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TOXICOLOGICAL SCIENCES 88(2), 434–446 (2005)
doi:10.1093/toxsci/kfi319
Advance Access publication September 14, 2005
A Study of the Relationship between Cornea Permeability and Eye
Irritation Using Membrane-Interaction QSAR Analysis
Yi Li, Jianzhong Liu, Dahua Pan, and A. J. Hopfinger1
Laboratory of Molecular Modeling and Design (MC 781), College of Pharmacy, University of Illinois at Chicago,
833 South Wood Street, Chicago, Illinois 60612-7231
Received July 7, 2005; accepted September 6, 2005
A methodology termed membrane-interaction QSAR (MIQSAR) analysis has been used to develop QSAR models to predict
drug permeability coefficients across cornea and its component
layers (epithelium, stroma, and endothelium). From a training set
of 25 structurally diverse drugs, significant QSAR models are
constructed and compared for the permeability of the cornea,
epithelium, and stroma plus endothelium. Cornea permeability is
found to depend on the measured distribution coefficient of the
drug, the cohesive energy of the drug, the total potential energy of
the drug-membrane ‘‘complex,’’ and three other energy refinement descriptor terms. The endothelium may be a more important
barrier in cornea permeation than the stroma. Moreover, an
investigation of the correlation between cornea permeation and
eye irritation is presented as an example of a cross study on
different ADMET properties using MI-QSAR analysis. Thirteen
structurally diverse drugs, whose molar-adjusted eye irritation
scores (MES) have been measured using the Draize rabbit-eye test,
were chosen as an eye irritation comparison set. A poor correlation (R2 ¼ 0.0232) between the MES measures and the predicted
cornea permeability coefficients for the drugs in the eye irritation
set suggests there is no significant relationship between eye
irritation potency and the cornea permeability.
Key Words: cornea permeability; eye irritation; membraneinteraction quantitative structure-activity relationships (MI-QSAR).
A challenge in drug delivery is the local administration of
drugs to the eye (Lang, 1995; Tasman, 1995). To be effective,
most drugs must pass through the eye’s tissue barriers to reach
therapeutic targets within the globe. The cornea is often the
dominant barrier to drug transport (Tasman, 1995). Thus, the
ability to predict drug transport across the cornea would be
useful in the development of new topical drugs for ophthalmic
diseases. Generating data to characterize corneal permeability
is time-consuming and uses animals. As an alternative, a few
1
To whom correspondence should be addressed at present address: College
of Pharmacy, MSC09 5360, 1 University of New Mexico, Albuquerque, NM
87131-0001. Fax: (505) 272-0704. E-mail: [email protected].
models have been developed to predict cornea permeability of
drug candidates. Most models of transcorneal transport can be
divided into two classes based either on classic transport
thermodynamics and kinetics (Edward and Prausnitz, 2001;
Grass et al., 1988; Yoshida and Topliss, 1996), or on statistical
analysis (Worth and Cronin, 2000).
Classic transport models require assumptions regarding
corneal structure, components and transport pathways, and
a number of physical properties, such as LogP and molecular
radius (Edward and Prausnitz, 1998, 2001). Classic transport
models can partially explain cornea permeation. Cellular membrane permeation has a nonspecific component with regard to
the chemical structure of the solute, largely captured by its
LogP. However, there is also a structure-specific component to
cornea permeability, reflected by the limitation of simply using
LogP in cornea permeability models. There is improvement in
model quality when structure-specific features are included,
e.g., hydrogen-bonding capacity and molecular shape (Worth
and Cronin, 2000).
Construction of a model from statistical analysis, such as
a QSAR model, requires few assumptions. However, the number of calculated trial descriptors of the compounds of the
training set is made as large as possible. A statistical method is
then employed to fit the data in constructing QSAR models.
Moreover, modeling chemically and structurally diverse solute
data sets only involves computation of intramolecular solute
properties. The underlying idea is that if enough solute features
are included, the key intramolecular solute properties of, in this
case, the cornea permeation mechanism will be captured into
the QSAR model. But two questions can be raised: Firstly, is
the trial set of the intramolecular solute descriptors chosen
adequate to capture the requisite mechanistic information?
Secondly, can intramolecular descriptors capture the intermolecular interactions between solutes and cornea cell membranes to adequately explain cornea permeability? Some type
of structure-based design QSAR approach may be necessary to
build a significant QSAR model.
A methodology termed membrane-interaction, MI, QSAR
analysis, where structure-based design is combined with classic
intramolecular QSAR analysis to model diverse compounds
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435
MEMBRANE-INTERACTION QSAR ANALYSIS
interacting with cellular membranes, has been designed to
build ADMET QSAR models (Kulkarni et al., 2001, 2002;
Kulkarni and Hopfinger, 1999). The composite phospholipidrich regions of a membrane bilayer of the cell is assumed to
constitute the ‘‘receptor’’ required in structure-based design.
Membrane-solute interaction properties determined from modeling the solute-membrane complex are added to the intramolecular physicochemical properties of the solute to enlarge
the trial descriptor pool, and supply information needed to
incorporate chemical and structural diversity into the QSAR
analysis.
Three tissues form the cornea: the epithelium, stroma, and
endothelium. The epithelium is composed of seven or so layers
of keratocyte on the external surface of the cornea. The stroma
is primarily composed of large collagen fibers embedded in
a proteoglycan matrix forming the bulk of the cornea. The
corneal endothelium is a monolayer of hexagonal packed cells
at the internal base of the cornea. The rate-limiting tissue
barrier for cornea permeation is the epithelium (Edward and
Prausnitz, 2001; Prausnitz and Noonan, 1998). Since the
epithelium is composed of a multi-layer packing of cells, MIQSAR analysis is ideally suited to construct QSAR models that
can capture the descriptors indicative of the cornea permeability of a drug. In this article we describe a set of MI-QSAR
analyses that model the permeability of cornea, as well as the
permeability of its components: the epithelium and stroma plus
endothelium. The role each tissue component plays in net
cornea permeability is discussed based on the MI-QSAR
models.
In a previous study, MI-QSAR analysis has been successfully applied to build a QSAR model from an eye irritation data
set in which the training set compounds have molar-adjusted
eye irritation scores (MES) measured using the Draize rabbiteye test (Kulkarni et al., 2001). In this current study, based on
the observed MES values and the predicted values of cornea
permeability for 13 compounds, an exploration of the possible
relationship between the cornea permeability and eye irritation
potency of a solute is presented.
MATERIALS AND METHODS
Permeabilities of the cornea, endothelium plus stroma, and epithelium. The dependent variables used in MI-QSAR analysis are the log values
of the permeabilities across the cornea and its components, the endothelium
plus stroma, and the epithelium. The reason for using log values of the
permeabilities is to obtain an approximately uniform distribution of this
dependent variable over its range.
