhibitors were
determined by a fluorescence resonance energy transfer (FRET)
method.5,26 Protease substrate, (Arg-Glu(EDANS)-Ser-Gln-Asn-
Tyr-Pro-Ile-Val-Gln-Lys(DABCYL)-Arg) was purchased from
Molecular Probes. The energy transfer donor (EDANS) and
acceptor (DABCYL) dyes were labeled at two ends of the
peptide, respectively, to perform FRET. Fluorescence measure-
ments were carried out on a fluorescence spectrophotometer
(Photon Technology International) at 30 °C. Excitation and
emission wavelengths were set at 340 and 490 nm, respectively.
Each reaction was recorded for about 10 min. Wild-type HIV-1
protease (Q7K) was desalted through PD-10 columns (Amer-
sham Biosciences). Sodium acetate (20 mM, pH 5) was used
as elution buffer. Apparent protease concentrations were around
50 nM estimated by UV spectrophotometry at 280 nm. All
inhibitors were dissolved in dimethylsulfoxide (DMSO) and
diluted to appropriate concentrations. Protease (2 µL) and
inhibitor (2 µL) or DMSO were mixed and incubated for 20-30
min at room temperature before initializing substrate cleavage
reaction. For all experiments, 150 µL of 1 µM substrate were
used in substrate buffer [0.1 M sodium acetate, 1 M sodium
chloride, 1 mM ethylenediaminetetraacetic acid (EDTA), 1 mM
dithiothreitol (DTT), 2% DMSO and 1 mg/mL bovine serum
albumin (BSA) with an adjusted pH 4.7]. Inhibitor binding
dissociation constant (Ki) values were obtained by nonlinear
regression fitting (GraFit 5, Erithacus software) to the plot of
initial velocity as a function of inhibitor concentrations based
on the Morrison equation.27 The initial velocities were derived
from the linear range of reaction curves.
3. Results
Three rounds of modeling and two rounds of synthesis were
carried out. The first additivity model (model 1) was generated
with the least-squares regression methodology using the pKi
values of 61 molecules that had been synthesized to date. On

742 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
Table 2. The R1, R2, and R3 Substituents of the Compounds Listed in Table 1a
a The attachment points to the scaffold are indicated by an asterisk. The indices of the compounds in which each substituent are found in are listed below
each substituent’s chemical structure.

AdditiVity Analysis of HIV Protease Inhibitors
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 743
Scheme 1. Reaction Scheme for the Synthesis of Designed Protease Inhibitorsa
a Reagents and conditions: (a) EtOH, 80 °C, 3 h; (b) aq Na2CO3, CH2Cl2, 0 °C to rt, 4-8 h; (c) Et3N, CH2Cl2, 0 °C to rt, 4-8 h; (d) TFA, CH2Cl2, rt,
1 h; (e) EDCI, HOBt, H2O-CH2Cl2 (1:1), 0 °C, 24 h; (f) acid activation: (COCl)2, rt, overnight; coupling: Et3N, THF, 0 °C to rt, 6 h.
the basis of this model, several further compounds were
proposed, synthesized, and tested. The second additivity model
(model 2) was generated after the pKi values of 39 more
compounds, including some of the proposed compounds,
became available. The second model was used to propose 7
more compounds, and these were designed, synthesized, and
tested. In addition, an evaluation of errors in the models led to
an adjustment in the treatment of the experimental data for the
highest affinity compounds. Finally, the third additivity model
(model 3) was constructed based upon the measured pKi values
of the 61 + 39 + 6 ) 106 compounds that had been studied
experimentally. This third model provides the current best
estimates of the affinity contributions of the various substituents.
Additional calculations were carried out to compare the
various regression methods with each other and to compare the
additivity model with traditional descriptor-based QSAR.
3.1. Additivity Models. 3.1.1. First Additivity Model
Figure 2. Comparison with experiment of calculated pKi values for
and Cycle of Inhibitor Design. The first additivity model was
constructed by using ordinary least-squares regression to fit 61
molecules’ pKi values to eq 1, with molecule 1 (Ki ) 0.1 nM)5
as the reference compound. Parameters for 19, 6, and 8
substituents at the R1, R2, and R3 positions, respectively, were
fitted. A plot of the fitted vs observed pKi values (Figure 2)
shows that there is a good fit of the data to eq 1. Some of the
data points have zero residual because their corresponding
molecules contain the only instances of their R1 substituents
(Table 1), and so the value of their corresponding R1 substituent
parameters take on values that yield zero error.
The fitted parameters listed in Table 3 approximately quantify
the change in pKi from 10 (Ki ) 0.1 nM) upon replacing a
substituent in the reference compound by the listed substituent.
These values range from 1.61 (R1 substituent 6) to -3.82 (R3
substituent 7). The bootstrap-derived 95% confidence limits’
ranges vary from 0.78 to 3.22 with median 1.16 and indicate
that comparison of the various substituent parameters must be
approached with caution due to the large uncertainties in these
values.
61 (fitted) plus 4 (predicted) HIV protease inhibitors (model 1). The
filled square corresponds to the reference compound, the unfilled squares
indicate compounds with only one example of a given R1 substituent,
and the unfilled diamonds represent the remaining 52 compounds in
the training set. The crosses represent four test set compounds whose
pKi values were predicted from the parameters obtained from this
training set (also see Table 4).
Of these, three (7, 13, and 14) are found in only one molecule
each, and the other two (9 and 10) are found in only two
molecules.
The fitted parameters in Table 3 show that there is one clearly
preferred moiety for the R2 position, substituent 1. This group’s
substituent parameter is more than one log unit greater than
those of the other R2 substituents, indicating that replacement
of R2 substituent 1 with any of the other R2 groups would be
expected to reduce binding affinity by more than 1 order of
magnitude.
The most potent contributor to binding affinity at the R3
position, substituent 1, again is the reference substituent for this
position. Three other R3 substituents decrease binding by less
than an order of magnitude relative to the corresponding
reference substituent, i.e., their fitted parameter substituents are
greater than -1. Two of these three moieties contain an oxygen
atom at the 4-position of the phenyl ring, as does the reference
substituent. The other is the 4-anilino group, which is also found
in the potent HIV protease inhibitors amprenavir28 and
darunavir.29
The parameters for all of the CC substituents (R1 substituents
1-6) are greater than or equal to zero. This observation
reinforces the general observation of the potency of compounds
that incorporate this moiety.5 The parameters from this least-
squares fit indicate that R1 substituent 6 is the most potent of
these moieties. In contrast, only five of the 13 non-CC R1
substituents have fitted parameters close to or greater than zero.

744 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
Table 3. Substituent Parameters Obtained from Least-Squares Fitting of
pKi Values for 61 Molecules (model 1)a
The parameter values for the R1 substituents 9, 10, and 13
each noticeably decrease from their respective values in the first
additivity model, presumably reflecting the inclusion of pKi
values lower than the values predicted from the first set of
parameters. The additivity analysis also identified three of the
new substituents as potent contributors to inhibitor binding: R1
substituent 22 (parameter value 0.23); R2 substituent 8 (param-
eter value 0.23), and R3 substituent 9 (parameter value 0.40).
The substituents identified as contributing to high affinity were
incorporated into a new set of additivity-designed compounds
(Table 6). Some of these compounds contained the most potent
non-CC substituents in the R1 position (substituents 7, 13, and
14). Others contained R1 substituent 6, the most potent of the
CC substituents according to this second additivity model (Table
5). Comparison of the predicted pKi values with those obtained
from experiment are shown in Table 6 and Figure 3. The pKi
value of compound 37, which had not been synthesized at this
point, also was predicted using the updated substituent parameter
values.
parameter
nb
95% CI
R1:
1
2
3
4
5
6
0.00
0.35
0.74
0.28
1.05
1.61
5
8
8
5
4
3
0.00-0.00
0.03-0.94
0.24-1.21
-0.03-0.77
0.56-1.44
1.08-2.10
7
8
9
1.07
-0.44
0.67
-0.01
-0.79
-0.31
0.80
1
1
2
2
1
1
1
1
1
1
5
5
5
0.64-1.84
-1.12-0.30
-1.76-1.46
-1.87-0.70
-1.59 to -0.08
-0.69-0.35
0.33-1.45
10
11
12
13
14
15
16
17
18
19
0.70
0.26-1.23
-0.66
-0.36
-0.44
-2.06
-1.65
-1.05-0.00
-0.76-0.29
-1.89-0.98
-3.18 to -0.41
-2.92 to -0.22
The observed pKi values of the newly synthesized compounds
are all less than predicted (Table 6), much as observed for the
previous set of predictions (Table 4). The predictions for the
non-CC compounds deviate from the observed values by -0.49
to -1.36. Two of these four compounds, 39 and 51, are more
potent than nearly all of the non-CC training set inhibitors (Table
1). Interestingly, these two compounds are the best predicted
of the new compounds and their observed pKi values are inside
the 95% confidence intervals of the corresponding predictions.
The observed pKi values of the three CC compounds are less
than predicted by more than one unit; i.e., the observed Ki values
are greater than predicted by more than an order of magnitude.
