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the Amber 94 force field in gas state. Second, they were
placed in a periodic solvent box whose volume was X=12 Å,
Y=10 Å, Z=24 Å, which included 96 water molecules. The
temperature was 298 K and the pressure was 101.325 kPa.
Then, the compounds in water were minimized by using the
method described earlier. The compounds in water were
simulated by using the Monte Carlo method at 300 K, and
minimized by using the method described earlier. The Monte
Carlo method, which samples from the random
conformations generated by the Boltzmann distribution under a
certain temperature, simulates the molecular movement and
kinetic properties of the equilibrium state. It uses a logarithm
to calculate a conformation based on the previous one, and
obtains a continuous conformation sequence that forms a
trace in image space. Dynamic simulation uses dynamic
equations to generate new conformations, whereas the Monte
Carlo method uses a statistical sampling technique to
produce the trace of the image space. That is to say, dynamic
simulation calculates average value according to time,
whereas the Monte Carlo method computes the statistical
mean value from averaging each conformation. If the
primary parameter is appropriate, both the Monte Carlo and the
dynamic method can reach equilibrium. However, the Monte
Carlo method is usually faster. Here, we used a Monte Carlo
simulation to gain the steady-state conformation of the
solute in the solvent[22].
The phospholipid dimyristoylphosphatidylcholine
(DMPC) was selected as the model phospholipid in the
present study. A single DMPC (Figure 1) molecule was built
using Hyperchem 7.5 from the available crystal structure
data[23]. A model of the DMPC membrane monolayer was constructed
by using the software Material Studio (version 2.2.1; Accelrys,
San Diego, CA, USA). According to the work done by van
der Ploeg and Berendsen, the DMPC monolayer is composed
of 25 DMPC molecules
(5×5×1)[24]. The unit cell parameters
used for building the DMPC monolayer were a=8 Å, b=8 Å,
c=32 Å, and g=96.0 º, which yield an average surface area per
phospholipid of 64 Å2, similar to the value found by Stouch
experimentally[25]. Therefore, we can consider the DMPC
membrane monolayer model to be reasonable.
Molecular dynamic simulation To prevent unfavorable
van der Waals interactions between a solute molecule and
the membrane DMPC molecules, one of the "center" DMPC
molecules was removed from the DMPC model described
and an organic compound (solute) was inserted in the space
created by the missing DMPC molecule to form a
solute-membrane complex. The solute was inserted at 3 different
positions in the DMPC model and 3 corresponding
molecular dynamic simulation (MDS) models were generated for
each compound. The 3 different positions (depths) were: (1)
solute molecule in the head group region; (2) solute
molecule between the head-group region and the aliphatic
chains; and (3) solute molecule in the tail region of the
aliphatic chains. MDS of the complex was performed by using
the Discover module of Material Studio, using a compass
force field. A simulation temperature of 311 K was selected
and 2-dimensional periodic boundary conditions
corresponding to the "surface plane" of the monolayer were used
(a=32 Å, b=32 Å, c=80 Å, and g=96.0°) for the DMPC model. In
order to equilibrate the solute-membrane complex gradually
and fully, the MDS course was carried out with 3 phases: (1)
simulation at 120 K for 1500 steps (1.5 ps); (2) simulation at
220 K for 1500 steps (1.5 ps); and (3) simulation at 311 K for
10 000 steps (10 ps).
Calculation of descriptors Most of the intramolecular
solute descriptors were calculated by using the commercial
software package CS Chem3D Ultra 7.0 (Chemoffice 2002;
Cambridgesoft, Cambridge, MA, USA), which included
molecular mechanism (MM) parameters (such as bending energy,
torsion energy and van der Waals energy), quantum
chemistry parameters (such as electronic energy, HOMO, and
LUMO energy), hydrophobic parameters (such as Clog
P), and stereo parameters (such as Es and Balaban index). The
data of QO,N and
QH comes from Fu and Liang¡¯s
study[20].
The intermolecular solute-membrane interaction
descriptors were extracted directly from the MDS trajectories in which
the solute-membrane complex had the lowest energy geometry. These descriptors were mainly energy parameters.
The total energy of a system can be expressed as
follows[21]:
Etotal=Evalence
+Ecrossterm+Enonbond
Construction and testing of MI-QSAR
models MI-QSAR models of permeation of the cornea by organic compounds
were constructed by using the partial sum of squares for
regression using the SPSS software package (Chicago,USA).
A training set of 28 structurally diverse compounds whose
corneal permeability coefficients have been measured
in vivo was used to construct the MI-QSAR models. Molecular
dynamics simulations were used to determine the explicit
interaction of each test compound with the DMPC model.
An additional set of intramolecular solute descriptors were
computed and considered in the trial pool of descriptors for
building MI-QSAR models. The MI-QSAR models were
optimized by using multidimensional linear regression fitting
and a stepwise method. A test set of 8 compounds was
evaluated by using the MI-QSAR models as part of a
validation process. A principal components analysis (PCA) was
performed by using SPSS to identify the principal
components of the constructed models.
