Conformational flexibility, internal hydrogen bonding, and passive membrane permeability: successful in silico prediction of the relative permeabilities of cyclic peptides.
ABSTRACT We report an atomistic physical model for the passive membrane permeability of cyclic peptides. The computational modeling was performed in advance of the experiments and did not involve the use of "training data". The model explicitly treats the conformational flexibility of the peptides by extensive conformational sampling in low (membrane) and high (water) dielectric environments. The passive membrane permeabilities of 11 cyclic peptides were obtained experimentally using a parallel artificial membrane permeability assay (PAMPA) and showed a linear correlation with the computational results with R(2) = 0.96. In general, the results support the hypothesis, already well established in the literature, that the ability to form internal hydrogen bonds is critical for passive membrane permeability and can be the distinguishing factor among closely related compounds, such as those studied here. However, we have found that the number of internal hydrogen bonds that can form in the membrane and the solvent-exposed polar surface area correlate more poorly with PAMPA permeability than our model, which quantitatively estimates the solvation free energy losses upon moving from high-dielectric water to the low-dielectric interior of a membrane.
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ABSTRACT: Self-assembled cyclic peptide nanotubes have attracted much attention because of their antimicrobial properties. Here, we present calculations on the formation of cyclic peptide dimers using basin-hopping and discrete path sampling. We present an analysis of the basin-hopping move sets that most efficiently explore the conformations of cyclic peptides. Group rotation moves, in which sections of the ring are rotated as a rigid body, are the most effective for cyclic peptides containing up to 20 residues. For cyclic peptide dimers, we find that a combination of group rotation intramolecular moves and rigid body intermolecular moves performs well. Discrete path sampling calculations on the cyclic peptide dimers show significant differences in the dimerization of hexa- and octapeptides.Journal of Chemical Theory and Computation 03/2014; 10(4):1810–1816. · 5.39 Impact Factor
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ABSTRACT: Sampling low energy conformations of macrocycles is challenging due to the large size of many of these molecules and the constraints imposed by the macrocycle. We present a new conformational search method (implemented in MacroModel) that uses brief MD simulations followed by minimization and normal-mode search steps. The method was parameterized using a set of 100 macrocycles from the PDB and CSD. It was then tested on a publicly available dataset for which there are published results using alternative methods; we found that when the same force field is used (in this case MMFFs in vacuum), our method tended to identify conformations with lower energies than what the other methods identified. The performance on a new set of 50 macrocycles from the PDB and CSD was also quite good; the mean and median RMSD values for just the ring atoms was 0.60 Å and 0.33 Å, respectively. However, the RMSD values for macrocycles with more than 30 ring-atoms were quite a bit larger compared to the smaller macrocycles. Possible origins for this and ideas for improving the performance on very large macrocycles are discussed.Journal of Chemical Information and Modeling 09/2014; 54(10):2680. · 4.30 Impact Factor
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ABSTRACT: Experimental and computational studies have shown that cellular membranes deform to stabilize the inclusion of transmembrane (TM) proteins harboring charge. Recent analysis suggests that membrane bending helps to expose charged and polar residues to the aqueous environment and polar head groups. We previously used elasticity theory to identify membrane distortions that minimize the insertion of charged TM peptides into the membrane. Here, we extend our work by showing that it also provides a novel, computationally efficient method for exploring the energetics of ion and small peptide penetration into membranes. First, we show that the continuum method accurately reproduces energy profiles and membrane shapes generated from molecular simulations of bare ion permeation at a fraction of the computational cost. Next, we demonstrate that the dependence of the ion insertion energy on the membrane thickness arises primarily from the elastic properties of the membrane. Moreover, the continuum model readily provides a free energy decomposition into components not easily determined from molecular dynamics. Finally, we show that the energetics of membrane deformation strongly depend on membrane patch size both for ions and peptides. This dependence is particularly strong for peptides based on simulations of a known amphipathic, membrane binding peptide from the human pathogen Toxoplasma gondii. In total, we address shortcomings and advantages that arise from using a variety of computational methods in distinct biological contexts.Journal of Membrane Biology 03/2014; · 2.48 Impact Factor
Conformational Flexibility, Internal Hydrogen Bonding, and
Passive Membrane Permeability: Successful in Silico
Prediction of the Relative Permeabilities of Cyclic Peptides
Taha Rezai,†Jonathan E. Bock,†Mai V. Zhou,†Chakrapani Kalyanaraman,‡
R. Scott Lokey,*,†and Matthew P. Jacobson*,‡
Contribution from the Department of Chemistry and Biochemistry, UniVersity of California at
Santa Cruz, Santa Cruz, California 95064, and Department of Pharmaceutical Chemistry,
UniVersity of California at San Francisco, 600 16th Street,
San Francisco, California 94143-2240
Received May 2, 2006; E-mail: email@example.com
Abstract: We report an atomistic physical model for the passive membrane permeability of cyclic peptides.