This unexpected result is considered in more detail later in the
next section.
R2:
R3:
1
2
3
4
5
6
0.00
-1.78
-1.45
-1.15
-1.71
-1.35
22
18
2
9
3
0.00-0.00
-2.34 to -1.40
-2.36 to -0.70
-1.89 to -0.63
-3.11 to -0.63
-2.83 to -0.15
6
1
2
3
4
5
6
7
8
0.00
-1.62
-1.80
-0.79
-0.64
-0.24
-3.82
-1.52
8
21
8
6
4
5
2
6
0.00-0.00
-2.06 to -1.25
-2.40 to -0.93
-1.25 to -0.46
-1.13 to -0.06
-0.72-0.20
-4.55 to -1.54
-2.63 to -0.08
a The cyclic carbamate R1 substituents are those above the solid line.
b n: number of training set molecules containing the specified substituent;
95% CI: 95% confidence interval.
3.1.3. Analysis of First and Second Additivity Models.
3.1.3.1. Overestimation of Affinities. As noted above, the pKi
values predicted with the additivity model consistently exceeded
the observed affinities, yielding inaccurate results in particular
for compounds containing R1 substituent 6. Additional calcula-
tions were performed to address this issue.
Compounds containing four of the five most potent non-CC
R1 substituents (groups 7, 9, 10, and 13), plus the relatively
potent reference R2 and R3 substituents, were proposed and
their pKi values predicted from additivity considerations (Table
4). These compounds were subsequently synthesized and tested
and were found to have subnanomolar affinity (Table 4). This
result contrasts with the corresponding training set molecules
for which the most potent non-CC inhibitor is molecule 56
(CARB-AD378) which has a Ki value of 23.9 nM (pKi 7.62).
This represents a successful application of the additivity method
to design molecules with increased affinity. On the other hand,
the measured binding constants of two of these compounds are
more than an order of magnitude less than their corresponding
predictions. Also, only two of the compounds’ pKi values lie
within their respective predictions’ 95% confidence limit.
The training set compounds with R1 substituent 6 are all of
high affinity (Table 1) and this contributes to the high value of
the fitted parameter for this substituent (Table 5). This in turn
appears to lead to excessively high pKi predictions for the three
designed compounds that contain this substituent (Table 6). It
has been reported that the binding constants of inhibitors whose
Ki values are below approximately 10 pM (pKi > 11) cannot
be reliably measured using the standard fluorometric assay.30
To crudely account for this uncertainty in the measured pKi
values, a new additivity model was constructed in which training
set pKi values greater than 11 were replaced with the range
11-13. Note, however, that no new compounds were added to
the data set. New predictions were made for the compounds in
Table 6; Table 7 shows the results. The predictions made with
the new model are closer to the experimentally determined pKi
values than those from the original model, and the improvements
are pronounced for the three compounds that contain R1
substituent 6. Of these, the errors in two of the three predictions
are within the range observed for the non-CC compounds. This
analysis suggests that one reason for overprediction of affinities
in the first and second additivity models is experimental
uncertainty in the highest measured pKi values. Allowing for
this uncertainty, as done here, improves the predictions.
Even after allowing for these uncertainties, however, the
predictions for two of the four non-CC compounds remained
3.1.2. Second Additivity Model and Cycle of Inhibitor
Design. In the course of this research, 36 additional molecules
from a separate inhibitor design project were synthesized and
tested, the MIT-2 library from ref 7. Some of the substituent
moieties in these molecules were not present in the 61-molecule
training set used in the first additivity model, so another fit of
parameters was performed. Additionally, the observed values
of three of the molecules in Table 4 were included in this new
training set. (Compound 37 had not yet been synthesized and
was therefore not included at this stage.) The fit of this set of
100 molecules is shown in Figure 3, and the substituent
parameters are presented in Table 5.

AdditiVity Analysis of HIV Protease Inhibitors
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 745
Table 4. Comparison of Predicted and Observed pKi Values for Four Molecules Not Present in the 61 Molecule Training Set (model 1)a
observed
predicted
error
molecule
R1
R2
R3
Ki (nM)
pKi
pKi
95% CI
37
41
44
49
7
9
10
13
1
1
1
1
1
1
1
1
0.117
0.39
0.17
9.93
9.41
9.77
11.07
10.67
9.99
-1.13
-1.26
-0.22
-0.77
10.64-11.84
8.24-11.46
8.13-10.70
10.33-11.45
0.093
10.03
10.80
a The predictions, including the bootstrap estimates of the 95% confidence intervals, were made prior to synthesis and testing of the compounds.
underpredicted. This change in the general direction of predic-
tion was accompanied by a decrease in the fitted parameter value
for the common R1 substituent 3. These results indicate that
overprediction of affinity is not a problem intrinsic to the
additivity method, but varies with the compounds in the training
set (Table 9).
3.1.3.2. Ridge Regression versus Ordinary Least-Squares
Regression. Least-squares fitting can overfit the training set data
and so the subsequent predictions can vary significantly with
small changes in the data such as changes due to measurement
error or differences in training set composition. The technique
of ridge regression attenuates this sensitivity by reducing the
magnitudes of the fitted parameters and decreases the risk of
overfitting the training data. Accordingly, this method was tested
for the various data sets (compounds whose pKi values were
predicted using models 1 and 2, and the test sets from models
A and B) with different values of the ridge parameter, λ, in
order to determine its effect on the quality of the predictions.
Note that the lowest value used, λ ) 10-12, reduces the method
Figure 3. Comparison with experiment of calculated pKi values for
100 (fitted) plus 6 (predicted) HIV protease inhibitors (model 2). The
to ordinary least-squares regression with mean-centered and
filled square corresponds to the reference compound, the unfilled squares
scaled data, and the predictions from this approach are similar
indicate compounds with only one example of a given R1 substituent,
to those from ordinary least-squares regression with a reference
the filled diamonds indicate the three compounds from Table 4 that
compound (Table 10).
were included in the 100 molecule training set, and the unfilled
diamonds represent the remaining 89 compounds in the training set.
The crosses and stars represent 6 test set compounds whose pKi values
were predicted with model 2 (Table 6): two contain the cyclic carbamate
moiety (stars) and four do not (crosses).
Assessment of the sum of squared coefficients from the
trained ridge regression models versus the training set sum-
squared residuals suggests optimal values of the ridge parameter,
λ, to be either 1 or 3, as these choices reduce the sum of squared
coefficients while only slightly increasing the sum-squared
residual for the training set. The test set rms prediction error
for λ ) 1 is approximately the same as our original, reference
molecule-based additivity-based method, and it is generally
slightly smaller for λ ) 3 (Table 10). As λ is increased to 10
and 100, however, the errors rise. These results suggest that
using ridge regression instead of ordinary least-squares regres-
sion may lead to a slight improvement in the pKi predictions,
given an appropriate choice of λ.
outside the calculated 95% confidence intervals. To investigate
these persistent overestimates, we constructed two artificial
training sets and corresponding test sets of molecules. The first
training and test sets (labeled A) consist of the compounds with
R1 substituents 1-5, with half of the compounds containing
R1 substituent 3 placed in the test set (Table 8). The second
training and test set (labeled B) were generated by exchanging
the first sets’ training and test compounds that contain R1
substituent 3. The pKi values of the molecules in the first test
set are all overpredicted, similar to what was observed for the
additivity-designed molecules (Tables 4, 6, and 7), but the pKi
values of three of the four molecules in the second test set were
3.1.4. Third and Final Additivity Model. A third additivity
model was constructed based on the full set of 106 compounds
and with all pKi values greater than 11 treated as ranges of

746 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
Table 5. Substituent Parameters Obtained from Least-Squares Fitting of
pKi Values for 100 Molecules (model 2)a
3.2. Additivity Approach versus Descriptor-Based QSAR.
As an alternative to the substituent additivity paradigm, QSAR
calculations were performed using the ridge regression and
partial least-squares techniques, with the molecules represented
via global molecular descriptors based on chemical structure.
Two sets of partial least-squares and ridge regression calcula-
tions were performed: one pair of calculations using a genetic
algorithm to find a small number of descriptor principal
components (usually six) that maximize a cross-validation-based
fitness function, and a second pair of calculations using all 39
descriptor principal components. While there are noticeable
differences in these pKi predictions, relative to those of the
additivity method, there does not seem to be a uniform
improvement in prediction accuracy (Table 12). Thus, these
traditional QSAR models do not appear to provide any
advantage over the additivity approach for this system.
parameter (1) parameter (2) n (2)
95% CI (2)
R1:
1
2
3
4
5
6
0.00
0.35
0.74
0.28
1.05
1.61
0.00
0.26
0.66
0.23
1.01
1.58
5
8
8
5
4
3
0.00-0.00
-0.07-0.71
0.16-1.18
-0.15-0.57
0.56-1.30
0.92-2.10
7
8
9
1.07
-0.44
0.67
-0.01
-0.79
-0.31
0.80
0.84
-0.67
0.01
-0.32
-1.02
-0.46
0.34
1
1
3
3
1
1
2
1
1
1
5
5
5
6
6
6
6
6
6
0.20-1.50
-1.26 to -0.06
-1.66-1.07
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
-1.58-0.19
-1.61 to -0.34
-0.93-0.26
0.03-1.04
0.08-1.14
-1.42 to -0.17
-1.01-0.08
-1.99-0.81
0.70
0.55
-0.66
-0.36
-0.44
-2.06
-1.65
-0.81
-0.52
-0.56
-2.18
-1.76
-0.60
-0.26
0.23
3.3. Crystallographic Correlations. 3.3.1. Structural Basis
of Additivity. Crystallographic data on a number of HIV
-3.51 to -0.72
-3.09 to -0.25
-1.07 to -0.23
-0.65-0.13
protease ligand complexes (molecules 15, 28, 31, 32, 34, 38,
42, 50, 52, 56, 57, 75, 82, 86, and 94)5,7,8
enable the
,unpublished
additivity approximation be rationalized on a structural basis.