Application package for models A forecasting
application package of the constructed models was built using the
MFC module of the commercial software packages Microsoft
Visual C++ (version 6.0; Microsoft Corporation, USA).
Results
Construction of solute molecules and a DMPC
monolayer Figure 2 shows the dominant conformation of
compound No 1 labeled by atom-type in water. The box denotes
the water solvent box defined in the Monte Carlo
simulation.
Molecular dynamic simulation The energy of a solute
inserted in the middle position of the DMPC model was lower
than that of a solute inserted in the other 2 positions. Figure
3 shows the dominant conformation of a solute-membrane
complex in the MDS. The DMPC molecules appear as white
sticks. The molecule depicted using spheres represents an
organic compound. The white box indicates the border of
the volume. Figure 4 is a "side" view of the molecule in
Figure 3.
Construction and testing of MI-QSAR
models MI-QSAR analysis was used to develop predictive models of corneal
permeability of some organic compounds and simulate the
interaction of a solute with the phospholipid-rich regions of
cellular membranes. Molecular descriptors of 28 compounds
in the training set and 8 compounds in the test set are listed
in Table 3 and Table 4, respectively. Six MI-QSAR equations
were constructed based on the information in Table 3:
log P=4.201-2.585
QH2
n=28 R=0.860 S=0.2750
R2=0.730 F=74.071 (1)
log P=3.972-2.388
QH2-0.207
QO,N
n=28 R=0.897 S=0.2433
R2=0.789 F=51.407 (2)
log P=4.488-5.230
QH2-0.236
QO,N+2.768 QH
n=28 R=0.939 S=0.193 1
R2=0.867 F=59.628 (3)
log P=4.354-4.925
QH2-0.216
QO,N+2.533
QH+1.576×10-3
dT
n=28 R=0.950 S=0.1785
R2=0.886 F=53.656 (4)
log P=4.324-4.396
QH2-0.288
QO,N+2.106
QH+2.163×10-3
dT+1.795×10-4 PMIX
n=28 R=0.962 S=0.1605
R2=0.908 F=54.355 (5)
log P=3.885-4.290
QH2-0.304Q
O,N+2.171QH+2.366×10
-3 dT
+3.453×10-4
PMIX-1.22×10-3 SAS
n=28 R=0.976 S=0.1301
R2=0.940 F=70.957 (6)
where QH is the sum of net atomic charges of hydrogen atoms attached to the heteroatoms (N, O),
QO,N is the sum of the absolute values of the net atomic charges of oxygen and
nitrogen atoms, dT is the conformational flexibility of the
solute-membrane complex, PMIX is the principal moment of
inertia (X), and SAS is the Connolly accessible area.
PMIX and SAS are intramolecular solute descriptors that came from
the CS calculation. dT is related to interactions between a
solute and the DMPC model. It represents the change in the
dihedral torsion energy of the solute-membrane complex,
compared with that of the DMPC model, that is,
DEtorsion. Here, n is the number of organic compounds,
R is the correlation coefficient, S is the standard deviation and
F is the F-statistic.
Figure 5 is a diagnostic plot of the MI-QSAR models:
R is the correlation coefficient and
S is the standard deviation of the best x-term model, where x is plotted on the X-axis for the
28 compounds of the training set. From this plot we can see
that with the increase of the variable from 1 to 6, the relativity
of MI-QSAR equations is also improved, and the predictive
ability of the models is enhanced. The observed and
predicted log P values of the training set are listed in Table 5.
A test set of 8 organic compounds was constructed as
one way to attempt to validate the MI-QSAR models given
by the 6 equations mentioned. The compounds of the test
set were selected from different groups of ophthalmic drugs.
The observed and predicted log P values for this test set are
given in Table 6. Figure 6 gives the linear relationship
between the experimental log P values (shown as the abscissa
Predict) and the corresponding predicted log
P as predicted by the 6-term MI-QSAR model (shown as the ordinate
Observed) for all the molecules in the training set and the
test set.
According to the result of the PCA, which has a
Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy value
of 0.543 and a Bartlett value of 94.955 (P<0.01), there are 3
principal components in the models. The cumulative
variance that they explain is 84.550%. Table 7 shows the rotated
component matrix. From it we can see that
QO,N, PMIX and
SAS can be replaced by the first component,
QH2 and
QH can be replaced by the second component,
and dT can be replaced by the third component.
Discussion
We have constructed a theoretical model of corneal
permeability of organic compounds. With the increase in the
number of variables, the relativity of the MI-QSAR equation
is also improved, and the predictive ability of the model is
enhanced. Equation 6 is most significant. Moreover, the
models have been validated by using the compounds of the
test set, and the 5_6 term MI-QSAR models could be used to
predict log P for other compounds during drug design.
These MI-QSAR models indicate that corneal
permeability depends on 5 parameters:
QH, QO,N,
dT, PMIX, and SAS.