The computational modeling was performed in advance of the experiments and did not involve the use of
“training data”. The model explicitly treats the conformational flexibility of the peptides by extensive
conformational sampling in low (membrane) and high (water) dielectric environments. The passive membrane
permeabilities of 11 cyclic peptides were obtained experimentally using a parallel artificial membrane
permeability assay (PAMPA) and showed a linear correlation with the computational results with R2)
0.96. In general, the results support the hypothesis, already well established in the literature, that the ability
to form internal hydrogen bonds is critical for passive membrane permeability and can be the distinguishing
factor among closely related compounds, such as those studied here. However, we have found that the
number of internal hydrogen bonds that can form in the membrane and the solvent-exposed polar surface
area correlate more poorly with PAMPA permeability than our model, which quantitatively estimates the
solvation free energy losses upon moving from high-dielectric water to the low-dielectric interior of a
Many previous studies have explored correlations between
various properties of small molecules and their membrane
permeability, a critical property underlying the bioavailability
of drugs and one determinant of success or failure in preclinical
development.1-10Predictive models of membrane permeability
have been developed,2-9usually by the application of multi-
variable regression to a “training set”, followed by evaluation
of the model on a separate “test set”. The molecular descriptors
most commonly employed in these studies are compound size
and the solvent-exposed polar surface area. It is physically
reasonable to expect both of these properties to affect membrane
permeability. Other approaches have used quantum mechanical
calculations to provide descriptors.11Beyond the reasonability
of the descriptors used, however, “knowledge-based” methods
of this type do not attempt to predict membrane permeability
on the basis of an atomistic physical model. The reliability of
existing models of membrane permeability is a subject of debate,
and failures in practical application have been reported12that
have been attributed, in part, to inadequate training sets.
We and others have used cyclic peptides as model systems
for studying membrane permeability.13-16The advantages of
cyclic peptides for this purpose include their relative ease of
synthesis and the ability to precisely modulate chemical
functionality and stereochemistry. The ability to rationally
engineer cyclic peptides with druglike passive membrane
permeability would also open new possibilities for using cyclic
†University of California at Santa Cruz.
‡University of California at San Francisco.
(1) Lipinski, C. A.; Lombardo, F.; Dominy, B. W.; Feeney, P. J. AdV. Drug
DeliVery ReV. 2001, 46, 3-26.
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Guldbrandt, M.; Christensen, M. S. J. Med. Chem. 2005, 48, 805-811.
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1998, 15, 972-978.
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Loncharich, R. J.; Wikel, J. H. J. Chem. Inf. Comput. Sci. 2001, 41, 1578-
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(8) Malkia, A.; Murtomaki, L.; Urtti, A.; Kontturi, K. Eur. J. Pharm. Sci. 2004,
(9) Fujikawa, M.; Ano, R.; Nakao, K.; Shimizu, R.; Akamatsu, M. Bioorg.
Med. Chem. 2005, 13, 4721-4732.
(10) Veber, D. F.; Johnson, S. R.; Cheng, H. Y.; Smith, B. R.; Ward, K. W.;
Kopple, K. D. J. Med. Chem. 2002, 45, 2615-2623.
(11) Fujiwara, S.; Yamashita, F.; Hashida, M. Int. J. Pharm. 2002, 237, 95-
(12) Stouch, T. R.; Kenyon, J. R.; Johnson, S. R.; Chen, X. Q.; Doweyko, A.;
Li, Y. J. Comput.-Aided Mol. Des. 2003, 17, 83-92.
(13) Rezai, T.; Yu, B.; Millhauser, G. L.; Jacobson, M. P.; Lokey, R. S. J. Am.
Chem. Soc. 2006, 128, 2510-2511.
(14) Gangwar, S.; Jois, S. D.; Siahaan, T. J.; Vander Velde, D. G.; Stella, V. J.;
Borchardt, R. T. Pharm. Res. 1996, 13, 1657-1662.
(15) Gudmundsson, O. S.; Vander Velde, D. G.; Jois, S. D.; Bak, A.; Siahaan,
T. J.; Borchardt, R. T. J. Pept. Res. 1999, 53, 403-413.
(16) Gudmundsson, O. S.; Jois, S. D.; Vander Velde, D. G.; Siahaan, T. J.;
Wang, B.; Borchardt, R. T. J. Pept. Res. 1999, 53, 383-392.
Published on Web 10/06/2006
10.1021/ja063076p CCC: $33.50 © 2006 American Chemical Society
J. AM. CHEM. SOC. 2006, 128, 14073-14080 9 14073
peptides to inhibit intracellular proteins. Most cyclic peptides
have poor membrane permeability, but there are exceptions,
including cyclosporine A, a cyclic undecapeptide that is used
as an orally active immunosuppressive drug.17In addition, in a
previous paper we identified a cyclic hexapeptide, cyclo(D-Leu-
D-Leu-Leu-D-Leu-Pro-Tyr), with passive membrane permeability
that slightly exceeds that of cyclosporine A.13
We report here a physics-based model for the passive
membrane permeability, as measured in a parallel artificial
membrane permeability assay (PAMPA), of cyclic peptides that
shows good predictive ability. The computational modeling was
performed in advance of the experiments and did not involve
the use of “training data”. The model involves extensive
conformational sampling of the peptides, represented in all-atom
detail, in low (membrane) and high (water) dielectric environ-
ments. The conformational sampling is needed to understand
the role of conformational flexibility, which is not explicitly
considered in many models of membrane permeability. Water
and the membrane are not treated in atomistic detail. Rather,
they are both treated as a dielectric continuum. Thus, our model
neglects atomic-level details of the membrane and water,
including the membrane-water interface. Implicit solvent
models have also been used in prior studies of membrane
permeability.18,19Our model is thus intermediate in both
computational speed and level of physical detail between
molecular dynamics simulations of membrane permeability
using explicit water and membranes20-24and knowledge-based
methods based on simple chemical descriptors.2-9
The passive membrane permeabilities of 11 cyclic peptides
were obtained experimentally using a PAMPA and showed a
linear correlation with the computational predictions with R2
) 0.96. The success of the model suggests that, although it does
not treat all aspects of the physics of membrane permeability,
it captures two critical elements: the ability of the peptides to
adopt multiple conformations with different populations in low-
and high-dielectric environments and the free energy cost of
desolvating the peptides upon entering the membrane. The
physical underpinnings of our model are considered in some
detail below, including possible improvements to the model.