Thus, as shown in Figure 4a, substituents at the three positions
of the scaffold occupy separate regions of the protease and do
not contact each other. Furthermore, the common chemical
scaffold of the various inhibitors (Figure 1) remains in es-
sentially the same pose for all of the inhibitors. The lack of
substituent-substituent contacts and of substituent-induced shifts
of the scaffold provides a structural rationale for the reliability
of the additivity model. It is likely that additivity would have
been less reliable if the phenyl group of the scaffold had
represented a fourth variable substituent because some of the
R1 substituents, notably the cyclic carbamates, interact with the
phenyl group (Figure 4A). Interestingly, the main-chain of Gly
48A in the protease adopts a somewhat different conformation
for the CC versus the non-CC inhibitors, possibly to avoid a
clash with the cyclic carbamate group (Figure 4B). If this shift
in the conformation of the protease in response to the CC
substituents had extended to other protease subsites, it might
have generated large deviations from independent substituent
additivity. In fact, however, the conformational shift is local to
the R1 group, so it can be accounted for by the fitted affinity
contributions of the R1 substituents. Thus, the substituent
parameters can incorporate more effects than simply the direct
interactions of ligand substituents with the protease.
-0.26-0.80
-0.89
-0.44
-0.59
-1.16 to -0.44
-0.80 to -0.19
-0.87 to -0.25
R2:
1
2
3
4
5
6
7
8
0.00
-1.78
-1.45
-1.15
-1.71
-1.35
0.00
-1.67
-1.45
-1.08
-1.64
-1.28
-0.49
0.23
37
18
2
9
3
6
12
12
0.00-0.00
-2.28 to -1.08
-2.21 to -0.76
-1.84 to -0.50
-3.09 to -0.28
-2.61-0.09
-0.86 to -0.13
-0.13-0.56
R3:
1
2
3
4
5
6
7
8
9
0.00
-1.62
-1.80
-0.79
-0.64
-0.24
-3.82
-1.52
0.00
-1.58
-1.69
-0.74
-0.58
-0.18
-3.45
-1.48
0.40
29
21
8
6
4
5
2
6
18
0.00-0.00
-1.92 to -1.21
-2.40 to -0.94
-1.11 to -0.36
-1.05 to -0.05
-0.56-0.31
-4.49 to -1.75
-2.55 to -0.37
0.13-0.64
a Cyclic carbamate R1 subsituents are above the solid line. Parameters
(1) from model 1 (Table 3) are included for comparison; (2) indicates data
for model 2.
11-13 (see above). This is arguably the best model because it
uses all the available data and includes the improved treatment
of experimental uncertainty. As summarized in Table 11, the
parameters for R1 substituents 6, 7, and 14 decrease relative to
the second model because of the inclusion of pKi values below
those predicted with the second additivity model. The parameter
value for R1 substituent 13 falls less than the other three,
presumably because the prediction for the compounds containing
this substituent was more accurate than the predictions for the
other six compounds (Table 6). The best of the non-CC R1
substituents are those numbered 7, 13, and 22, and the best of
the CC R1 substituents are 3, 5, and 6.
3.3.2. Structural Analysis of Substituents and Affinities.
3.3.2.1. R1 Substituent. No single chemical feature is common
to the most potent R1 substituents, but a number of them contain
a carbonyl group that forms a hydrogen bond to the main chain
nitrogen of Asp 29A. These include the CC substituents
(substituent parameters -0.02-0.70) whose other contacts are
nonpolar in nature. The non-CC substituents 7 and 22 (parameter
values 0.30 and 0.37, respectively) also make hydrogen bonds
to the main chain nitrogen of Asp 29A and the main chain
oxygen of Gly 48A similar to those made by the bound
substrate.9 The less efficacious substituent 20 (parameter value
-0.46) lacks a group to make the second of these two hydrogen
bonds although its atoms occupy similar positions to those of
R1 substituents 7 and 22. The R1 substituent 17 makes hydrogen
bonds to the same two protease atoms as do substituents 7 and
22 but with a different geometry, a consequence of its amide
group being in the opposite orientation to those in R1 substit-
uents 7 and 22. (Table 2). This suggests that the precise
geometry of these hydrogen bonds may be important for binding.
The parameter value of R2 substituent 8 fall from 0.23 to
-0.01, relative to the second model, suggesting that this
substituent’s contribution to binding is approximately the same
as that of R2 substituent 1. These two moieties are the most
potent contributors to binding in the R2 position. The best of
the R3 substituents are 1, 6, and 9. There are no major changes
for R3 substituent parameters between the second and third
additivity models.

AdditiVity Analysis of HIV Protease Inhibitors
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 747
Table 6. Comparison of Predicted (model 2) and Observed pKi Values for Seven Molecules Not Present in the Second Training Set
observed
predicted
error
molecule
R1
R2
R3
Ki (nM)
pKi
pKi
95% CI
35
36
37
39
51
53
6
6
7
7
13
14
8
8
1
8
8
8
1
9
1
1
9
1
0.232
0.019
0.117
0.046
0.033
0.38
9.63
10.72
9.93
10.34
10.48
9.42
11.81
12.21
10.84
11.07
10.97
10.78
-2.18
-1.49
-0.91
-0.73
-0.49
-1.36
11.01-12.45
11.39-12.87
10.20-11.50
10.30-11.83
10.34-11.76
10.21-11.43
Table 7. Comparison of Original Model 2 Predictions with New Model 2 Predictions Where Training Data Account for the Imprecision of High pKi
Data by Using a Range
model 2
95% CI
modified model 2
95% CI
molecule
R1
R2
R3
obs
preda
error
pred
error
35
36
37
39
51
53
6
6
7
7
13
14
8
8
1
8
8
8
1
9
1
1
9
1
9.63
10.72
9.93
10.34
10.48
9.42
11.81
12.21
10.84
11.07
10.97
10.78
11.01-12.45
11.39-12.87
10.20-11.50
10.30-11.83
10.34-11.76
10.21-11.43
-2.18
-1.49
-0.91
-0.73
-0.49
-1.36
11.29
11.69
10.77
11.01
10.93
10.70
10.91-13.48
11.18 -13.98
10.18 -11.31
10.30 -11.68
10.32-11.70
10.15-11.37
-1.65
-0.97
-0.84
-0.67
-0.45
-1.28
a Pred: predicted pKi value using the substituent parameters from the corresponding least-squares fit.
R1 substituents 13, 14, and 21 (substituent parameter values
0.71, -0.15, and -0.12, respectively), which are all substituted
phenyls, also tend to generate potent inhibitors. Crystal structures
of representative bound ligands containing these substituents,
compounds 50 (MIT-1-KK80), 52 (MIT-1-KK81), and 82 (MIT-
2-AD93),7 show that they make mainly hydrophobic contacts
with the protease, although the hydroxyl groups of the latter
two also make hydrogen bonds with the protease. The substitu-
ent parameters of several less potent substituents can also be
understood from an examination of these three crystal structures.
The low affinity parameters of R1 substituents 12 and 15
(substituent parameters -0.74 and -1.09), which are chemically
similar to 13, 14, and 21, can be rationalized in terms of
expected steric clashes of substituents on their respective
benzene rings with the protease. The low values of the
substituent parameters of R1 substituents 8 and 18 (-0.88 and
-2.57, respectively) can be rationalized by the lack of nearby
hydrogen bond donor moieties from the protease in appropriate
geometries (unpublished model building). The R1 substituent
9, which is nearly as potent as the larger R1 substituent 1,
interacts with the protease through hydrophobic contacts.
3.3.2.2. R2 Substituent. The most potent of the R2 substit-
uents studied in this work, substituents 1, 7, and 8, contain no
rings or heteroatoms. Examination of the crystal structures of
relevant HIV protease-inhibitor complexes (compounds 15, 28,
31, 32, 34, 75, 82, 86, and 94) shows that the corresponding
atoms of these substituents closely superimpose. In contrast,
substituent 4, which is a cyclized version of R2 substituent 1,
occupies a similar region of space as substituent 1 but has a
slightly smaller volume. Replacement of substituent 1 with
substituent 4 leads to a reduction in affinity of approximately 1
order of magnitude, suggesting that the precise shape comple-
mentarity of this group is important for inhibitor binding.