The experiments to determine the permeability of a rabbit cornea for various
compounds have been conducted by researchers from different labs, the details
of which can be found in the cited literatures in a study of library construction
for literature permeability data (Prausnitz and Noonan, 1998). For example, the
measurement of cornea permeability of hydroxypropyl beta cylcodextrin has
been described in detail in a previous study (Tirucherai and Mitra, 2003).
Briefly, it is performed in an incubator at 34C (temperature of the rabbit
cornea). Each compound of interest is placed in isotonic phosphate buffer
solution (IPBS) of a particular pH, and then added to the epithelial side of the
cornea (donor chamber) at concentrations of saturation solubility. In the other
half chamber (receiver chamber), pure IPBS at the same pH value is added. The
cumulative amount of the compound in the receiver chamber is plotted as
a function of time to determine the cornea permeability based on Equation 1:
Permeability ¼
dM=dt
ACd
ð1Þ
In Equation 1, dM/dt is the rate of appearance of solute in the receiver
chamber, Cd is the initial concentration of the solute in the donor chamber, and
A is the cross-sectional area of the barrier available for diffusion.
Prausnitz and coworkers have collected literature permeability data for
almost 150 compounds for transport across the cornea, sclera, and conjunctiva,
as well as the epithelium, stroma, and endothelium (Prausnitz and Noonan,
1998). They subsequently developed theoretical models, based on 25 compounds from the original data set which have permeabilities measures for
both the cornea, and endothelium plus stroma at pH 7.6 ~ 7.65 (Edward and
Prausnitz, 2001). These 25 structurally and chemically diverse compounds,
which also vary in net charge at the common pH, were used as the training set in
the study represented here. Since the cornea is composed of epithelium, stroma
and endothelium layers, the permeability of the epithelium can be expressed as:
1
1
1
¼
Pepi Pcornea Pendoþ stroma
ð2Þ
In Equation 2, Pepi is the estimated permeability of epithelium, and Pcornea,
Pendoþstroma are the measured permeabilities of the cornea and, endothelium
plus stroma, respectively. Log values of the measured and calculated permeabilities of the 25 compounds in the training set are listed in Table 1.
Seven structurally diverse compounds from the original literature permeability data set were used as a test set in this study, and are shown in Table 1.
The cornea permeabilities of the test set compounds were measured at the same
pH as the compounds of the training set.
Thirteen compounds from different chemical classes were used as the eye
irritation data set and are shown in Table 2. These compounds were selected
from a previous MI-QSAR study using the European Center for Ecotoxicology
and Toxicology of Chemicals (ECETOC) data set (Ubels et al., 2000). The
measured molar-adjusted eye scores (MES) of these thirteen compounds are
close to the predicted scores from the resulting MI-QSAR model suggesting the
descriptors of the MI-QSAR model for these compounds are significant.
Solute molecules. The compounds of the training set, test set and eye
irritation data set were constructed using HyperChem software (Hyperchem,
2000). The AM1 partial atomic charges were then added to these molecules.
Structural optimization of each of these training set compounds was carried out
using the Chemlab-II software (Perlstain, 1988).
Construction of the DMPC monolayer. A single dimyristoylphosphatidylcholine (DMPC) molecule was built using HyperChem from available
crystal structure data (Hauser et al., 1981). The aliphatic chains of the DMPC
molecule were assigned the trans-planar, local minimum energy conformation.
The AM1 Hamiltonian in Mopac 6.0 was used for the estimation of partial
atomic charges on all molecules (Mopac, 1990). DMPC is the phospholipid
used in the model membrane in this study. The structure of a DMPC molecule is
shown in Figure 1. An assembly of 25 DMPC molecules (5 3 5 3 1) in (x,y,z)
directions, respectively, was used as the model membrane monolayer. The size
of the monolayer simulation system was selected based on the work done by
van der Ploeg and Berendsen (1982). Additional information regarding
construction of the model DMPC monolayer used in this MI-QSAR analysis
is given in previous references (Kulkarni et al., 2001, 2002; Kulkarni and
Hopfinger, 1999).
To prevent unfavorable van der Waals interactions between a solute
molecule and the membrane DMPC molecules, the ‘‘center’’ DMPC molecule,
located at position (x,y) ¼ (3,3) of the 5 3 5 DMPC monolayer model, was
removed from the monolayer, and a test solute molecule inserted in the space
created by the missing DMPC molecule. Each of the test solute molecules of
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LI ET AL.
TABLE 1
Log Values of the Measured and Calculated Permeabilities
of the Compounds in the Training and Test Sets
TABLE 2
Measured Molar-Based Eye Irritation Scores (MES), and
Predicted Log Values of Cornea Permeability of Compounds
in the Eye Irritation Data Set
Training set
Name
Name
Acebutolol
Acetazolamide
Acetazolamide der. 1c
Acetazolamide der. 2d
Alpha_Yohimbine
Atenolol
Benzolamide
Bromacetazolamide
Chlorzolamide
Clonidine
Corynathine
Levobunolol
Methazolamide
Methazolamide der.e
Metoprolol
Nadolol
Oxprenolol
Phenylephrine
Rauwolfine
Timolol
Trichlormethazolamide
Trifluormethazolamide
Vidarabine
Yohimbine
Measured
LogPcorneaa
Measured
LogPendoþstrom
Calculated
LogPepib
6.07
6.29
6.22
6.25
4.64
6.17
6.86
6.42
4.74
4.51
4.96
4.77
5.43
6.11
4.62
5.80
4.59
6.03
5.04
4.92
4.98
5.41
5.77
4.74
5.03
5.01
5.08
5.01
4.42
4.80
4.96
5.04
4.44
4.33
4.51
4.60
4.70
4.77
4.55
4.82
4.43
4.68
4.64
4.59
4.42
4.74
4.80
4.43
6.03
6.27
6.19
6.23
4.23
6.15
6.85
6.40
4.44
4.06
4.74
4.28
5.33
6.09
3.77
5.74
4.06
6.01
4.82
4.66
4.82
5.30
5.72
4.43
Measured
LogPcornea
Measured
LogPendoþstrom
Calculated
LogPepi
4.14
5.17
4.66
5.72
6.30
5.35
4.44
—
—
—
—
—
—
—
—
—
—
—
—
—
—
Test set
Butyl cellosolve
2,4-Difluoronitrobenzene
1,3-Diisopropylbenzene
2,2-Dimethylbutanoic
Methyl acetate
Methyl isobutyl ketone
Propylene glycol
Cellosolve acetate
Cyclohexanol
1,9-Decadiene
Ethyl acetate
4-Fluoroaniline
Glycerol
Measured MES
Predicted LogPcorneaa
8.99
0.40
0.38
5.59
3.14
0.59
0.10
2.03
8.29
0.37
1.47
6.62
0.12
4.15
3.82
2.67
4.14
3.65
3.59
5.08
3.22
3.73
2.26
3.51
3.73
4.68
a
Predicted log values of cornea permeability were obtained using Equation 8,
the 6-term MI-QSAR model for cornea permeability, as explained in the
Results section.
trial positions of the solute molecule in the monolayer. The three trial positions
are (1) the solute molecule in the headgroup region, (2) the solute molecule
between the headgroup region and the aliphatic chains, and (3) the solute
molecule in the tail region of the aliphatic chains.