In general, the results support the hypothesis, already well-
established in the literature,8,14-16,18,25that the ability to form
internal hydrogen bonds is critical for passive membrane
permeability and can be the distinguishing factor among closely
related compounds, such as those studied here. However, we
have found that the number of internal hydrogen bonds that
can form in the membrane and the solvent-exposed polar surface
area each correlate somewhat weakly with membrane perme-
ability. The implicit solvent model used in our approach reflects
the internal hydrogen bonding and polar surface area but
provides a quantitative free energy difference that can be thought
of as a measure of the overall lipophilicity/hydrophilicity of a
particular conformation of the compound (i.e., the one that we
postulate is adopted in the low-dielectric membrane).
Finally, we also discuss limitations of our model, the most
important of which is that it currently can only be used to predict
relative PAMPA permeabilities in a series of compounds and
not absolute permeabilities. One important reason for this is
that the model does not account for translational, rotational, and
internal entropy losses of compounds upon entering the mem-
Results and Discussion
Overview of the Computational Model. Figure 1 schemati-
cally depicts the conceptual underpinnings of our model. Note
that, although we depict a bilayer in this schematic, the artificial
membrane in the PAMPA is considerably thicker (approximately
30 Å) and the interior contains a hydrocarbon, dodecane in this
work. It is also important to emphasize that this work does not
consider the effects of changing the composition of the
membrane on permeability, but only the effects of changing
the chemical structure of the permeant, using an artificial
membrane of constant composition.
We assume that the peptides adopt multiple, rapidly inter-
converting conformations in water, but that membrane perme-
ation is dominated by a single conformation. (Conformational
entropy losses upon entering the membrane have been observed
in molecular dynamics simulations.21,22) In practice, we identify
this conformation as the lowest energy state found by extensive
sampling of the peptide in a low-dielectric solvent (see the
Methods). In the following, we will refer to this conformation
as the “low-dielectric conformation”, LDC. The LDC generally
has maximal internal hydrogen bonding, but we identify the
LDC by the internal energy, which includes intramolecular
strain, electrostatics, and dielectric screening treated by an
implicit solvent model. The relationship between hydrogen
bonding and permeability is considered in greater detail below.
We further assume that the LDC is contained within the
ensemble of peptide conformations in water; i.e., it is at least
transiently populated in water (this assumption is supported by
computational evidence, as discussed below). The flux across
the membrane is assumed to be limited by the rate of the LDC
passing from the high-dielectric water into the low-dielectric
membrane. More precisely, we postulate that the measured
PAMPA permeability is proportional to the partition coefficient
of the LDC between water (high dielectric) and the membrane
interior (low dielectric) or, equivalently, that the log of the
permeability coefficient (log Pe) is proportional to the free
energy of transferring the LDC from a high-dielectric environ-
ment to a low-dielectric environment (∆GI, the free energy of
“insertion”). In the language of transition-state theory, this
implies that the LDC in the membrane can be considered the
“transition state” for diffusion through the membrane.
This model bears some similarity to the classical solubility-
diffusion model of passive membrane transport;24,26i.e., Pe)
KpD/d, where Peis the permeabililty (cm/s), Kpis the unitless
partition coefficient of the compound in the membrane, D is
the diffusion coefficient in the membrane (cm2/s), and d is the
membrane thickness (cm). Our model has two important
(17) Schreiber, S. L.; Crabtree, G. R. Immunol. Today 1992, 13, 136-142.
(18) Goodwin, J. T.; Mao, B.; Vidmar, T. J.; Conradi, R. A.; Burton, P. S. J.
Pept. Res. 1999, 53, 355-369.
(19) Parsegian, A. Nature 1969, 221, 844-846.
(20) Marrink, S. J.; Berendsen, H. J. C. J. Phys. Chem. 1996, 100, 16729-
(21) Bemporad, D.; Luttmann, C.; Essex, J. W. Biophys. J. 2004, 87, 1-13.
(22) Bemporad, D.; Luttmann, C.; Essex, J. W. Biochim. Biophys. Acta 2005,
(23) Wilson, M. A.; Pohorille, A. J. Am. Chem. Soc. 1996, 118, 6580-6587.
(24) Pohorille, A.; New, M. H.; Schweighofer, K.; Wilson, M. A. Curr. Top.
Membr. 1999, 48, 49-76.
(25) Goodwin, J. T.; Conradi, R. A.; Ho, N. F.; Burton, P. S. J. Med. Chem.
2001, 44, 3721-3729.
(26) Walter, A.; Gutknecht, J. J. Membr. Biol. 1986, 90, 207-217.
A R T I C L E S
Rezai et al.
14074 J. AM. CHEM. SOC.9VOL. 128, NO. 43, 2006
differences. First, we assume that differences in the rate of
intramembrane diffusion are unimportant for the relatively
similar compounds we consider here. Second, we calculate the
partition coefficient for one member of the ensemble of possible
peptide conformations, rather than the overall partition coef-
ficient, which would reflect the overall ensembles in the two
different environments. Indeed, experimentally measured phase
partitioning with bulk solvents sometimes correlates weakly with
the membrane permeability, especially for flexible compounds
capable of forming internal hydrogen bonds.8
Finally, we point out one important limitation of our model,
which is that it does not account for differences in the size or
shape of the cyclic peptides. Molecular size is frequently
included as a descriptor in parametrized models of membrane
permeability, and both computational and experimental studies
have suggested the importance of size and shape effects in
passive membrane permeability.20,24,26-29Evidently, among the
relatively similar compounds tested here, this limitation does
not substantially degrade the predictive ability of the model
when the data obtained are compared to PAMPA data. However,
it is clear that we will need to address this limitation of our
model, and probably others, in extending this work to more
Cyclic Peptide Virtual Libraries. As discussed in the
Methods, all of the peptides contained one L-tyrosine, which
was radiolabeled by methylating the tyrosine -OH with14CH3I.