3.3.2.3. R3 Substituent. The crystal structures of complexes
with compounds 15, 28, 31, 32, 34, 75, 82, 86, and 94 show
that the three R3 substituents with the largest parameter values,
substituents 1, 5, 6, and 9, each have an atom at the 4-position

748 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
Table 8. Least-Squares Fitting and Subsequent pKi Prediction for Two Different Permutations of Training and Test Set Molecules
training set A
training set B
molecule
R1
R2
R3
obs
fit
dev
molecule
R1
R2
R3
obs
fit
dev
1
2
3
4
5
6
7
8
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
1
1
1
2
2
3
1
1
1
1
2
2
3
4
1
1
2
2
1
1
1
1
4
1
1
1
1
1
2
4
2
3
2
1
4
5
6
2
3
2
1
1
6
2
3
1
4
5
6
1
1
4
5
6
10.00
8.42
9.28
6.62
6.77
7.38
10.08
9.77
10.15
9.97
6.72
6.80
6.82
9.59
10.00
8.42
9.50
6.64
6.46
7.01
10.19
9.68
9.75
10.14
6.83
6.65
7.19
9.48
10.76
10.71
7.40
7.23
10.06
9.56
0.00
0.00
-0.22
-0.02
0.30
0.37
-0.11
0.09
1
2
3
4
5
6
7
8
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
1
1
1
2
2
3
1
1
1
1
2
2
3
4
1
1
1
4
1
1
1
1
4
1
1
1
1
1
2
4
2
3
2
1
4
5
6
2
3
2
1
2
4
5
1
1
4
5
6
1
1
4
5
6
10.00
8.42
9.28
6.62
6.77
7.38
10.08
9.77
10.15
9.97
6.72
6.80
6.82
9.59
9.08
9.74
10.10
9.10
10.18
9.64
9.46
10.07
9.24
10.00
8.60
9.47
6.58
6.68
7.00
10.19
9.67
9.80
10.10
6.77
6.88
7.20
9.30
8.90
9.78
9.91
9.41
10.10
9.57
9.71
10.00
9.21
10.83
10.31
10.44
10.74
0.00
-0.17
-0.20
0.05
0.08
0.37
-0.11
0.10
0.35
-0.13
-0.05
-0.08
-0.37
0.29
0.17
-0.04
0.18
-0.32
0.08
0.07
-0.24
0.07
0.03
0.17b
0.07
-0.30
0.06
9
0.40
9
10
11
12
13
14
15
19
20
21
23
24
25
26
27
28
29
30
31
-0.17
-0.11
0.14
10
11
12
13
14
16
17
18
22
23
24
25
26
27
28
29
30
31
-0.37
0.11
>11a
0.24b
0.08
10.80
7.53
6.78
10.18
9.64
9.46
0.13
-0.45
0.12
0.08
-0.16
0.06
-0.11
0.17b
0.05
-0.25
0.02
9.62
10.01
9.35
10.83
10.32
10.39
10.78
10.07
9.24
>11a
>11a
10.38
10.14
10.80
10.38
10.14
10.80
rms deviation
0.21
0.98
68
rms deviation
0.19
0.98
61
R2
F
R2
F
P-value
<0.0001
P-value
<0.0001
test set A
R3
test set B
R3
molecule
R1
R2
obs
pred
error
molecule
R1
R2
obs
>11a
10.80
pred
error
16
17
18
22
3
3
3
3
1
1
1
4
2
4
5
1
9.08
9.74
10.10
9.10
9.18
10.26
10.33
10.05
-0.11
-0.52
-0.23
-0.96
15
19
20
21
3
3
3
3
1
1
2
2
1
6
2
3
10.31
10.21
6.88
0.69b
0.59
0.65
7.53
6.78
6.99
-0.22
a pKi range specified as 11-13 for the calculation. b Calculation performed assuming an observed pKi of 11.
superior pharmacokinetics relative to substituents 1 and 6,29 and
this advantage apparently outweighs a small sacrifice in affinity.
This reminds us that binding affinity is not the sole criterion
for selection of substituents in drug candidates.
Table 9. Comparison of Fitted Parameters Obtained from the Two
Training Sets of Table 8
model A
model B
parameter n
95% CI
parameter n
95% CI
difference
R1: 1
0.00
0.19
0.76
0.06
0.83
5 0.00-0.00
0.00
0.19
0.31
0.10
0.83
5 0.00-0.00
8 -0.15-0.59
4 -0.27-0.75
5 -0.30-0.44
4 0.35-3.00
0.00
-0.01
0.45
-0.04
-0.01
2
3
4
5
8 -0.11-0.59
4 0.10-3.00
5 -0.38-0.36
4 0.35-3.00
4. Discussion
The approximation of substituent additivity is found to be
informative and useful for a series of HIV protease inhibitors
having a common chemical scaffold. Statistical analysis yields
significant least-squares fits of measured and modeled pKi
values, and the fitted substituent parameters enabled the design
of new inhibitors with subnanomolar binding affinities.
R2: 1
0.00 16 0.00-0.00
0.00 17 0.00-0.00
0.00
0.24
0.18
0.18
2
3
4
-1.78 6 -2.31 to -1.36 -2.02
4 -2.59 to -1.54
2 -2.35 to -1.04
3 -1.43 to -0.42
-1.41
-0.71
2 -2.07 to -1.04 -1.59
2 -1.13 to -0.33 -0.89
R3: 1
0.00
-1.58
-1.76
-0.50
-0.44
-0.05
6 0.00-0.00
0.00
6 0.00-0.00
0.00
A major virtue of the additivity method is its obvious
interpretability and its consequent utility for designing molecules
that consist of new combinations of substituents already tested
in a partial combinatorial set of inhibitors. The non-CC
compounds that were designed from additivity considerations
used R1 groups that were originally found in inhibitors with
only moderate potency, yet these new compounds bind the
protease target with better than 1 nM affinity, representing a
successful application of the methodology. Application of
additivity to design CC compounds with increased affinity was
less successful, but it should be noted that two of the three
2
3
4
5
5
6 -1.78 to -1.12 -1.40
3 -2.35 to -1.20 -1.30
4 -0.73 to -0.09 -0.53
6 -1.73 to -0.86 -0.17
2 -1.79 to -0.71 -0.46
5 -0.75 to -0.14
4 -0.80-0.19
3 -0.45-0.22
0.03
-0.04
0.05
3 -0.90-0.17
4 -0.43-0.33
-0.39
-0.10
of a six-membered ring, which can accept a hydrogen bond from
Asp 30B. (This should also occur for substituent 5, which is
not represented in any of the crystal structures). The next best
R3 substituent is the 4-anilino group (substituent 4), which is
found in the HIV protease inhibitors amprenavir28 and
darunavir.29 Interestingly, the 4-anilino group is associated with

AdditiVity Analysis of HIV Protease Inhibitors
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 749
Table 10. Comparison of pKi Predictions Made by Least-Squares Regression and Ridge Regression Approaches to Fitting the Additivity Modela
molecule
R1
R2
R3
obse
add
LS
RR1
RR3
RR10
RR100
Model 1c
37
41
44
49
7
9
10
13
1
1
1
1
1
1
1
1
9.93
9.41
9.77
10.97
10.58
9.90
11.11
10.72
10.04
10.85
11.06
10.62
9.95
10.91
10.41
9.77
10.57
9.99
9.43
9.42
9.05
8.83
9.38
10.03
10.71
10.84
10.76
10.49
training set sum-squared residuals
training set sum-squared coefficient
training set rms error
1.83
1.73
0.45
0.19
0.98
1.81
0.40
0.20
0.92
2.08
0.36
0.21
0.79
3.45
0.29
0.27
0.52
31.51
0.10
0.83
0.65
0.20
0.85
test set rms error
Model 2c
35
36
37
39
51
53
6
6
7
7
13
14
8
8
1
8
8
8
1
9.63
10.72
9.93
10.34
10.48
9.42
11.29
11.69
10.77
11.01
10.93
10.70
11.24
11.64
10.76
11.00
10.93
10.69
11.20
11.58
10.75
10.95
10.84
10.61
11.10
11.43
10.64
10.79
10.70
10.47
10.85
11.09
10.36
10.41
10.39
10.15
10.07
10.13
9.56
9.46
9.61
9.35
9
1
1
9
1
training set sum-squared residuals
training set sum-squared coefficient
training set rms error
6.47
6.46
0.93
0.28
1.03
6.70
0.60
0.28
0.98
7.14
0.51
0.29
0.87
8.74
0.39
0.32
0.63
31.28
0.16
0.61
0.61
0.28
1.06
test set rms error
Model A
16
17
18
22
3
3
3
3
1
1
1
4
2
9.08
9.74
10.10
9.10
9.18
10.26
10.33
10.05
9.08
10.24
10.33
10.05
9.14
10.21
10.29
10.02
9.18
10.15
10.22
9.95
9.16
10.01
10.06
9.77
9.04
9.47
9.49
9.28
4
5
1
training set sum-squared residuals
training set sum-squared coefficient
training set rms error
1.11
1.04
0.38
0.20
0.55
1.06
0.36
0.20
0.53
1.18
0.34
0.21
0.48
2.14
0.27
0.28
0.37
21.05
0.06
0.88
0.34
0.20
0.56
test set rms error
Model B
15
19
20
21
3
1
1
2
2
1
6
2
3
>11d
10.80
7.53
6.78
10.31
10.21
6.88
10.34
10.22
6.87
10.31
10.20
6.92
10.26
10.16
7.02
10.11
10.06
7.28
9.57
9.60
8.33
8.28
3
3
3
6.99
6.98
7.01
7.08
7.27
training set sum-squared residuals
training set sum-squared coefficient
Training set rms error
0.98
0.97
0.38
0.19
0.56e
0.99
0.37
0.19
0.56e
1.08
0.34
0.20
0.57e
1.85
0.27
0.26
0.64e
17.00
0.06
0.19
0.79
Test set rms error
0.57e
1.26e
a The test sets are the two sets of molecules for which predictions from models 1 and 2 were made, and also test sets A and B. b obs: observed pKi values;
add: pKi predictions from the original additivity method; LS: least-squares using ridge regression code and with λ ) 10-12; RR1: ridge regression with λ )
1; RR3: ridge regression with λ ) 3; RR10: ridge regression with λ ) 10; RR100: ridge regression with λ ) 100. c Compounds 56-70 were omitted from
training set, as discussed in the Methods section. d pKi range specified as 11-13 for the calculation. e Calculation performed assuming an observed pKi of
11 for compounds with pKi > 11.