The lowest energy geometry of the solute molecule in the monolayer was
sought from the MDS trajectories of each of the three trial solute positions. The
three different initial MDS positions of phenylephrine, one of the training set
solute molecules, are shown in Figure 2a to illustrate this modeling and
simulation procedure. The energetically most favorable geometry of this solute
molecule in the model DMPC monolayer is shown in Figure 2b.
Note. The cornea and endothelium plus stroma permeabilities of the training
set are measured while the epithelium permeabilities are computed.
a
All permeabilities, i.e., Pcornea, Pendoþstrom, and Pepi, are in cm/s.
b
As mentioned in the ‘‘Materials and Methods’’ section, the calculated log
values of epithelium permeability were obtained using Equation 2.
c
Acetazolamide derivative 1: 2-Benzoylamino-1,3,4-thiadiazole-5sulfonamide.
d
Acetazolamide derivative 2: 2-Isopentenylamino-1,3,4-thiadiazole-5sulfonamide.
e
Methazolamide derivative: 5-Imino-4-methyl-1.3.4-thiadiazoline-2sulfonamide.
f
Ethoxzolamide derivative: 6-Nitro-2-benzothiazole-sulfonamide.
Molecular dynamic simulation. MDS were carried out using the Molsim
package with an extended MM2 force field (Doherty, 2000). The selection of
the simulation temperature was based on the phase transition temperature for
DMPC, which is 297 K (Bloom et al., 1991). A simulation temperature of 311
K was selected since it is body temperature, and it is also above the primary
DMPC phase transition temperature. Temperature was held constant in the
MDS by coupling the system to an external fixed temperature bath (Berendsen
et al., 1984). The trajectory step size was 0.001 ps over a total simulation time
of 10 ps for each solute of the training set, the test set, and the eye irritation data
set. Every membrane-solute system, for each of the solutes of the training and
test sets of this study, reached equilibrium by about 1500 trajectory steps, that is
1.5 ps. The MDS trajectory for phenylephrine is shown in Figure 3, and the
lowest energy equilibrium step on the trajectory, near 5300 steps, corresponds
to the phenylephrine-membrane complex geometry shown in Figure 2b. Twodimensional periodic boundary conditions, PBC, corresponding to the ‘‘surface
plane’’ of the monolayer, were adhered to (a ¼ 38 A2, b ¼ 38A2, c ¼ 80 A2, and
c ¼ 96.0) for the DMPC molecules of the monolayer model but not the test
solute molecule. By using PBC, it is possible to simulate an infinite system. The
angle c is the angle an extended DMPC molecule makes with the ‘‘planar
surface’’ of the monolayer. Only a single solute molecule was explicitly
considered in each MDS. Additional details of the membrane-solute MDS can
be found in previous references (Kulkarni et al., 2001, 2002; Kulkarni and
Hopfinger, 1999).
the cornea permeation data set was inserted at three different positions (depths)
in the DMPC monolayer with the most polar group of the solute molecule
‘‘facing’’ toward the headgroup region of the monolayer. Three corresponding
MDS trajectories were generated for each solute molecule with regard to the
Calculation of descriptors. The QSAR descriptors are the various
properties and features of molecules. A descriptor can be intramolecular—an
inherent property of a molecule obtained solely from its chemical structure. The
other class of descriptors is the set of intermolecular properties and features that
Name
Bufuralol
Ethoxzolamide derviative f
Ibuprofen
Sulfacetamide
Sulfanilamide
Glycerol
Aniline
MEMBRANE-INTERACTION QSAR ANALYSIS
437
FIG. 1. The chemical structure of a DMPC molecule having arbitrary atom number assignments.
depend, in part, on the environment in which a molecule is located. These
properties and features are normally computed from the interaction between
two, or more, molecules. Moreover, the descriptors used in the MI-QSAR
analysis can also be divided into (a) general intramolecular solute descriptors,
(b) solute aqueous dissolution and solvation descriptors, and (c) solutemembrane interaction descriptors. A trial pool composed of 65 descriptors
was used in this study.
The general intramolecular solute descriptors included as part of the trial
descriptor pool are defined in Part A of Table 3. The term general is used
because solute descriptors in this class may be useful in building models for
a range of endpoint measures of a solute.
The intermolecular solvation and dissolution descriptors are reported as
Part B of Table 3. Ecoh, the cohesive energy, is a measure of the energy
required to remove a molecule from being surrounded by other molecules
identical to itself. TM, the hypothetical crystal-melt temperature of a solute,
measures the crystal packing strength of a molecule. TG, the glass transition
temperature of a solute, measures the amorphous packing strength of a
molecule. Ecoh, TM, and TG can be considered the properties reflecting the
dissolution behavior of a solute. FH2O, FOCT, and LogP, are the aqueous and 1octanol solvation free energies of the solutes, and the corresponding 1-octanol/
water partition coefficient, respectively. LogDM, the octanol-to-water distribution coefficient of a solute, is the product of the partition coefficient of the unionized solute and the un-ionized fraction of the solute at a selected reference
pH. LogDM is included in the descriptor pool of this study because most of the
solutes in the training and test sets are ionizable molecules, and it is assumed
that only the un-ionized form can partition into membrane. FH2O, FOCT, LogP,
and LogDM can be used to describe the aqueous solvation and lipophilic
properties of a solute. It should be noted that although these seven descriptors
are called intermolecular descriptors, they are all normally computed using
intramolecular computational methods.
The intermolecular solute-membrane interaction descriptors can be extracted directly from the MDS trajectories and are listed in Part C of Table 3.
These particular intermolecular descriptors were calculated using the most
stable (lowest total potential energy) solute-membrane geometry realized from
MDS sampling of the three initial positions, see Figure 2a, for each of the
solutes. Figure 3 shows a plot of the total potential energy versus simulation
time from which the most energetically favorable position of phenylephrine
(one of the solutes of the training set) in DMPC is identified which is shown in
Figure 2b. Details regarding the methods and algorithms used to compute these
solute-membrane descriptors can be found in previous references (Kulkarni
et al., 2001, 2002; Kulkarni and Hopfinger, 1999).
Construction and testing of QSAR models. MI-QSAR models were fit
using multidimensional linear regression (MLR) and optimized using the
genetic function approximation, GFA. GFA is a multidimensional optimization
method based on the genetic algorithm paradigm (Rogers, 1994; Rogers and
Hopfinger, 1994). Statistical significance in the optimization of a QSAR model
using GFA is based on Friedman’s lack of fit (LOF) measure (Friedman, 1988).
438
LI ET AL.
FIG. 2. (a) A ‘‘side’’ view of a phenylephrine molecule inserted at three
different positions in the DMPC model monolayer prior to the start of each of
the three corresponding MDS used in the MI-QSAR analysis. (b) The lowest
energy geometry of a DMPC-phenylephrine complex in the MDS.