The cyclic peptides used in the computational study were
generated as a set of sublibraries categorized by ring size, the
number of prolines, and proline spacing (Figure 2). The
hexapeptides contained either one or two prolines, and the
heptapeptides contained one, two, or three prolines. Within each
sublibrary, the stereochemistry of the L-Tyr(OMe) was held
constant, while the stereochemistries of the remaining residues
were permuted to give all possible diastereomers. Permutation
of ring size and stereochemistry thus provided access to a diverse
array of conformations, while inclusion of proline residues was
expected to induce turn structures and limit the number of low-
energy conformers available to a given scaffold. Leucine was
chosen for the remaining positions since it is one of the most
hydrophobic natural amino acids that does not have a branching
?-carbon, ensuring efficient couplings during the synthesis. A
total of 128 hexapeptides and 320 heptapeptides were included
in the study. Detailed data on the entire libraries are provided
in the Supporting Information.
The results on the virtual libraries allow us to investigate
correlations between predicted permeability and various struc-
tural properties of the peptides. The good correlation of ∆GI
with the experimental PAMPA permeability, for the subset of
cyclic peptides that were characterized experimentally, suggests
that these predictions may be valid, but the relatively small
(27) Deyoung, L. R.; Dill, K. A. Biochemistry 1988, 27, 5281-5289.
(28) Deyoung, L. R.; Dill, K. A. J. Phys. Chem. 1990, 94, 801-809.
(29) Xiang, T. X.; Anderson, B. D. J. Membr. Biol. 1994, 140, 111-122.
Figure 1. Qualitative overview of the model. The peptides in water are assumed to adopt multiple, rapidly interconverting conformations. The low dielectric
of the membrane promotes the formation of internal hydrogen bonds, and the conformation in the membrane (the low-dielectric conformation, LDC) is
assumed to be populated in the ensemble of water conformations. The key predictive quantity is ∆GI, the free energy for transferring the LDC from water
to the low-dielectric environment.
Figure 2. Cyclic peptides included in the computational study. Sublibraries
1-4 contain 128 cyclic hexapeptides with one or two prolines. Sublibraries
5-9 contain 320 cyclic heptapeptides with one, two, or three prolines. All
indicated stereochemical combinations were included within each sublibrary.
Relative Permeabilities of Cyclic Peptides
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 128, NO. 43, 2006 14075
number of cyclic peptides tested experimentally does not permit
direct confirmation of all of these predictions.
First, we investigated the relationships between the predicted
passive permeability and the number of hydrogen bonds in the
low-dielectric environment. Specifically, we computed the
number of hydrogen bonds in the LDC using a simple measure
based on the distance between any two electronegative atoms
(this distance must be less than the sum of the van der Waals
radii). The averages values of ∆GIfor the cyclic peptides with
different numbers of hydrogen bonds in the LDC are shown in
Table 1. There is clearly a correlation, but it is somewhat weak,
and the standard deviation of the averages is quite large. As
discussed further below, some compounds with multiple internal
hydrogen bonds have relatively poor PAMPA permeability
(predicted or measured) and vice versa.
The relationship between permeability and the number of
proline residues is also of interest. On one hand, the Pro residues
do not contain a hydrogen bond donor group, while the
remaining amino acids have a free NH group. This would
suggest that increasing numbers of prolines might increase
permeability. On the other hand, the prolines have greatly
reduced backbone flexibility, which could reduce the ability of
the peptides to adopt conformations with good internal hydrogen
bonds. In addition, the Leu side chain has a somewhat larger
hydrophobic surface area than Pro, and thus, increasing the
number of prolines could arguably decrease the overall hydro-
phobicity of the molecule. However, it is not clear that this
difference in the side chain hydrophobicity would outweigh the
elimination of the backbone NH group. The computational
results are unambiguous that increasing numbers of prolines
reduce the predicted passive permeability, on average. For the
hexapeptides, the average values of ∆GIare 0.2 and 2.2 kcal/
mol for the peptides with one and two Pro residues, respectively.
For the heptapeptides, the trend is similar: the average values
of ∆GIare -1.4, -0.7, and 1.6 kcal/mol for the peptides with
one, two, and three Pro residues, respectively. On the basis of
the present results, we cannot distinguish whether this effect is
due to rigidification or decreased hydrophobicity caused by
increasing numbers of prolines.
Overall, the heptapeptides were predicted to have a larger
range of permeabilities and on average to be somewhat more
permeable than the hexapeptides with the same number of Pro
residues (data in the Supporting Information). We attribute this
computational result in part to the greater flexibility of the
heptapeptides, on average, making it easier for them to form
internal hydrogen bonds. However, when hexa- and heptapep-
tides with the same number of internal hydrogen bonds are
considered, the heptapeptides are still predicted to have higher
permeability, possibly due to the larger number of hydrophobic
side chains. As discussed above, we do not explicitly take
molecular size or weight into account in our model, and thus,
this prediction may be incorrect, given the generally observed
inverse correlation between molecular weight and permeability.
The size of the experimental data set is not sufficient to confirm
or refute this prediction, although the hexa- and heptapeptides
tested experimentally do fall on the same line in the plot of
PAMPA permeability vs ∆GI.