designed compounds have affinities close to the limit of
measurement accuracy, 10 pM (pKi ) 11).
the replacement of the R2 substituent 1 with substituent 8 is
-0.01 (Table 11). The differing consequences of the methyl
group for these two pairs of compounds point to a breakdown
of additivity or perhaps experimental uncertainties greater than
supposed.
The generality of the present conclusions regarding additivity
are necessarily limited by the number and accuracy of the
available data. For example, some of the models described here
were generated using a training set that includes only one or a
few instances of a given substituent. The affinity contributions
assigned to such substituents are therefore not optimally tested
and, to the extent that the system is nonadditive, the apparent
accuracy of the additive model will depend upon which specific
compounds appear in the training and test sets, as reported in
Section 3.1.3.1. On the other hand, the tests reported here are
strengthened by the fact that they involve blind predictions of
The prediction errors of the CC compounds were generally
larger than those of the non-CC compounds. However, the
magnitude of these errors decreased when the highest training
set pKi values were replaced by ranges that more realistically
expressed the uncertainty of these experimental data. This
approach effectively capped the pKi values at 11 and reduced
the predicted affinities to values closer to those observed
experimentally. The prediction error of compound 36 with
observed pKi ) 9.63, was still relatively large, however. This
compound differs only in its R2 substituent from that of the
more potent compound 32 (pKi > 11);5 the R2 substituents are
8 and 1, respectively, which only differ by a methyl group. From
additivity considerations, one would expect their pKi difference
to be very small, as the value of the additivity parameter for

750 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
Table 11. Third Additivity Model (model 3), with Substituent
Parameters Obtained from Least-Squares Fitting of pKi Values from 107
Molecules and with pKi Values above 11 Replaced by the Range
11-13a
least-squares fit
parameter parameter
n
(3)
parameter (3)
(1)b
(2)
95% CI (3)
R1:
1
2
3
4
5
6
0.00
0.24
0.58
0.15
0.87
1.10
0.00
0.16
0.50
0.10
0.82
1.05
0.00
0.03
0.37
-0.02
0.70
5
8
8
5
4
5
0.00-0.00
-0.30-0.56
-0.11-0.80
-0.44-0.40
0.18-3.00
0.54
-0.21-2.96
7
8
9
0.97
-0.54
0.58
-0.10
-0.88
-0.40
0.71
0.77
-0.74
-0.02
-0.35
-1.08
-0.54
0.30
0.30
-0.88
-0.09
-0.43
-1.23
-0.74
0.17
-0.15
-1.09
-0.79
-0.95
-2.57
-2.16
-0.46
-0.12
0.37
3
1
3
3
1
1
3
2
1
1
5
5
5
6
6
6
6
6
6
-0.07-0.79
-1.51 to -0.33
-0.59-0.80
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
-1.84 to -0.08
-1.74 to -0.82
-1.31 to -0.27
-0.09-0.75
0.61
0.47
-0.81-0.68
-0.75
-0.45
-0.66
-2.28
-1.86
-0.89
-0.59
-0.77
-2.39
-1.97
-0.60
-0.26
0.23
-1.56 to -0.62
-1.39 to -0.32
-2.40-0.47
-3.75 to -1.09
-3.62 to -0.62
-1.00 to -0.03
-0.48-0.20
Figure 4. Superimposed HIV protease inhibitors. (A) Molecules 38
(magenta), 42 (brown), 56 (green-cyan), 28 (cyan), 32 (blue), 75 (cobalt
blue), 82 (orange), 94 (pink), 15 (violet), 57 (green-yellow), 31 (off-
white), 34 (gold), 86 (gray), 50 (lime green), 52 (salmon pink). (B)
Superimposed CC HIV protease inhibitors 28 (cyan), 32 (blue) and 15
(violet), and the non-CC inhibitors 56 (green-cyan), 57 (green-yellow)
and 50 (lime green). The orientations of the Gly 48A carbonyl groups
in the HIV protease structures with CC inhibitors bound are seen to
differ from those in the non-CC inhibitor-bound crystal structures. For
simplicity, only one protease monomer is shown for each structure.
-0.17-0.94
-0.89
-0.44
-0.59
-0.75
-0.31
-0.45
-1.09 to -0.29
-0.61 to -0.03
-0.71 to -0.15
R2:
1
2
3
4
5
6
7
8
0.00
-1.77
-1.48
-1.01
-1.58
-1.22
0.00
-1.67
-1.48
-0.95
-1.51
-1.15
-0.49
0.23
0.00
-1.53
-1.48
-0.82
-1.38
-1.03
-0.61
-0.01
38 0.00-0.00
18 -2.13 to -0.90
2
9
3
6
-2.13 to -0.91
-1.64 to -0.22
-3.03 to -0.30
-2.43-0.23
the affinities of new compounds. It is also worth emphasizing
that, although a more redundant data set would make the
statistics more informative and reliable, it would not necessarily
improve the additivity of the models, which derives not from
the statistics but from the physics of the protein-ligand system
(see below). In fact, if the system were perfectly additive, then
a training set with only M1 + M2 + M3 compounds, where Mi
is the number of different substituents at site Ri, would allow
us to predict the affinities of all M1 × M2 × M3 - (M1 + M2 +
M3) other compounds in the combinatorial library with perfect
accuracy. Finally, it is worth emphasizing that experimental
uncertainty can lead even an additive system to appear nonad-
ditive, and it is worth accounting explicitly for least the larger
known uncertainties when constructing and testing an additive
model (Section 3.1.3.1).
As just discussed, the accuracy of the pKi predictions can
depend upon the molecules in the training set. Thus, interchang-
ing four molecules between test and training sets with a total
of 27 + 4 ) 31 compounds led to noticeably different
accuracies. In one case, the predicted pKis were consistently
too high, and in the other, the pKis were too low. In addition,
the parameter of the R1 substituent common to the interchanged
molecules was assigned values differing by 0.45 pKi units. These
artificial training and test sets exhibit behavior similar to that
of the previous sets of molecules, which displayed consistent
overprediction of pKi values and changes in parameter values
upon changes to the training set. Thus, the model generated by
a given set of pKi values should necessarily be seen as
provisional and should be updated upon obtaining relevant new
data. We sought to reduce the sensitivity of the predictions to
the choice of training set data by using ridge regression instead
12 -0.96 to -0.23
17 -0.35-0.33
R3:
1
2
3
4
5
6
7
8
9
0.00
-1.54
-1.72
-0.61
-0.49
-0.05
-3.74
-1.43
0.00
-1.50
-1.62
-0.56
-0.43
0.01
-3.41
-1.40
0.40
0.00
-1.44
-1.61
-0.39
-0.31
0.20
-3.48
-1.33
0.37
33 0.00- 0.00
21 -1.79 to -0.94
8
6
4
5
2
6
-2.30 to -0.75
-0.76-0.08
-0.80-0.27
-0.20-0.97
-4.40 to -1.89
-2.69 to -0.27
20 0.11-0.60
a Parameters that are italicized are for substituents not used to train
models 1 or 2. b Number in parentheses indicates refers to the relevant
additivity model. Cyclic carbamate compounds are above the solid line.
of ordinary least-squares. The apparently optimal value of the
ridge parameter, λ ) 3, the largest value tried that did not
increase the sum-squared residuals by an excessive amount,
generally led to only a minor improvement in prediction
accuracy. This suggests that the use of ordinary least-squares
regression is not a major reason for errors in the original
predictions. Still, for three of the four test sets, increasing the
value of λ did somewhat improve the pKi predictions (Table
10).