The LOF measure is designed to resist overfitting, which is a problem often
encountered in constructing statistical models. Since the number of descriptors
available in a MI-QSAR analysis normally exceeds the number of observations
(training set compounds), the ability to prevent overfitting using GFA is critical
to the successful construction of a statistically significant MI-QSAR model.
Smoothing factors of 0.5–3.0, which control model size, and 100,000 GFA
crossover operations were used to optimize the MI-QSAR models having
different numbers of descriptor terms using the WOLF software (Rogers,
1994). For a given smoothing factor, optimization of a QSAR model was
considered to be realized when descriptor usage became constant and
independent of an increasing number of crossover operations. A crossover
operation is the ‘‘birth’’ of a child model from its parent models.
All 64 intramolecular and intermolecular descriptors in the MI-QSAR trial
descriptor pool were used as linear terms during the evolution of genetic
function approximation to generate MI-QSAR models. In addition, non-linear
terms consisting of spline functions and quadratic term representations of the
descriptors were permitted to be randomly created during the GFA optimization
process and, therefore, used to generate trial MI-QSAR models.
The quality of a QSAR model can be described in two ways, goodness-of-fit
and predictive power. The goodness-of-fit of a MI-QSAR model can be
evaluated using the correlation coefficient of fit, r2. Higher values of r2 indicate
better fitting of the model to the training set data. The predictive power can be
evaluated in two ways. First, the higher the value of the leave-one-out cross
validation coefficient, xv-r2, the higher the predictive capability of the MIQSAR model. Second, the LogPcornea values of the test set compounds can be
predicted using the MI-QSAR model constructed from the training set. Small
differences (residuals) between corresponding observed and predicted
LogPcornea values of the test set compounds indicate high predictivity of the
MI-QSAR model. Moreover, the extent of chance effects/correlations can be
evaluated using ‘‘scrambling’’ experiments, in which the measured dependent
variables, the LogPcornea values of the training set, are randomly ‘‘scrambled’’
with respect to the training set compounds. If meaningful correlations (QSARs)
are found among the scrambled data sets, the significance of a QSAR model is
suspect (Liu et al., 2003; Waterbeemd, 1995). The absence of any significant
correlation for each of the scrambled data sets is taken as evidence of the
significance of the MI-QSAR models with respect to the original, nonscrambled data set.
The overall operational steps and strategy of an MI-QSAR analysis has been
described in detail in a previous reference (Kulkarni et al., 2001).
Correlation between cornea permeability and eye irritation potency. The
LogPcornea for each of the 13 compounds of the eye irritation data set can be
predicted using the MI-QSAR cornea permeation model. The correlation
coefficient of the observed molarity-adjusted eye irritation scores, MES, versus
the predicted LogPcornea values of the compounds in the eye irritation set is then
used to explore the relationship between cornea permeability and eye irritation
potency of a solute molecule.
FIG. 3. The molecular dynamics simulation (MDS) trajectory plot of the total potential energy versus time (ps) for phenylephrine embedded in the model
DMPC monolayer.
439
MEMBRANE-INTERACTION QSAR ANALYSIS
TABLE 3
The Trial MI-QSAR Descriptor Pool
TABLE 3—Continued
Symbols
Symbols
Part A: General intramolecular solute descriptors
MW
Kappa1
Kappa2
Kappa3
Kappa4
Kappa5
Kappa6
Kappa7
Chi1
Chi2
Chi3
Chi4
Chi5
Chi6
Chi7
Chi8
Chi9
Chi10
Chi11
Chi12
D
Dx
Dy
Dz
HOMO
LUMO
Dipole
Molecular weight of solute
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Topological indices
Diffusion coefficient
Diffusion coefficient in x direction
Diffusion coefficient in y direction
Diffusion coefficient in x direction
Highest occupied molecular orbital energy
Lowest occupied molecular orbital energy
Dipolar moment
Part B: Intermolecular solvation and dissolution descriptors
Ecoh
Tg
Tm
FH20
FOCT
LogP
LogDM
Cohesive energy
The hypothetical glass transition temperature of the solute
The hypothetical crystal-melt transition temperature of the
solute
Solvation free energy in water
Solvation free energy in octanol
Calculated octanol/water partition coefficient
Measured octanol/water distribution coefficient
Part C: Intermolecular solute-membrane interaction descriptors
EST
EBD
ETOR
E14
EVDW
ECHG
ESOL V
EHBD
ETOT
INTV
INTC
LEST
LEBO
LETOR
LE14
LEVDW
LECHG
Description of descriptors
Description of descriptors
Total complex stretch energy
Total complex bending energy
Total complex torsional energy
Total complex 1–4 interaction energy
Total complex van der Waals interaction energy
Total complex charge interaction energy
Total complex solvation energy
Total complex hydrogen bonding energy
Total complex total potential energy
Intermolecular van der Waals interaction between solute and
membrane lipid
Intermolecular charge interaction between solute and
membrane lipid
Solute stretch energy
Solute bending energy
Solute torsional energy
Solute 1–4 interaction energy
Solute van der Waals interaction energy
Solute charge interaction energy
LESOLV
LEHBD
LETOT
DEST
DEBD
Solute solvation energy
Solute hydrogen bonding energy
Solute total potential energy
Change (complex-solute alone-membrane
Change (complex-solute alone-membrane
energy
DETOR Change (complex-solute alone-membrane
energy
DE14
Change (complex-solute alone-membrane
interaction energy
DEVDW Change (complex-solute alone-membrane
Waals interaction energy
DECHG Change (complex-solute alone-membrane
interaction energy
DESOLV Change (complex-solute alone-membrane
solvation energy
DEHBD Change (complex-solute alone-membrane
bonding energy
DETOT Change (complex-solute alone-membrane
potential energy
Pos
Docking position of solute
alone) of stretch energy
alone) of bending
alone) of torsional
alone) of 1–4
alone) of van der
alone) of charge
alone) of
alone) of hydrogen
alone) of total
RESULTS
MI-QSAR Models for Cornea Permeability
The combination of linear terms, e.g., 65 general intramolecular solute, intermolecular solvation/dissolution, and intermolecular membrane-solute descriptors, and non-linear terms,
e.g., the spline functions and quadratic functions of those
descriptors, wsere used in the construction of the MI-QSAR
models. Interestingly, no non-linear terms are found in any of
the optimized MI-QSAR models.
Based on the genetic function approximation (GFA) optimization, the best MI-QSAR models, with different numbers of
descriptor terms, for cornea permeability are:
1-term model
LogPcornea ¼ 5:390 þ 0:254LogDM
2
ð3Þ
2
n ¼ 25; r ¼ 0:365; xv r ¼ 0:279
2-term model
LogPcornea ¼ 2:460 þ 0:363LogDM 0:087Ecoh
2
ð4Þ
2
n ¼ 25; r ¼ 0:683; xv r ¼ 0:562
3-term model
LogPcornea ¼ 9:440 þ 0:329LogDM
0:070Ecoh þ 0:004ETOT
2
2
n ¼ 25; r ¼ 0:804; xv r ¼ 0:699
ð5Þ
440
LI ET AL.