Finally, the computational results can be used to directly
assess the validity of our assumption that the LDC is contained
among the ensemble of rapidly interconverting conformations
in water. The relevant quantity for assessing this assumption is
the free energy difference between the energy of the LDC in
water and the lowest energy state found in water (∆GW). With
adequate sampling, i.e., if the lowest energy state found in water
is truly the global minimum, this value should always be
positive. The average value of this quantity for the 128
hexapeptides is 1.1 kcal/mol, and for the 320 heptapeptides it
is 1.0 kcal/mol. Since thermal energy at room temperature (RT)
corresponds to 0.6 kcal/mol, the computational data largely
support our simple model, subject to the limitations of the
sampling and the energy model. That is, for most of the cyclic
peptides, the calculations suggest that the free energy of the
LDC in water is in fact low enough that it can be at least
transiently populated at room temperature. The rate of inter-
conversion among the different low-energy states of the peptide
in water is much more difficult to evaluate, and we do not
attempt to do so. However, it is highly likely that the different
conformations can interconvert on a time scale much faster than
that of the PAMPA measurements.
Choice of Peptides for Experimental Investigation. A total
of eight cyclic hexapeptides and eight cyclic heptapeptides from
the virtual library were chosen for synthesis and experimental
testing. These were chosen to span the range of calculated ∆GI
values and to have a variety of different predicted properties,
especially the number of hydrogen bonds predicted for the LDC
(see Table 2). Due to low cyclization yields, however, four cyclic
heptapeptides and seven cyclic hexapeptides were successfully
Experimental Results and Correlation with Computa-
tional Predictions. The experimental PAMPA data are sum-
marized in Table 2. The correlation between the log Pe
determined by the PAMPA assay and the computationally
determined values of ∆GIis shown in Figure 3. Clearly, there
is a strong, linear correlation (R2) 0.96), which is highly
encouraging because the computations were performed in
advance of the experiments and did not use a training set. The
Table 1. Correlation of ∆GIwith the Number of Internal Hydrogen Bonds, Obtained from the Computational Analysis of the Virtual Cyclic
aThe column “no. of H bonds” refers to the number of internal hydrogen bonds, “no. of peptides” is the number of cyclic peptides with that number of
hydrogen bonds, “av ∆GI” is the value of the insertion free energy quantity (kcal/mol) averaged over all peptides with the specified number of hydrogen
bonds, and “std dev” and “std error” are the standard deviations and standard errors of these values (kcal/mol).
A R T I C L E S
Rezai et al.
14076 J. AM. CHEM. SOC.9VOL. 128, NO. 43, 2006
only adjustable parameters are thus the slope and intercept of
the linear fit.
The slope of the linear fit is -0.098. This observed slope
deviates significantly from the value predicted by our simple
model that the passive permeability is directly proportional to
the partition coefficient of the LDC, which implies that log Pe
∝ -∆GI/2.3RT. The slope of the line would thus be predicted
to be -0.71, using energy units of kilocalories per mole, which
is obviously much larger in magnitude than the observed slope.
One possible contribution to this discrepancy is our choice
of dielectric to represent the interior of the membrane. Largely
due to the availability of parameters for the implicit solvent
model, we chose chloroform to represent the low-dielectric
environment, with a dielectric constant of 4.8. This is lower
than many estimates of the dielectric constant of the interior of
the membrane and also neglects electrostatic screening from
high-dielectric water outside the membrane.19The values of ∆GI
are highly sensitive to the choice of the membrane dielectric
and scale approximately as 1/?hi- 1/?lo, where ?hiand ?loare
the high and low dielectrics, because the transfer free energies
are dominated by the difference in the solvation free energy
computed by the generalized Born solvent model. However,
using a membrane dielectric of 10 would only change the slope
by a factor of 2. Clearly, other factors must also play a role. A
related possibility is that the free energy cost of partitioning
into the membrane is reduced by the peptide “dragging” water
with it as it passes through the membrane, as has been observed
in molecular dynamics simulations of passive membrane
Finally, it is important to note that we do not account for
entropic losses of the peptides upon moving from water to the
membrane. The loss of translational and rotational entropy will
be determined largely by the size (and shape) of the molecules.
Changes in internal entropy are difficult to estimate but would
certainly oppose permeation, as has been seen in molecular
dynamics simulations.22The loss of internal entropy would
likely vary among the compounds, with larger entropic losses
for those compounds forming the best internal hydrogen bonds
in the membrane. The loss of internal entropy is thus likely to
reduce the observed slope.
Hydrogen Bonding and Polar Surface Area. Our results
suggest that the differing PAMPA permeabilities of the cyclic
peptides are related to their ability to form internal hydrogen
bonds.8,14-16,18,25That is, in general, the ability to form internal
hydrogen bonds can promote passive membrane permeability
by reducing the free energy cost of desolvating the peptides
upon insertion into the membrane. However, as can be seen in
Figure 4, the number of hydrogen bonds, by itself, provides
only a relatively weak correlation with the PAMPA data (see
also Table 1). Figures5 and 6 depict the computationally
predicted conformations of three of the experimentally studied
cyclic peptides in the low-dielectric medium. The two cyclic
heptapeptides in Figure 5 represent the most and least permeable
cyclic peptides, as predicted by computation and confirmed by
the PAMPA results. The most permeable cyclic peptide shows
three internal hydrogen bonds, while the least permeable cyclic
peptide has only one. For the most part, the relative perme-
abilities of the other cyclic peptides investigated correlate loosely
with the number of hydrogen bonds, but there are exceptions.