The accuracy of the additivity approach was furthermore
compared to that of standard descriptor-based QSAR methods.
The results were mixed, with each method yielding slightly
better accuracy in some cases but not in others. However, the
additivity method is arguably superior in the present application
because it provides clear guidance on the contributions of
individual substituents to affinity. Thus, it is trivial to use
additivity information to propose new molecules for synthesis,

AdditiVity Analysis of HIV Protease Inhibitors
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 751
Table 12. Comparison of pKi Predictions via Additivity with
2. Changing one substituent should not shift the position of
the other substituents in the binding site. For example, changing
from a small R1 substituent to a bulky one could generate
nonaddivity by shifting the entire ligand and thereby forcing
R2 to move away from its original position. This requirement
is perhaps most easily met if all the substituents are similar in
size, the ligand has a flexible scaffold, and small changes in
the conformation of the scaffold do not lead to significant
changes in its interaction with the protein (for example, the
flexible part of the scaffold might be solvent-exposed).
3. Changing R1 must not cause a change in protein confor-
mation that propagates to the interaction site of R2, because
this, too, would alter the interaction of R2 with the protein.
Meeting this requirement may be facilitated if all the substituents
at a given site make similar interactions with the protein and if
the protein is very rigid or, perhaps, so soft that conformational
shifts remain local.
Predictions from Whole Molecule Descriptor-Based QSAR Methodsa
QSAR
molecule
R1 R2 R3 obsd add RR GARR PLS GAPLS
Model 1
37
41
44
49
7
9
10
13
1
1
1
1
1
1
1
1
9.93 10.97 9.88 10.05 9.74 10.57
9.41 10.58 9.82 10.99 9.68 11.02
9.77 9.90 9.64 10.24 9.56 10.27
10.03 10.71 10.42 10.65 10.46 11.12
rms prediction
error
0.85 0.29 0.88 0.29
1.05
Model 2
35
36
37
39
51
53
6
6
7
7
13
14
8
1
9.63 11.29 10.55 10.48 10.48 10.78
10.72 11.69 11.10 10.70 11.11 11.22
9.93 10.77 9.66 10.15 9.72 10.18
10.34 11.01 9.48 9.48 9.45 9.60
10.48 10.93 10.60 10.14 10.70 10.34
9.42 10.70 9.56 9.21 9.61 9.44
8
1
8
8
8
9
1
1
9
1
There may also be nonadditive effects on conformational
fluctuations, and hence the entropy, of the ligand and the protein,
but it is not clear what additional requirements avoiding these
nonadditivities places on the system.
rms prediction
error
1.06 0.55 0.53 0.55 0.61
The protein-ligand series considered here does, arguably,
go a long way to meeting these requirements, given the
flexibility of the scaffold (Figure 1) and the fact that the
substituents bind in discrete regions of the protein without
contacting each other (Figure 4). In addition, the substituents
at each site are fairly similar in size, and the largest variations
in size occur at R1 and R3, which lie at the two entrances of
the active site tunnel where substituents of varied size can be
accommodated without steric clashes or protein reorganization.
The available crystal structures bear out the expectation that
changes at one ligand site produce minimal perturbation at the
other sites. The additivity approximation may well be useful
for other protein-ligand systems that meet the requirements
laid out above.
Model A
16
17
18
22
3
3
3
3
1
2
9.08 9.18 9.42 9.96 9.61 9.89
9.74 10.26 9.98 10.16 9.99 10.13
10.10 10.33 10.49 10.72 10.29 10.65
9.10 10.05 10.06 10.11 10.20 10.11
1
1
4
4
5
1
rms prediction
error
0.56 0.56 0.77 0.63 0.74
Model B
10.31 10.34 10.15 10.23 10.17
10.80 10.21 10.37 10.25 9.90 10.13
7.53 6.88
6.78 6.99
15
19
20
21
3 1 1 >11c
3 1 6
3 2 2
3 2 3
6.96
7.12
7.12
7.61
7.01
7.49
7.09
7.60
5. Summary
rms prediction
error
0.57d 0.52d 0.69d 0.74d 0.71d
The concept of substituent additivity proves to be a pleasingly
simple and practical way to use existing binding affinity data
for the design of new HIV protease inhibitors with high affinity
and a good fit to the substrate envelope. The present study also
has broader significance, because there are few other articles in
which an additivity analysis was followed up and tested by
synthesis of compounds containing the most favorable substit-
uents (but see ref 31). The accuracy of initial predictions with
the additive model motivated a careful look at this methodology,
highlighting the provisional nature of the mathematical models
obtained and the importance of accounting for measurement
imprecision for high affinity compounds. Correlations with
crystallographic data rationalize the observed additivity and the
contributions of the various substituents to binding affinity.
Analysis of the physical requirements for substituent indepen-
dence provide guidance to the identification of other systems
where additivity analysis is likely to be useful.
a The tests set are the same as in Table 10. b obs: observed pKi values;
add: pKi predictions from the original additivity method; RR: ridge
regression; GARR: ridge regression with genetic algorithm used for
descriptor selection; PLS: partial least-squares; GAPLS: partial least-squares
with genetic algorithm used for descriptor selection. c pKi range specified
as 11-13 for the calculation. d Calculation performed assuming an observed
pKi of 11.
albeit with the restriction that the substituents must have been
included in at least one training set molecule. Furthermore, the
additivity-based method can distinguish between chemically
similar substituents, such as R1 substituents 14 and 15, whose
contributions to binding affinity differ by approximately 1 order
of magnitude. In contrast, a QSAR method, which represents
molecules by whole-molecule descriptors, is less well suited to
make such fine distinctions.
Why does the additivity approximation work so well for the
present ligand-protein series, and will it be equally applicable
to other systems? These question may be addressed by consider-
ing some of the physical requirements that must be met in order
for the simple additivity model to work, as follows:
6. Experimental Section (Chemistry)
6.1. General. Proton nuclear magnetic resonance (1H NMR) and
carbon nuclear magnetic resonance (13C NMR) spectra were
recorded with a Varian Mercury 400 MHz NMR spectrometer
operating at 400 MHz for 1H and 100 MHz for 13C NMR. Chemical
shifts are reported in ppm (δ scale) relative to the solvent signal,
and coupling constant (J) values are reported in Hertz. Data are
represented as follows: chemical shift, multiplicity (s ) singlet, d
) doublet, t ) triplet, q ) quartet, m ) multiplet, dd ) doublet of
1. The substituents should not contact each other in either
the bound or free state, or else changing R1, for example, would
change the relative affinities of ligands with different R2
substituents. This requirement is most easily met by a large
ligand with small, widely separated substituents.

752 Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3
Jorissen et al.
doublets, br ) broad), coupling constant in Hz, and integration.
High resolution mass spectra (HRMS) were recorded on Waters
Q-TOF Premier mass spectrometer by direct infusion of solutions
of each compound using electrospray ionization (ESI) in positive
mode. All reactions were performed in oven-dried round-bottomed
or modified Schlenk flasks fitted with rubber septa under N2
atmosphere unless otherwise noted. All final coupling reactions were
carried out at 0.5 mmol scale unless stated otherwise. Air- and
moisture-sensitive liquids, and solutions were transferred via syringe
or stainless steel cannula. Organic solutions were concentrated under
reduced pressure by rotary evaporation at 35-40 °C. Flash and
column chromatography was performed using silica gel (230-400
mesh, Merck KGA). Analytical thin-layer chromatography (TLC)
was performed using silica gel (60 F-254) coated aluminum plates
(Merck KGA) and spots were visualized by exposure to ultraviolet
light (UV) and/or exposure to an acidic solution of p-anisaldehyde
(anisaldehyde) followed by brief heating. Dichloromethane was
dried over P2O5 and distilled, tetrahydrofuran (THF) was distilled
from sodium/benzophenone, and anhydrous N,N-dimethylforma-
mide was purchased from Aldrich and used as received. All other
reagents and solvents were purchased from commercial sources and
used as received.
0.90-0.86 (m, 6H). 13C NMR (100 MHz, CDCl3) δ 197.66, 168.69,
158.32, 155.89, 153.07, 138.09, 138.07, 137.37, 135.63, 134.66,
129.73, 129.58 (2C), 128.67 (2C), 126.79, 125.09, 124.84, 124.72,
123.04, 122.60, 117.58, 72.46, 69.94, 57.62, 53.88, 53.52, 48.26,
35.70, 33.73, 26.98, 26.67, 17.15, 11.28. HRMS (ESI) m/z: calcd
for C34H39N4O7S2 [M + H]+ 679.2260; found, 679.2287.