4-term model
LogPcornea ¼ 7:080 þ 0:337LogDM 0:068Ecoh
þ 0:004ETOT 0:013ETOR
2
ð6Þ
2
n ¼ 25; r ¼ 0:872; xv r ¼ 0:777
5-term model
LogPcornea ¼ 5:870 þ 0:347LogDM 0:076Ecoh
þ 0:003ETOT 0:015ETOR
0:006DEVDW
2
ð7Þ
energies corresponding to the lowest total potential energy state
of the model system found in the three molecular dynamics
simulations (MDS) for the three initial solute positions in the
membrane.
Kappa5, is a molecular connectivity index, which measures
size and shape features of a molecule (Kier, 1980). It is a general intramolecular solute descriptor.
The computed values of LogDM, Ecoh, ETOT, ETOR,
DEVDW, and INTC found in the 1–6 term MI-QSAR models
for each compound in the training and test sets are listed in
Table 4. The energy term descriptors are expressed in kcal/mol.
The observed and predicted values of cornea permeability of
the training and test set compounds, using the 4–7 term MIQSAR models, are given in Table 5. None of the compounds in
2
n ¼ 25; r ¼ 0:914; xv r ¼ 0:830
6-term model
TABLE 4
Computed Values of the Six Descriptors Found to be the
Significant MI-QSAR Descriptor Terms in Equations 3–8
LogPcornea ¼ 5:310 þ 0:238LogDM 0:054Ecoh
þ 0:003ETOT 0:018ETOR
0:009DEVDW 0:006INTC
2
ð8Þ
Name
LOGDM Ecoh
2
n ¼ 25; r ¼ 0:933; xv r ¼ 0:886
LogPcornea ¼ 13:800 þ 0:225LogDM 0:053Ecoh
þ 0:004ETOT 0:017ETOR 0:010DEVDW
2
ETOR DEVDW INTC
Training set
7-term model
0:006INTC 0:043Kappa5
ETOT
ð9Þ
2
n ¼ 25; r ¼ 0:939; xv r ¼ 0:892
The number of compounds used to construct the correlation
equation is given by n, r2 is the coefficient of determination,
and xv-r2 is the leave-one-out-cross-validation coefficient of
determination.
LogDM, defined as the observed octanol/water distribution
coefficient, is the product of un-ionized octanol/water partition
coefficient and the fraction of un-ionized solute at pH of 7.6.
Ecoh, the solute cohesive energy, is the average energy needed
to remove a solute molecule from its nearest neighbors.
LogDM and Ecoh are intermolecular solvation and dissolution
descriptors.
ETOT, is the total energy of the entire solute-membrane
system and ETOR is the torsional energy component of the
entire solute-membrane system. DEVDW is the difference between the van der Waals interaction energy of the entire solutemembrane system and the van der Waals interaction energy of
solute alone plus that of membrane alone. INTC is the intermolecular electrostatic energy between solute and membrane.
It is re-iterated that ETOT, ETOR, DEVDW, and INTC are the
Acebutolol
Acetazolamide
Acetazolamide der. 1
Acetazolamide der. 2
Alpha_Yohimbine
Atenolol
Benzolamide
Bromacetazolamide
Chlorzolamide
Clonidine
Corynathine
Levobunolol
Methazolamide
Methazolamide der.
Metoprolol
Nadolol
Oxprenolol
Phenylephrine
Rauwolfine
Sotalol
Timolo
Trichlormethazolamide
Trifluormethazolamide
Vidarabine
Yohimbine
0.07
1.31
0.38
0.53
2.15
2.11
1.38
2.02
1.49
2.16
2.24
0.56
0.38
3.60
0.80
1.77
0.01
2.72
0.70
2.30
0.09
2.50
1.28
1.46
2.10
39.57 1826.22
32.81 1703.35
39.29 1611.11
31.13 1715.65
36.04 1842.40
33.01 1803.19
39.34 1743.09
36.55 1715.99
33.47 1749.03
20.62 1841.75
36.77 1749.75
31.39 1910.03
32.20 1802.06
26.05 1774.71
27.09 1826.72
39.86 1850.61
26.85 1939.57
25.11 1759.84
34.65 1875.58
30.04 1844.41
36.97 1884.3
37.56 1825.33
33.07 1787.50
37.90 1826.56
36.77 1730.95
Test set
217.97
199.04
221.80
239.36
195.29
205.86
200.48
183.64
191.35
187.20
193.49
231.37
203.94
201.36
187.92
190.66
200.47
202.97
220.23
210.92
203.26
216.35
197.90
188.97
181.80
Bufuralol
Ethoxzolamide der.
Ibuprofen
Sulfacetamide
Sulfanilamide
Glycerol
Aniline
1.40
2.00
0.68
2.62
0.72
2.32
0.92
26.90
31.74
20.36
25.81
19.66
21.76
10.59
191.10 20.38
192.00
34.01
191.98
9.62
192.85
9.19
203.35
47.30
168.38 5.13
182.32
56.86
1925.14
1786.50
1818.72
1607.44
1794.56
1879.95
1811.13
7.84
57.24
43.30
54.21
13.40
65.38
1.88
52.84
30.81
10.15
21.50 125.13
23.10
79.76
23.61
96.53
12.00
46.37
21.79
21.75
7.37
42.71
3.47
18.07
6.43
11.43
12.39 132.17
7.65
10.47
42.20 125.40
16.44
56.34
38.2
43.86
3.22
28.49
47.82
72.15
21.70
58.54
48.70 29.98
39.96
84.52
47.70
49.19
10.39
43.59
46.44
50.94
13.36
66.10
134.69
116.59
82.50
Note. The descriptors are defined in Table 3. All energies are in kcal/mol.
MEMBRANE-INTERACTION QSAR ANALYSIS
TABLE 5
The Observed and Predicted Log Values of Cornea Permeability
Using the 4–7 Term MI-QSAR Models
Name
Obsd LogPcornea 4-term 5-term 6-term 7-term
Training set
Acebutolol
Acetazolamide
Acetazolamide der. 1
Acetazolamide der. 2
Alpha_Yohimbine
Atenolol
Benzolamide
Bromacetazolamide
Chlorzolamide
Clonidine
Corynathine
Levobunolol
Methazolamide
Methazolamide der.