Notably, Figure 6 depicts the predicted conformation of a cyclic
hexapeptide with two internal hydrogen bonds, which nonethe-
less has one of the poorest permeabilities according to both the
predicted ∆GIand the experimental PAMPA results. One key
feature underlying this discrepancy appears to be that all four
carbonyl groups not involved in hydrogen bonds point outward
and are not buried by the Leu side chains. These carbonyls
Table 2. Cyclic Peptides Studied Experimentallya
compd cyclic peptide
H bondsPSAlog Pe
-6.47 ( 0.07
-7.05 ( 0.03
-7.27 ( 0.06
-7.16 ( 0.05
-6.52 ( 0.01
-6.68 ( 0.08
-7.29 ( 0.08
-6.75 ( 0.13
-6.95 ( 0.20
-7.12 ( 0.01
-6.41 ( 0.08
aThe cyclic peptides were chosen to have a wide range of predicted properties, on the basis of the computational results; see the text for details. The
values of ∆GI(see Figure 1) are in kilocalories per mole. The cyclic peptides chosen span nearly the entire range of predicted values of ∆GI. The column
“compd” lists the cyclic peptide identification number, “cyclic peptide” specifies the amino acid sequence, “no. of H bonds” refers to the number of hydrogen
bonds observed in the lowest energy structure in the low-dielectric simulation, “PSA” is the polar surface area (Å2), and “log Pe” is the PAMPA permeability
(cm/s). The uncertainties are calculated from the standard deviation of the three replicate measurements.
Figure 3. The calculated free energy of insertion (∆GI) shows a strong
correlation with the permeability determined in the PAMPA (log Pe). The
units of Pe are centimeters per second. The correlation coefficient R2is
0.96. The cyclic hexapeptides are represented by black circles and the cyclic
heptapeptides by red squares.
Relative Permeabilities of Cyclic Peptides
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 128, NO. 43, 2006 14077
would thus incur a significant desolvation cost upon moving
from water to the membrane interior.
The exposed polar surface area is also frequently used as a
descriptor in models of membrane permeability. Conformations
with greater polar surface area are generally expected to be less
permeable because they will incur a larger free energy cost of
desolvating the compounds as they pass into the membrane.
However, as can be seen in Figure 4, the polar surface area
does not correlate nearly as well (R2) 0.34) with the PAMPA
data as the calculated free energy of insertion (∆GI).
Initial Testing with Small-Molecule Inhibitors. Significant
additional work will be required to demonstrate the utility of
our model for small-molecule drug discovery. However, as an
initial proof-of-concept, we have applied the same model that
we used for the cyclic peptides to a series of fluoroquinolones,
for which PAMPA data are available in the literature.50
These compounds have significantly fewer rotatable bonds
than the cyclic peptides, and for this reason the only sampling
we performed was direct energy minimization in the low-
dielectric environment, i.e., to generate the LDC. On the other
hand, the fluoroquinolone compounds contain a more diverse
set of functional groups than the cyclic peptides. For this reason,
it is encouraging that a strong linear correlation, R2) 0.83, is
observed between ∆GIand the intrinsic PAMPA permeability
for this series (Figure 7), albeit not as strong as for the cyclic
In vivo absorption data for these compounds are also
available, specifically the results of rat gut in situ perfusion
assays (Table 3 in ref 50). A linear correlation between the
logarithm of the measured absorption and ∆GIis observed, with
These results provide additional support for the utility of the
free energy of insertion (∆GI) as a descriptor for predicting
relative permeabilities within a series of relatively closely related
compounds. Because the slope and intercept of the linear fit
are different between the cyclic peptides and the fluoroquino-
lones, the results also highlight that additional work will be
needed to develop a model capable of predicting absolute
PAMPA permeability that is valid across highly diverse sets of
compounds. We believe that accurate estimates of translational,
rotational, and internal entropy losses upon entering the
membrane will be needed to achieve this goal.
Computational Methods for Predicting Cyclic Peptide Confor-
mations. Some prior studies have used molecular dynamics methods
to sample molecular conformations in the context of studying funda-
mental aspects of passive permeability20-24or predicting permeation
Figure 4. Correlations of permeability with the number of internal hydrogen bonds (left) and the polar surface area (Å2) (right) in the LDC.
Figure 5. Predicted lowest energy conformations, in a low-dielectric
environment, for the most and least permeable cyclic peptides. Only the
C? atoms of the Leu/D-Leu side chains are shown for clarity. Hydrogen
bonds are shown as cyan lines. Left: Cyclic heptapeptide no. 294, which
is the most permeable of those tested experimentally and is also predicted
to be the most permeable according to ∆GI. This conformation contains
three hydrogen bonds. Right: Cyclic heptapeptide no. 112, which is the
least permeable of those tested experimentally and is also predicted to be
the least permeable according to ∆GI. Only one, somewhat strained,
hydrogen bond is formed in this conformation.
Figure 6. Predicted low-dielectric conformation of cyclic hexapeptide no.
42. Only the C? atoms of the Leu/D-Leu side chains are shown for clarity.
Hydrogen bonds are shown as cyan lines.
A R T I C L E S
Rezai et al.