6.3. Typical Procedure for the Coupling Reactions (Method
B). 6.3.1. (2S)-2-(Acetylamino)-N-[(1S,2R)-2-hydroxy-3-[[(4-
methoxyphenyl)sulfonyl](2-methylpropyl)amino]-1-(phenyl-
methyl)propyl]-propanamide (37). To a solution of the N-[(1S,2R)-
2-Hydroxy-3-[[(4-methoxyphenyl)sulfonyl](2-methylpropyl)amino]-
1-(phenylmethyl)propyl]-carbamic acid tert-butyl ester5 (0.254 g,
0.5 mmol) in CH2Cl2 (15 mL) was added TFA (5 mL) and the
mixture was stirred at room temperature for 1 h. Solvents were
removed under reduced pressure, and the residue was dissolved in
CH2Cl2, washed with 10% aqueous NaHCO3 solution, dried
(Na2SO4), filtered, and evaporated under reduced pressure to provide
the free amine as white solid. To an ice-cooled solution of this
amine in a mixture of H2O-CH2Cl2 (1:1) (12 mL) were added
N-Ac-Ala-OH (0.079 g, 0.6 mmol) followed by HOBt (0.092 g,
0.6 mmol) and EDCI (0.115 g, 0.6 mmol) under N2 atmosphere.
The reaction mixture was stirred at 0-4 °C until the reaction was
complete (monitored by TLC). A small amount of CH2Cl2 was
added and layers were separated. The organic extract was washed
with saturated aqueous NaCl solution, dried (Na2SO4), filtered, and
evaporated under reduced pressure. The residue was purified by
flash chromatography on silica gel using CHCl3-MeOH (19:1)
mixture as eluent to provide the target compound (0.235 g, 90%)
as white solid. 1H (400 MHz, CDCl3) δ. 7.74-7.70 (m, 2H),
7.27-7.16 (m, 5H), 6.99-6.95 (m, 2H), 6.65 (d, J ) 8.8 Hz, 1H),
5.87 (d, J ) 7.6 Hz, 1H), 4.32 (m, 1H), 4.15 (m, 1H), 4.07 (d, J )
3.6 Hz, 1H), 3.86 (s, 3H), 3.85 (m, 1H, overlapping signal),
3.14-3.02 (m, 3H), 2.92-2.84 (m, 3H), 1.88 (s, 3H), 1.84 (m,
1H), 1.19 (d, J ) 6.8 Hz, 3H), 0.87 (d, J ) 6.8 Hz, 3H, overlapping
signal), 0.86 (d, J ) 6.4 Hz, 3H, overlapping signal). 13C NMR
(100 MHz, CDCl3) δ 172.82, 170.29, 163.24, 138.05, 130.19,
127.72 (2C), 129.58 (2C), 128.65 (2C), 126.71, 114.57 (2C), 72.79,
58.93, 55.86, 54.20, 53.55, 49.13, 35.44, 27.41, 23.38, 20.34, 20.18,
18.27. HRMS (ESI) m/z: calcd for C26H38N3O6S [M + H]+
520.2481; found, 520.2461.
6.2. Typical Procedure for the Coupling Reactions (Method
A). 6.2.1. (5S)-3-(3-Acetylphenyl)-N-[(1S,2R)-2-hydroxy-3-[[(4-
methoxyphenyl)sulfonyl][(2S)-2-methylbutyl]amino]-1-(phenyl-
methyl)propyl]-2-oxo-oxazolidine-5-carboxamide (35). Excess
oxalyl chloride was added to solid (S)-3-(3-acetylphenyl)-2-oxo-
oxazolidine-5-carboxylic acid (0.125 g, 0.5 mmol), and the resulting
mixture was stirred at room temperature overnight. The oxalyl
chloride was removed by distillation under reduced pressure and
residue dried under high vacuum for 30 min. A solution of the
resulting acid chloride in dry THF (5 mL) was used in the coupling
reaction. To an ice-cooled mixture of the Boc deprotected amine
(0.5 mmol) in dry THF (5 mL) was added Et3N (0.15 mL, 1.1
mmol), followed by the slow addition of the acid chloride solution.
After 15 min, the reaction mixture was warmed to room temperature
and stirred until reaction was complete (monitored by TLC). Small
amounts of water and ethyl acetate were added, and layers were
separated. The organic extract was washed with saturated aqueous
NaCl solution, dried (Na2SO4), filtered, and evaporated. The residue
was purified by flash chromatography on silica gel using ethyl
acetate-hexanes (3:1) mixture as eluent to provide the target
6.3.2. (2S)-2-(Acetylamino)-N-[(1S,2R)-2-hydroxy-3-[[(4-
methoxyphenyl)sulfonyl][(2S)-2-methylbutyl]amino]-1-(phenyl-
methyl)propyl]-propanamide (39). Coupling method B; solvent
for flash chromatography: EtOAc-hexanes (3:2); yield: 0.235 g,
1
compound (0.30 g, 92%) as white solid. H (400 MHz, CDCl3) δ
7.89 (t, J ) 2.0 Hz, 1H), 7.83 (m, 1H), 7.77 (m, 1H), 7.76-7.72
(m, 2H), 7.52 (t, J ) 8.4 Hz, 1H), 7.13 (dd, J ) 8.4, 1.6 Hz, 2H),
7.03-6.98 (m, 4H), 6.86 (dt, J ) 8.4, 1.2 Hz, 1H), 6.75 (d, J )
10.0 Hz, 1H), 4.80 (dd, J ) 9.6, 5.6 Hz, 1H), 4.25 (m, 1H), 4.08
(t, J ) 9.6 Hz, 1H), 3.92 (m, 1H), 3.87 (s, 3H), 3.65 (d, J ) 2.4
Hz, 1H), 3.41 (dd, J ) 9.6, 6.0 Hz, 1H), 3.20 (dd, J ) 15.6, 9.6
Hz, 1H), 3.12-3.04 (m, 2H), 2.98 (dd, J ) 15.2, 2.8 Hz, 1H),
2.82 (dd, J ) 13.2, 7.2 Hz, 1H), 2.76 (dd, J ) 13.6, 10.4 Hz, 1H),
2.65 (s, 3H), 1.62 (m, 1H), 1.52 (m, 1H), 1.11 (m, 1H), 0.90-0.86
(m, 6H). 13C NMR (100 MHz, CDCl3) δ 197.64, 168.60, 163.37,
153.04, 138.12, 138.08, 137.42, 129.79 (2C), 129.76, 129.72, 129.60
(2C), 128.63 (2C), 126.73, 124.77, 123.04, 117.56, 114.65 (2C),
72.40, 69.91, 57.61, 55.89, 53.87, 53.39, 48.25, 35.66, 33.74, 26.98,
26.65, 17.16, 11.26. HRMS (ESI) m/z: calcd for C34H42N3O8S [M
+ H]+ 652.2693; found, 652.2714.
1
88%; white solid. H (400 MHz, CDCl3) δ 7.74-7.70 (m, 2H),
7.27-7.16 (m, 5H), 6.99-6.95 (m, 2H), 6.61 (d, J ) 8.8 Hz, 1H),
5.86 (d, J ) 7.6 Hz, 1H), 4.33 (m, 1H), 4.16 (m, 1H), 4.02 (d, J )
3.6 Hz, 1H), 3.86 (s, 3H), 3.83 (m, 1H), 3.12-3.0 (m, 3H),
2.97-2.88 (m, 2H), 2.82 (dd, J ) 13.2, 7.6 Hz, 1H), 1.89 (s, 3H),
1.60 (m, 1H), 1.44 (m, 1H), 1.20 (d, J ) 6.8 Hz, 3H), 1.05 (m,
1H), 0.86-0.82 (m, 6H). 13C NMR (100 MHz, CDCl3) δ 172.81,
170.27, 163.24, 138.0, 130.11, 129.73 (2C), 129.60 (2C), 128.65
(2C), 126.72, 114.57 (2C), 72.73, 57.58, 55.86, 54.11, 53.54, 49.13,
35.45, 33.63, 26.79, 23.37, 18.35, 17.12, 11.33. HRMS (ESI) m/z:
calcd for C27H40N3O6S [M + H]+ 534.2638; found, 534.2630.
6.3.3. N-[(1S,2R)-2-Hydroxy-3-[[(4-methoxyphenyl)sulfonyl](2-
methylpropyl)amino]-1-(phenylmethyl)propyl]-3-methyl-4,4,4-
trifluoro-2-butenamide (41). Coupling method B; solvent for flash
chromatography: EtOAc-hexanes (1:1); yield: 0.240 g, 88%;
gummy solid. 1H (400 MHz, CDCl3) δ 7.70-7.66 (m, 2H),
7.32-7.20 (m, 5H), 6.99-6.95 (m, 2H), 6.14 (m, 1H), 5.95 (d, J
) 8.8 Hz, 1H), 4.26 (m, 1H), 3.99 (d, J ) 2.8 Hz, 1H), 3.87 (s,
3H), 3.11 (dd, J ) 15.2, 8.8 Hz, 1H), 3.03 (dd, J ) 14.0, 5.6 Hz,
1H), 2.99-2.90 (m, 3H), 2.79 (dd, J ) 13.6, 6.8 Hz, 1H), 2.04 (d,
J ) 1.6 Hz, 3H), 1.83 (m, 1H), 0.90 (d, J ) 6.4 Hz, 3H), 0.87 (d,
J ) 6.4 Hz, 3H). 13C NMR (100 MHz, CDCl3) δ 164.74, 163.34,
138.64 (q, J ) 30.0 Hz), 137.69, 129.90, 129.67 (2C), 129.52 (2C),
128.90 (2C), 126.95, 124.82 (t, J ) 272.6 Hz), 123.50 (q, J ) 5.2
Hz), 114.60 (2C), 72.74, 59.09, 55.87, 53.92, 53.85, 34.90, 27.55,
20.34, 20.13, 12.17. HRMS (ESI) m/z: calcd for C26H34F3N2O5S
[M + H]+ 543.2141; found, 543.2100.