Metoprolol
Nadolol
Oxprenolol
Phenylephrine
Rauwolfine
Sotalol
Timolo
Trichlormethazolamide
Trifluormethazolamide
Vidarabine
Yohimbine
6.07
6.29
6.22
6.25
4.64
6.17
6.86
6.42
4.74
4.51
4.96
4.77
5.43
6.11
4.62
5.80
4.59
6.03
5.04
6.00
4.92
4.98
5.41
5.77
4.74
Test set
5.92
6.09
6.84
6.18
4.58
6.09
6.43
6.33
4.92
4.88
4.92
5.02
5.43
6.17
4.93
6.07
4.40
5.88
5.18
5.87
5.29
4.90
4.91
5.90
4.88
5.85
6.23
6.69
6.10
4.67
5.88
6.51
6.37
4.70
4.83
4.84
4.96
5.37
6.11
4.72
5.77
4.38
5.97
5.11
6.09
5.10
5.14
5.03
6.13
4.80
5.77
6.21
6.58
6.18
4.66
6.05
6.45
6.34
4.74
4.70
4.93
4.95
5.12
6.40
4.45
5.73
4.61
5.91
5.07
6.21
5.02
5.00
5.47
5.95
4.85
5.93
6.21
6.63
6.21
4.61
6.16
6.43
6.33
4.74
4.61
4.89
4.95
5.10
6.27
4.59
5.72
4.69
5.86
4.89
6.26
5.05
5.03
5.50
5.86
4.85
Bufuralol
Ethoxzolamide der.
Ibuprofen
Sulfacetamide
Sulfanilamide
Glycerol
Aniline
4.14
5.17
4.66
5.72
6.30
5.35
4.44
3.86
4.50
4.06
6.32
4.71
4.63
3.21
3.58
4.56
3.90
6.18
4.81
4.40
3.26
3.76
4.87
4.01
6.10
5.68
4.68
4.14
3.70
4.82
4.02
6.12
5.61
4.59
4.08
either the training or test sets is an outlier for any of the 4–7
term MI-QSAR models.
A QSAR model is usually considered significant if it has
a coefficient of determination (r2) greater than 0.7. The 1-term
MI-QSAR model, Equation 3, has r2 of 0.365, which suggests
that no descriptor, by itself, can significantly explain the variance of the dependent variable, LogPcornea. The 2-term and 3term models represent a distinctly large statistical improvement
over the 1-term model since the coefficient of determination, r2,
increases from 0.365 to 0.804 as the number of terms increases
from 1 to 3. The 3-term MI-QSAR model may capture the
essential features of the mechanism responsible for cornea
permeability as represented by the LogPcornea values, see the
Discussion section. However, increasing the number of descriptor terms in the MI-QSAR models from 3 to 7, increases
r2 from 0.804 to 0.939, which may indicate that the 4–7-term
MI-QSAR models successively refine, as opposed to overfit,
441
the 3-term model for the training set. The possible significance
of the descriptors added in the 4–7 term MI-QSAR models is
that they begin to further reveal the essence of the mechanism
of cornea permeation that may only be further ascertained by
consideration of an expanded training set.
The predictive power of a QSAR model can be explored
using the cross-validation coefficient of determination, xv-r2,
for the training set, and the differences between observed and
predicted values of the dependent variable for the test set.
Figure 4 contains a plot of xv-r2 for the training set as a function
of the number of descriptor terms in the model. The 6-term and
7-term models have the highest values of xv-r2, 0.886 and
0.892, which may indicate that the 6-term and 7-term models
have the most predictive capability. Figure 5 shows the
observed versus predicted LogPcornea values for the test set
using the 4–7 term MI-QSAR models. The smallest average
difference between the observed and the measured cornea
permeability of the test set is obtained using the 6-term model.
This finding suggests that the 7-term model may somewhat
overfit the training set data, and that the 6-term model has the
highest predictive power.
Scrambling experiments to ascertain the validity of the 6term model lead to scrambled models with an average xv-r2
value of 0.477 as shown in Table 6. These low xv-r2 values for
the scrambling experiments suggest that the 6-term model is
a significant MI-QSAR model, and not the result of chance
correlation.
Still, the 4-term model, Equation 6, seemingly captures the
essential features of cornea permeation. This model has an r2 of
0.872 and a xv-r2 of 0.777, indicating it is a significant model.
Therefore, descriptors in the 4-term model might most reflect
the biological mechanism of cornea permeation. The significance of other descriptor terms in the 5-term and 6-term models
need to be further explored by expanding the size of the
training set.
FIG. 4. The leave-one-out-cross-validation coefficients of determination,
xv-r2, for 1–7 term MI-QSAR models versus the numbers of terms in the
corresponding models.
442
LI ET AL.
FIG. 5. The observed versus predicted log values of cornea permeability, LogPcornea, for the compounds of the test set using the 4–7 term MI-QSAR models.
4-term model
MI-QSAR Models for Permeability of the Cornea
Components
The best MI-QSAR models with different numbers of
descriptor terms for epithelium permeability of the training
set compounds listed in Table 1 are:
LogPepi ¼ 7:098 þ 0:405LogDM 0:091Ecoh
þ 0:005ETOT 0:017ETOR
n ¼ 25; r2 ¼ 0:851; xv r2 ¼ 0:761
1-term model
LogPepi ¼ 5:186 þ 0:299LogDM
2
ð10Þ
2
5-term model
LogPepi ¼ 5:470 þ 0:423LogDM 0:102Ecoh
n ¼ 25; r ¼ 0:318; xv r ¼ 0:228
þ 0:004ETOT 0:019ETOR
2-term model
LogPepi ¼ 1:343 þ 0:442LogDM 0:114Ecoh
0:009DEVDW
ð11Þ
2
2
3-term model
þ 0:004ETOT
ð12Þ
TABLE 6
The Leave-One-Out Cross Validation Coefficients, xv-r2, of the
MI-QSAR Models from the Ten Scrambled Data Sets
2
3
4
5
6
7
LogPepi ¼ 4:710 þ 0:275LogDM 0:072Ecoh
þ 0:004ETOT 0:023ETOR
0:013DEVDW 0:009INTC
n ¼ 25; r2 ¼ 0:780; xv r2 ¼ 0:675
8
9
10
0.587 0.798 0.459 0.541 0.341 0.477 0.343 0.387 0.543 0.292
xv-r2
Average 0.477 < 0.886a
xv-r2
0.886 is the value of xv-r2 of the 6-term MI-QSAR model, Equation 8,
from the original training set.
a
2
6-term model
LogPepi ¼ 10:126 þ 0:400LogDM 0:093Ecoh
1
ð14Þ
n ¼ 25; r ¼ 0:904; xv r ¼ 0:814
2
n ¼ 25; r ¼ 0:0:659; xv r ¼ 0:537
Set
ð13Þ
2
ð15Þ
2
n ¼ 25; r ¼ 0:936; xv r ¼ 0:891
The descriptors found in Equations 10–15 are exactly the same
as those found in Equations 3–8. The values of the coefficient
of determination, r2, and the cross-validation coefficient of
determination, xv-r2, of Equations 10–15, are similar to those
corresponding values of Equations 3–8, indicating that the MIQSAR models for epithelium permeability, Equations 3–8,
may have a similar goodness-of-fit and predictive power to the
MI-QSAR models for cornea permeability, Equations 10–15.
MEMBRANE-INTERACTION QSAR ANALYSIS
The 4-term model for epithelium permeability, Equation 13,
can be considered as the best QSAR model to describe the basic
features of epithelium permeation behavior of a compound
relative to the size of the training set.