14078 J. AM. CHEM. SOC.9VOL. 128, NO. 43, 2006
rates (e.g., by averaging the polar surface area4). Here we use a different
sampling technology based on dihedral angle sampling,18adapted from
a reported method for protein loop sampling. The advantage of this
method is that it samples the conformational space in an unbiased
manner and the time scales for converting between different conforma-
tions are irrelevant. Several other computational methods for predicting
cyclic peptide structures have also been reported in the literature.30-36
All calculations were performed with version “1-9e” of the Protein
Local Optimization Program (PLOP), the software platform developed
in the Jacobson group. The program is freely available to academic
researchers and is part of the commercial Prime package (Schro ¨dinger,
Cyclic peptide conformations were generated using the loop predic-
tion algorithm of Jacobson et al.37In brief, candidate backbone
conformations were generated by splitting the cyclic peptide in half
and using a buildup procedure for each side, eventually joining in the
middle. The buildup algorithm employs a rotamer-like library of
acceptable backbone dihedral angle combinations (φ, ψ); Pro and Gly
were treated separately from other amino acids, and D-amino acids were
treated by inverting the standard Ramachandran preferences. During
the buildup procedure, conformations were rejected primarily on the
basis of steric clashes and also if there was insufficient space for the
side chain to fit adequately or if the peptide could not close, on the
basis of geometric criteria. When all acceptable conformations of the
C- and N-terminal halves of the peptide had been identified, at a given
sampling resolution, closed peptides were generated by pairing halves
whose end points were close in space. The resultant closed peptides
were filtered on the basis of whether the backbone dihedrals of the
closure residue were within Ramachandran-allowed regions, whether
steric clashes existed between the two halves, and whether side chains
could fit acceptably given the backbone conformation.
Rather than choose in advance the sampling resolution for the
backbone dihedral angles, the resolution was adaptively controlled to
produce an acceptable number of peptide candidate structures. In this
case we generated a minimum of 100 closed peptide backbones. To
reduce redundancy among the candidate structures, we employed a
K-means clustering algorithm38,39to select a representative subset for
scoring (52 in this work, a number that was obtained empirically; i.e.,
doubling the number of clusters did not significantly change the results).
Each of the peptides among the subset was then subjected to side chain
optimization,37,40followed by complete energy minimization.
Side chain sampling was accomplished primarily by using a highly
detailed (10° resolution) rotamer library constructed by Xiang and Honig
from a database of 297 proteins.41This library contains, for example,
2086 rotamers for lysine. The computational expense of such a detailed
library was mitigated by prescreening the rotamers using only hard-
sphere overlap as a criterion (using a cell list for computational
efficiency), allowing many rotamers to be excluded before any energy
evaluations were performed. The method we used for the combinatorial
optimization was also adapted from the method of Xiang and Honig,41
which is similar in spirit to earlier work.42In brief, all side chains were
initially built onto the fixed backbone in a random rotamer state, and
then each side chain in the protein was optimized one at a time, holding
the others fixed. The procedure was iterated until no side chains changed
rotamer states. After convergence was achieved, all side chains were
simultaneously energy minimized in Cartesian coordinates.
The all-atom OPLS force field43,44was used to describe the peptide
intramolecular energetics. The OPLS torsional energy parameters have
recently been refined using high-level quantum chemical calculations44
and validated using protein side chain prediction;40the updated
parameters were used here. The solvation free energy was estimated
using an implicit solvent model consisting of the surface generalized
Born (SGB) model of polar solvation.45Correction terms have also
been developed to improve the agreement between SGB and Poisson-
Boltzmann solvation free energy calculations.45,46The simulations in
water used a dielectric of 80. To treat the low-dielectric environment
of the membrane, we modified the generalized Born implicit solvent
model to treat chloroform by changing the solvent dielectric constant
to 4.8. The “nonpolar” term, which represents the free energy of cavity
formation, was treated with a standard surface-area-dependent term,
i.e., a + b(SASA), where SASA stands for solvent-accessible surface
area, and the values of the constants a and b were taken from previous
work by Gilson and co-workers.47The GB/SA solvent model, for water
and chloroform, has also been used in prior studies of membrane
The experimental strategy for measuring the membrane permeability,
described below, required the use of radiolabeled O-methyltyrosine.
The force field parameters for this modified amino acid were obtained
using an automated “atom-typing” program implemented in the Impact
(30) Riemann, R. N.; Zacharias, M. J. Pept. Res. 2004, 63, 354-364.
(31) Baysal, C.; Meirovitch, H. Biopolymers 1999, 50, 329-344.
(32) Baysal, C.; Meirovitch, H. Biopolymers 2000, 53, 423-433.
(33) Baysal, C.; Meirovitch, H. Biopolymers 2000, 54, 416-428.
(34) Deem, M. W.; Bader, J. S. Mol. Phys. 1996, 87, 1245-1260.
(35) Nikiforovich, G. V.; Kolodziej, S. A.; Nock, B.; Bernad, N.; Martinez, J.;
Marshall, G. R. Biopolymers 1995, 36, 439-452.
(36) Che, Y.; Marshall, G. R. J. Med. Chem. 2006, 49, 111-124.
(37) Jacobson, M. P.; Pincus, D. L.; Rapp, C. S.; Day, T. J.; Honig, B.; Shaw,
D. E.; Friesner, R. A. Proteins 2004, 55, 351-367.
(38) Hartigan, J. A.; Wong, M. A. Appl. Stat. 1979, 28, 100-108.
(39) Hartigan, J. A. Clustering Algorithms; Wiley: New York, 1975.
(40) Jacobson, M. P.; Kaminski, G. A.; Friesner, R. A.; Rapp, C. S. J. Phys.
Chem. B 2002, 106, 11673-11680.
(41) Xiang, Z. X.; Honig, B. J. Mol. Biol. 2001, 311, 421-430.
(42) Bruccoleri, R. E.; Karplus, M. Biopolymers 1987, 26, 137-168.
(43) Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. Soc. 1988, 110, 1657-
(44) Kaminski, G. A.; Friesner, R. A.; Tirado-Rives, J.; Jorgensen, W. L. J.
Phys. Chem. B 2001, 105, 6474-6487.