6.2.2. (5S)-3-(3-Acetylphenyl)-N-[(1S,2R)-3-[(6-benzothiazo-
lylsulfonyl)[(2S)-2-methylbutyl]amino]-2-hydroxy-1-(phenyl-
methyl)propyl]-2-oxo-oxazolidine-5-carboxamide (36). Coupling
method A; solvent for flash chromatography: EtOAc-hexanes (4:
1
1); yield: 0.310 g, 91%; white solid. H NMR (400 MHz, CDCl3)
δ 9.22 (s, 1H), 8.49 (d, J ) 1.6 Hz, 1H), 8.27 (d, J ) 8.4 Hz, 1H),
7.93-7.90 (m, 2H), 7.82-7.76 (m, 2H), 7.52 (t, J ) 8.4 Hz, 1H),
7.13 (dd, J ) 8.4, 1.6 Hz, 2H), 7.02 (t, J ) 8.0 Hz, 2H), 6.89-6.82
(m, 2H), 4.80 (dd, J ) 9.6, 5.6 Hz, 1H), 4.26 (m, 1H), 4.08 (t, J )
9.6 Hz, 1H), 3.98 (m, 1H), 3.63 (d, J ) 3.6 Hz, 1H), 3.43 (dd, J
) 9.2, 5.6 Hz, 1H), 3.25 (dd, J ) 15.2, 9.2 Hz, 1H), 3.16-3.05
(m, 3H), 2.93 (dd, J ) 13.2, 6.8 Hz, 1H), 2.78 (dd, J ) 13.6, 10.8
Hz, 1H), 2.65 (s, 3H), 1.66 (m, 1H), 1.51 (m, 1H), 1.12 (m, 1H),

AdditiVity Analysis of HIV Protease Inhibitors
Journal of Medicinal Chemistry, 2009, Vol. 52, No. 3 753
6.3.4. N-[(1S,2R)-2-Hydroxy-3-[[(4-methoxyphenyl)sulfonyl](2-
methylpropyl)amino]-1-(phenylmethyl)propyl]-4-oxo-2-pentena-
mide (44). Coupling method B; solvent for flash chromatography:
EtOAc-hexanes (3:2); yield: 0.225 g, 89%; white foamy solid. 1H
(400 MHz, CDCl3) δ 7.70-7.66 (m, 2H), 7.31-7.19 (m, 5H),
7.99-6.93 (m, 2H), 6.91 (d, J ) 15.6 Hz, 1H), 6.59 (d, J ) 15.2
Hz, 1H), 6.22 (d, J ) 8.8 Hz), 4.28 (m, 1H), 4.06 (d, J ) 2.8 Hz,
1H), 3.93 (m, 1H), 3.87 (s, 3H), 3.10 (dd, J ) 15.2, 8.4 Hz, 1H),
3.03-2.96 (m, 3H), 2.91 (dd, J ) 14.0, 8.4 Hz, 1H), 2.79 (dd, J )
13.6, 6.8 Hz, 1H), 2.31 (s, 3H), 1.82 (m, 1H), 0.88 (d, J ) 6.8 Hz,
3H, overlapping signal), 0.86 (d, J ) 6.8 Hz, 3H, overlapping
signal). 13C NMR (100 MHz, CDCl3) δ 197.81, 164.51, 163.33,
137.61, 137.21, 133.64, 129.89, 129.67 (2C), 129.52 (2C), 128.91
(2C), 126.98, 114.62 (2C), 72.65, 59.07, 55.88, 54.46, 53.75, 34.84,
29.11, 27.52, 20.35, 20.14. HRMS (ESI) m/z: calcd for C26H35N2O6S
[M + H]+ 503.2216; found, 503.2221.
for pointing out that our additivity analysis “reinvented the
wheel” first devised by Free and Wilson. A generous gift of
chiral epoxides from Kaneka USA is gratefully acknowledged.
This publication was made possible by grants nos. GM066524
and GM061300 from the National Institute of General Medical
Sciences (NIGMS) of the NIH. The contents of this publication
are solely the responsibility of the authors and do not necessarily
represent the official views of the NIGMS.
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1
foamy solid. H (400 MHz, CDCl3) δ 7.71 (m, 2H), 7.33-7.21
(m, 5H), 7.10-7.0 (m, 2H), 6.98 (m, 2H), 6.78 (dd, J ) 7.6, 1.2
Hz, 1H), 5.98 (d, J ) 8.8 Hz, 1H), 4.38 (m, 1H), 3.99 (m, 1H),
3.87 (s, 3H), 3.21-3.12 (m, 3H), 3.01-2.93 (m, 2H), 2.86 (dd, J
) 13.2, 6.8 Hz, 1H), 2.07 (d, J ) 2.0 Hz, 3H), 1.89 (m, 1H), 0.93
(d, J ) 6.8 Hz, 3H), 0.89 (d, J ) 6.8 Hz, 3H). 13C NMR (100
MHz, CDCl3) δ 169.43 (d, J ) 2.9 Hz), 163.33, 161.54 (d, J )
243.9 Hz), 138.40 (d, J ) 4.4 Hz), 137.89, 129.99, 129.68 (2C),
129.57 (2C), 128.91 (2C), 127.24 (d, J ) 8.1 Hz), 126.98, 123.73
(d, J ) 18.3 Hz), 122.21 (d, J ) 3.7 Hz), 117.0 (d, J ) 22.7 Hz),
114.62 (2C), 73.19, 59.19, 55.88, 54.40, 53.94, 35.14, 27.58, 20.35,
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1
solid. H (400 MHz, CDCl3) δ 9.21 (s, 1H), 8.44 (d, J ) 1.6 Hz,
1H), 8.25 (d, J ) 8.8 Hz, 1H), 7.88 (dd, J ) 8.8, 1.6 Hz, 1H),
7.33-7.21 (m, 5H), 7.11-7.0 (m, 2H), 6.79 (dd, J ) 8.8, 1.2 Hz,
1H), 6.03 (d, J ) 8.4 Hz, 1H), 4.39 (m, 1H), 4.02 (m, 1H), 3.22
(m, 2H), 3.16 (dd, J ) 14.0, 5.2 Hz, 1H), 3.10 (dd, J ) 13.6, 7.6
Hz, 1H), 3.0 (dd, J ) 14.0, 9.6 Hz, 1H), 2.94 (dd, J ) 13.6, 8.0
Hz, 1H), 2.08 (d, J ) 2.0 Hz, 3H), 1.68 (m, 1H), 1.49 (m, 1H),
1.09 (m, 1H), 0.88-0.82 (m, 6H). 13C NMR (100 MHz, CDCl3) δ
169.49 (d, J ) 3.0 Hz), 161.55 (d, J ) 243.9 Hz), 158.27, 155.83,
138.29 (d, J ) 4.4 Hz), 137.75, 135.81, 134.63, 129.56 (2C), 128.97
(2C), 127.29 (d, J ) 8.1 Hz), 127.09, 125.03, 124.68, 123.76 (d, J
) 18.3 Hz), 122.47, 122.20 (d, J ) 3.7 Hz), 117.0 (d, J ) 22.8
Hz), 73.09, 57.67, 54.54, 53.76, 35.16, 33.77, 26.74, 17.12, 11.35
(d, J ) 3.0 Hz), 11.33. HRMS (ESI) m/z: calcd for C30H35FN3O4S2
[M + H]+ 584.2053; found, 584.2068.
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raphy: EtOAc; yield: 0.160 g, 57%; white solid. H (400 MHz,
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7.18 (m, 1H), 7.14 (d, J ) 2.0 Hz, 1H), 7.0 (dd, J ) 8.8, 2.4 Hz,
1H), 6.91-6.87 (m, 2H), 6.80 (d, J ) 8.0 Hz, 1H), 6.68 (d, J )
8.4 Hz, 1H), 4.28 (m, 1H), 3.92 (m, 1H), 3.82 (s, 3H), 3.16 (dd, J
) 14.8, 4.0 Hz, 1H), 3.04 (d, J ) 6.8 Hz, 1H), 2.96 (dd, J ) 14.8,
7.6 Hz, 1H), 2.85 (d, J ) 7.2 Hz, 1H), 2.16 (m, 2H), 1.60 (m, 1H),
1.36 (m, 1H), 1.01 (m, 1H), 0.83-0.78 (m, 6H). 13C NMR (100
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