Finally, the best MI-QSAR models with different numbers of
descriptor terms for endothelium plus stroma permeability for
the training set compounds listed in Table 1 are:
1-term model
LogPendo þ stroma ¼ 4:676 þ 0:063LogDM
2
ð16Þ
2
n ¼ 25; r ¼ 0:223; xv r ¼ 0:107
2-term model
LogPendo þ stroma ¼ 3:643 þ 0:102LogDM 0:031Ecoh ð17Þ
n ¼ 25; r2 ¼ 0:609; xv r2 ¼ 0:480
3-term model
LogPendo þ stroma ¼ 5:691 þ 0:092LogDM
0:026Ecoh þ 0:001ETOT
ð18Þ
n ¼ 25; r2 ¼ 0:711; xv r2 ¼ 0:569
4-term model
LogPendo þ stroma ¼ 4:624 þ 0:094LogDM 0:025Ecoh
þ 0:001ETOT 0:006ETOR
2
ð19Þ
2
n ¼ 25; r ¼ 0:837; xv r ¼ 0:754
5-term model
LogPendo þ stroma ¼ 4:814 þ 0:095LogDM 0:024Ecoh
443
The four terms in Equations 16–19 are the same as the
corresponding terms in Equations 3–6. However, two terms,
LETOR and Kappa3, in Equations 20 and 21, are different
from two terms, DEVDW and INTC, in Equations 7 and 8.
LETOR is the intramolecular torsional energy of the solute
molecule in the solute-membrane complex having the lowest
total potential energy state. Although LETOR describes an
intramolecular property of the solute, it is classified as an intermolecular solute-membrane interaction descriptor because
it is calculated using data explicitly determined for the
membrane-solute complex. Kappa3, a topological index, is a
general intramolecular descriptor measuring the size and shape
of the solute.
The values of r2 and xv-r2 of Equations 16–21 are less than
those of Equations 3–8, respectively. Thus, the MI-QSAR models
for endothelium plus stroma, Equations 16–21, have less significant fit to the training set, and less predictive power, than the
MI-QSAR models for cornea permeability, Equations 3–8.
The 4-term model for endothelium plus stroma permeability,
Equation 19, can be considered as the best QSAR model to describe the basic features of endothelium plus stroma permeation behavior of a compound relative to the limited size of the
training set.
Correlation between Eye Irritation Potency and Cornea
Permeability
The 6-term MI-QSAR model, Equation 8, is used to predict
the LogPcornea values of the thirteen compounds in the eye
irritation set listed in Table 2. The MES values in Table 2 are
the molar-adjusted eye irritation scores for the thirteen compounds. The larger the MES value, the greater the eye irrtation
potency. Moreover, Figure 6 contains a plot of the predicted
values of LogPcornea versus the MES values of the eye irritation
set of compounds. The corresponding correlation coefficient
squared, R2, is 0.023, which indicates there is no correlation
between eye irritation potency and the cornea permeability of
a solute. That is, for the data sets used in this study, eye
irritation is not correlated to cornea permeability.
þ 0:001ETOT 0:004ETOR
0:007LETOR
2
ð20Þ
2
n ¼ 25; r ¼ 0:863; xv r ¼ 0:774
6-term model
LogPendo þ stroma ¼ 5:370 þ 0:095LogDM 0:020Ecoh
þ 0:001ETOT 0:004ETOR
0:010LETOR 0:025Kappa3
2
2
n ¼ 25; r ¼ 0:904; xv r ¼ 0:832
ð21Þ
FIG. 6. The predicted log values of cornea permeability versus the
observed molar-adjusted eye irritation score (MES) for the compounds of the
eye irritation set.
444
LI ET AL.
DISCUSSION
MI-QSAR Models for Cornea Permeability
The octanol/water distribution coefficient, LogDM, of
a molecule is the product of the neutral octanol/water partition
coefficient, LogP, and the fraction of the un-ionized solute
molecule. In the MI-QSAR model of highest predictivity for
cornea permeability, Equation 8, LogDM is positively correlated to LogPcornea indicating that increasing solute LogP, and/
or increasing the population of the solute in the un-ionized
form, can increase cornea permeation. This finding is similar to
reported observations where logDM has been shown to have
a direct positive relationship to cornea permeability (Edward
and Prausnitz, 2001; Prausnitz and Noonan, 1998). An increase
in LogP, reflecting an increase in lipophilicity, always corresponds to an increase in cornea permeability. Moreover, it is
thought that only the un-ionized form of a solute permeates the
membrane. Hence, less ionized solute molecules permeate the
cornea in higher concentrations of un-ionized form, which
corresponds to higher cornea permeabilities. It is important to
note that although the descriptor pool used for MI-QSAR
model construction includes both LogP and LogDM, only
LogDM is found in the optimized MI-QSAR models. This
finding strongly suggests that the ionization behavior of
a solute in water is, in turn, a factor in its cornea permeation
behavior.
Ecoh, the cohesive energy, which is the interaction energy of
a molecule with its like neighbors, describes the dissolution
behavior of a molecule. The greater the value of Ecoh, the more
difficult it is to dissolve a solute molecule in a solvent. Ecoh has
a negative regression coefficient in Equation 8, indicating an
increase in Ecoh corresponds to a decrease in cornea permeability. This relationship suggests that as dissolution of a solute
becomes more difficult, the lower will be cornea permeability
of the solute molecule.
ETOT, the total potential energy of the solute-membrane
complex, is positively correlated to cornea permeability in
Equation 8. This relationship indicates that a higher total
potential energy of the complex corresponds to higher cornea
permeability of the solute. The value of ETOT represents the
strength of solute binding to the membrane and the stability of
solute-membrane complex. A higher ETOT corresponds to less
binding of the solute to the membrane structure and, hence,
greater permeation across the cornea membrane.
ETOR, the total torsion energy of the solute-membrane complex, is always positive in energy value and measures the extent
of torsional deformation energy that occurs in the membranesolute system. The greater the value of ETOR, the greater
torsional deformation energy needed for the solute to navigate
through the membrane (Kulkarni et al., 2002). The regression
coefficient for this descriptor is negative in Equation 8, and
LogPcornea is predicted, as expected, to decrease as ETOR
increases.
DEVDW is the difference between the van der Waals interaction energy of the entire solute-membrane system, and the
van der Waals interaction energy of solute alone plus that of
membrane alone. This term is a measure of the steric deformation in the solute-membrane complex that occurs with uptake
of the solute. The negative regression coefficient of DEVDW
in Equation 8 indicates, as expected, that an increase in
steric deformation energy interaction of the membrane, due
to solute uptake, corresponds to a decrease in solute cornea
permeability.
INTC, the electrostatic interaction energy between the solute
and membrane, is negatively correlated to LogPcornea in
Equation 8, indicating that cornea permeability decreases as
the value of INTC increases. This relationship between
LogPcornea and INTC is counter-intuitive. As INTC increases,
there is less electrostatic binding of the solute to the membrane,
and, consequently, LogPcornea should increase. Perhaps INTC is
a ‘‘correction term’’ to the more significant descriptors involving membrane-solute interactions found in Equations 3–5.