QH seems to be the dominant descriptor in these MI-QSAR
models, which is a parameter that is closely related to the
hydrophilic groups such as -COOH, -NH2, -OH, and -NH-. A
compound with greater corneal permeability usually has
adequate hydrophilic groups. Relative to the stroma, the
barrier effect of epithelium is more prominent, so when a
compound has a QH value that is too high, its corneal
permeability will decrease markedly. This is why log
P is directly proportional to
QH, but inversely proportional to
QH2. The
QH value is also relevant to the capacity of a compound to
form hydrogen bonds, which is the same as the descriptor
QO,N. When
QO,N lessens, the value of log
P will increase, which indicates that weak hydrogen bond potential is
favorable for corneal penetration. This is a similar situation to the
transport of compounds through other biological membranes
such as skin[26,27], small
intestine[28], Caco-2 cell
monolayers[29,30], and the blood-brain
barrier[31]. PMIX is the moment of inertia
(X) when the Cartesian coordinate axes are the principal axes
of the molecule. The inertia of a molecule is determined by
its 3-dimensional structure, and describes the molecule shape.
The MI-QSAR models reveal that with the accretion of
inertia (X), the solute compound becomes more easily to
penetrate through the cornea. It can be inferred that quadrate
molecules are more likely to permeate the cornea.
SAS represents the area of the solute that contacts the solvent, and
can be considered as an index of the solute¡¯s hydrophobic
properties. When SAS increases, the value of log
P decreases. Thus, it can be concluded that hydrophobic (lipophilic)
molecules can cross the corneal barrier more easily.
The other descriptor, dT, reflects the interaction of the
solute with the membrane and the behavior of the entire
membrane-solute complex. Here, the greater
dT is, the more the value of log P increases. This indicates that for a small molecule-membrane complex in the combined state, the log
P value is low when its Etorsion
is stable, which means that the more tightly a small molecule combines with the membrane,
the more difficultly it has in penetrating through the corneal
barrier. This suggests that as the solute becomes more
flexible within the membrane, its log P value would decrease.
This may be due to the complex amphiphilic structure of the
corneal barrier.
On the basis of the results of the PCA, the capability of a
organic compound to permeate the cornea is mainly related
to 3 principal components, which can be related to the
molecular structure and shape, the hydrophilicity of a solute
molecule, and the strength of the combination of a small
molecule with the membrane, respectively. The molecular
structure and shape are described by 3 parameters:
QO,N, PMIX and SAS.
QO,N and SAS represent the strength of
hydrogen bonds in a compound and PMIX represents the shape
of a solute molecule. Generally, a quadrate molecule with
weak hydrogen bond potential has good potential to
penetrate the cornea. The hydrophilicity of a solute molecule is
described by 2 descriptors, namely
QH2 and
QH. Generally, organic compounds with proper hydrophilic groups, in which
lipophilicity is greater than hydrophilicity, are easily able to
penetrate through the cornea. The strength of the
combination of a small molecule with the membrane is described by
one parameter, namely DEtorsion. The more tightly a small
molecule combines with the membrane, the more difficulty it
has in penetrating through the corneal barrier.
For QSAR models, the less comparable the studied
molecules are, the more universally significant the equations
are. On the other hand, the precision of a MI-QSAR
simulation may be greatly increased when a series of organic
compounds with similar structures comprise the training set.
Although our MI-QSAR models are noncongeneric models
based on several types of organic compounds, there are still
many types of compounds that cannot be included in these
models. For further studies, we should pay more attention
to the experimental component, in order to expand the
research range of molecules and search for new models that
can unify more types of compounds, to improve the
practical value of the constructed models.
In conclusion, we have developed an extension of the
traditional QSAR approach by combining it with a
solute-membrane complex that simulates the corneal environment.
MI-QSAR analysis is a structure-based design
methodology combined with classic intramolecular QSAR analysis to
model the interactions of different compounds with cellular
membranes. Although still applying the structural
information in a 2-dimensional, "structure-function relationship"
manner, this method also takes into account the powerful
3-dimensional behavior displayed by membrane structures, and
thus improves on past QSAR methods. With the help of the
model, the membrane penetration process can be reliably
described for structurally diverse molecules whose
interactions with the phospholipid-rich regions of cellular
membranes are explicitly considered. The MI-QSAR models
indicate that the corneal permeability of organic molecules is not
only influenced by organic solutes themselves, but is also
related to the properties of the solute-membrane complex,
that is, interactions between the molecule and the
phospholipid-rich regions of cellular membranes. Compared with the
work of Iyer and coworkers, which paid more attention to the
energy parameters of the solute-membrane
system[21], our models achieve a better correlation coefficient and smaller
standard deviation by taking a wider range of descriptors
into account, and thus have a better predictive ability.
Moreover, we use PCA to identify the descriptors involved
in the models, which makes the data analysis more clear and
reliable. In addition, by building an application for the
constructed models, we recognize the human-machine dialog in
the prediction process, and make the work easier.
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