Based on the analysis of the terms in Equation 8, MI-QSAR
models for cornea permeability can be mechanistically interpreted as consisting of the following contributing factors:
Lipophilicity—An increase in lipophilicity of the solute, as
measured by an increasing value of LogDM, increases
cornea permeability.
Fraction of un-ionized solute—A higher fraction of un-ionized
solute corresponds to a higher cornea permeability.
Dissolution—A solute that is hard to completely dissolve in an
aqueous solvent, as measured by a high value of Ecoh, has
low cornea permeability.
Distortion of the membrane-solute complex—The more the
structural distortion of the membrane-solute complex, the
lower the cornea permeability.
Solute-membrane binding—The greater the binding of the
solute to the membrane, the less is the cornea permeability.
MI-QSAR analysis is able to generate meaningful ADME
property models for cornea permeability employing a limited
number of descriptors that can be directly interpreted in terms
of a physically reasonable mechanism of action.
MI-QSAR Models for Permeability of the Cornea
Components
The MI-QSAR models for epithelium permeability, Equations 10–15, have the same respective descriptor terms as the
MI-QSAR models for cornea permeability, Equations 3–8.
That is, epithelium permeation appears to be nearly identical,
in terms of mechanistic action, to permeation across the entire
cornea. Moreover, the epithelium is the main barrier in passing
through the cornea for 20 of the 25 compounds of the training
set. This behavior is indicated by the lower permeability values
of epithelium of the 20 compounds than the corresponding
permeation values for the stroma plus endothelium given in
445
MEMBRANE-INTERACTION QSAR ANALYSIS
Table 1. Thus, permeation of the epithelium largely governs
permeation behavior across the entire cornea.
The endothelium and stroma are, in composite, the main
barrier of cornea permeation for the other five compounds
in the training set, which are alpha-yohimbine, clonidine,
levobunolol, metoprolol, and oxprenolol. Based on a comparison of the descriptor terms, and the corresponding regression coefficients in the 4-term models, Equations 13 and
19, permeation in the epithelium may be faster than
permeation in the endothelium and stroma if a solute has
high values of LogDM, ETOT, and/or low values of
Ecoh, ETOR. As shown in Table 4, alpha-yohimbine and
levobunolol have high values of LogDM, while clonidine,
metoprolol and oxprenolol have low values of Ecoh.
Moreover, all five compounds have high values of ETOT
and low values of ETOR.
The values of r2 and xv-r2 of the 4-term MI-QSAR model
for permeability of the stroma plus endothelium, Equation 19,
are 0.837 and 0.754, respectively. This information may give
some hint as to which component, stroma or endothelium,
plays a more important role in the permeation through the
cornea in the absence of the epithelium. MI-QSAR analysis is
designed for investigating ADMET properties where the cell
membranes play a role. Therefore, MI-QSAR analysis can
only yield significant QSAR models that involve membranesolute interaction descriptors for a training set in which the
main barriers to cornea permeation involve membranes, that
is, the epithelium or the endothelium, but not the stroma. The
MI-QSAR model for stroma plus endothelium, Equation 19, is
significant since it has a value of r2 greater than 0.7, and half
the descriptors are explicit membrane-solute descriptors.
These QSAR features suggest that the endothelium cellular
component is the main-barrier to solute permeation across
a cornea without an epithelium layer. Since both Equations 13
and 19 are QSAR models for permeation dominated by the
endothelium and the epithelium cellular components, respectively, it is not surprising that these two models have common
descriptor terms. The comparison between the MI-QSAR
models for the cornea and its components leads to revealing
information with respect to the main barriers in solute
permeation.
Correlation between Eye Irritation Potency and Cornea
Permeability
A major finding from this study is that there is no meaningful relationship between eye irritation potency and cornea
permeability based on the data sets used in the analyis. This
non-relationship can be gleaned from the low value of the
square of the correlation coefficient, R2, between the predicted
values of LogPcornea versus the observed MES values for the
thirteen compounds in the eye irritation set.
Employing a similar descriptor pool to that used in this
current study, a significant QSAR model for eye irritation has
been constructed using MI-QSAR analysis in a previous study
(Kulkarni et al., 2001):
MES ¼ 0:660 0:010Eðchg þ vdwÞ
0:480FðH2 OÞ þ 0:390LUMO
2
ð22Þ
2
n ¼ 36; r ¼ 0:710; xv r ¼ 0:650
Where, MES is the molar-adjusted eye score, E(chgþvdw)
is the electrostatic plus van de Waals interaction energy
between the solute and the membrane at the total system
minimum potential energy, F(H2O) is the aqueous solvation
energy computed using a hydration shell model (Hopfinger,
1973), and LUMO is the lowest unoccupied molecular orbital energy. This QSAR model suggests that the eye irritation potency of a solute is partially related to its chemical
reactivity potency, as represented by the LUMO descriptor.
However, in the QSAR model for cornea permeability,
Equation 6, no descriptor related to reactivity potencyis
present. This difference in the two QSAR models may account, at least in part, for the lack of a relationship between
eye irritation potency and cornea permeability. In addition, for
Equation 22 as E(chgþvdw) becomes more negative in value,
the binding of the solute to the membrane increases, and the
eye-irritation potency correspondingly increases. However, in
the QSAR model for cornea permeability, Equation 6, as
ETOT becomes more negative in value, the binding of the
solute to the membrane increases, but cornea permeability
decreases. Thus, solute-membrane binding leads to something
of an inverse relationship between eye irritation potency and
cornea permeability according to the QSAR models. The lack
of a relationship between cornea permeability and eye irritation potency, based on the MI-QSAR analysis, suggests
that a change in the value of any term (molecular property)
in the MI-QSAR model for cornea permeability, Equation 6,
will change cornea permeability, but have a minimal effect on
eye irritation potency, and vice versa.
In general, MI-QSAR analysis can be employed to do cross
comparison studies on pairs of ADMET properties provided
significant MI-QSAR models can be constructed for each
property of the pair. If there is no apparent relationship
between a pair of ADMET properties, then it is likely that
a change in the value of any descriptor (property) of the MIQSAR model for one of the pair, will not produce a change in
the other ADMET property. If a relationship is established for
a pair of ADMET properties, then a change in the value of any
term (property) in the MI-QSAR model of one ADMET
property of the pair, can be used to estimate the change in the
other ADMET property. This ‘‘design’’ capability should be
useful to optimize the influence of multiple, and coupled,
ADMET properties that may be both good and bad features,
but which are governed by very similar molecular mechanisms and interactions.
446
LI ET AL.
ACKNOWLEDGMENTS
Resources of the Laboratory of Molecular Modeling and Design at UIC, and
of The Chem21 Group Inc. were used in performing this work. We are also
grateful for support from Avon and The Procter & Gamble Company in
performing this study.
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