(45) Ghosh, A.; Rapp, C. S.; Friesner, R. A. J. Phys. Chem. B 1998, 102, 10983-
(46) Gallicchio, E.; Zhang, L. Y.; Levy, R. M. J. Comput. Chem. 2002, 23,
(47) Luo, R.; Head, M. S.; Given, J. A.; Gilson, M. K. Biophys. Chem. 1999,
Figure 7. Correlations of the calculated free energy of insertion (∆GI) for a series of fluoroquinolones with PAMPA intrinsic permeability (P0, cm/s) and
rat in situ absorption (Papp, cm/s). Experimental data were taken from ref 50, Tables 1 and 3.
Relative Permeabilities of Cyclic Peptides
A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 128, NO. 43, 2006 14079
software package. The partial charges on the O-methyl group were
assigned to be -0.35 (O), 0.02 (C), and 0.06 (H). The remaining partial
charges on the residue were retained from the standard force field
parameters for Tyr.
The overall computational expense for sampling one cyclic peptide
in either a high-dielectric environment or a low-dielectric environment
was approximately 6 min for the hexapeptides and approximately 15
min for the heptapeptides, using a single 2.8 GHz Xeon processor.
Computational Methods for Predicting Membrane Permeability.
Having identified the lowest energy conformations of the cyclic peptides
in the low- and high-dielectric media, the values of ∆GIwere computed
as defined in Figure 1. As discussed in the Results and Discussion, we
also computed ∆GW, the free energy difference between the energy of
the LDC in water and the lowest energy state found in water. This
value of ∆GWdirectly assesses the validity of our assumption that the
LDC is at least transiently populated in water. It also permits an
assessment of the effectiveness of the sampling method. If the
computational method succeeds in identifying the lowest energy
conformations in the two dielectrics, then ∆GWmust be a positive value.
In practice, we used a cutoff of ∆GW> -1.0 kcal/mol to account for
the inherent precision of the calculations (vide infra). Two of the 128
cyclic hexapeptides and 25 of the 320 cyclic heptapeptides showed
evidence of incomplete sampling according to this criterion and were
excluded from further analysis. Overall, this measure of internal
consistency suggests that the conformational sampling is satisfactory
for the cyclic hexapeptides and generally satisfactory for the cyclic
heptapeptides. Larger cyclic peptides would likely require qualitatively
more sampling than we have performed here.
We also performed a series of calculations aimed at estimating the
inherent precision of the computational values. Specifically, we
computed the values of the transfer free energies for pairs of
enantiomers, specifically for all cyclic hexapeptides with the sequence
cyclo(Leu-Leu-Leu-Leu-Leu-O-Me-Tyr), with all combinations of
stereochemistries for the Leu residues (32 total, 16 pairs). The pairs of
enantiomers should, of course, have identical physical properties
including permeability and phase partitioning. However, due to technical
aspects of the calculations, the results can be obtained completely
independently and are not identical. The RMS values of ∆GIwere ∼1.0
kcal/mol over the 16 pairs of enantiomers, which we consider a rough
estimate for the precision of the computations.
Synthesis. All cyclic peptides were synthesized utilizing Fmoc solid-
phase peptide synthesis,with linkage to the solid phase via the tyrosine
side chain as the silyl ether.13,48Each reaction was performed on 100
mg of resin. After cyclization and cleavage from the resin, each peptide
was purified by preparative HPLC and lyophilized to dryness. The
purified peptides were then methylated by dissolving the peptide in
DMF (6 mM) and adding K2CO3(2 equiv) and14CH3I (0.12 mCi, 10
equiv). When the methylation had gone to completion (∼24 h), the
reaction mixtures were filtered through disposable C18 cartridges and
the resin was rinsed with 5 column volumes of water. The peptides
were then eluted with acetonitrile, and the solvent was evaporated under
a stream of air. HPLC analysis of the resulting products showed >98%
purity for all products except one, which showed double methylation,
likely the result of a small amount of N-methylation. This peptide was
discarded from the study.
PAMPA. DMSO stocks (1 mM) of the radiolabeled cyclic peptides
were made, and each peptide was analyzed by liquid scintillation
counting to determine its specific activity. Next, 2.5 µM solutions of
each peptide were made in PBS (containing 0.25% DMSO) as starting
donor well solutions for the PAMPA (MultiScreen-IP hydrophobic
plate, cat. no. MAIPN4510/Millipore). A 1% solution of lecithin in
dodecane was then applied to each filter well at 5 µL per well.
Immediately after application of the lipid membrane, donor solutions
were added to the wells. Incubation times for all peptides were 19 h,
after which the acceptor well radioactivity was measured by adding
200 µL from the acceptor well to 10 mL of scintillation fluid and
submitting it to liquid scintillation counting. Final log Pe values for
each cyclic peptide were obtained as averages of the values from three
wells (calculated according to ref 49).
Acknowledgment. This work was supported in part by NIH
Grants AI035707 and GM56531 (to M.P.J.) and CA104569-03
(to R.S.L.). We thank the anonymous reviewers for their helpful
suggestions. M.P.J. thanks Ken Dill (UCSF) for illuminating
Supporting Information Available: Detailed experimental
procedures on compound synthesis and PAMPA, computation-
ally predicted low-dielectric structures for all cyclic peptides
tested experimentally, and detailed computational data for the
virtual cyclic peptide library. This material is available free of
charge via the Internet at http://pubs.acs.org.
(48) Tallarico, J. A.; Depew, K. M.; Pelish, H. E.; Westwood, N. J.; Lindsley,
C. W.; Shair, M. D.; Schreiber, S. L.; Foley, M. A. J. Comb. Chem. 2001,
(49) Schmidt, D.; Lynch, J. Application Note AN1725EN00; Millipore Corp.:
(50) Bermejo, M.; Avdeef, A.; Ruiz, A.; Nalda, R.; Ruell, J. A.; Tsinman, O.;
Gonzalez, I.; Fernandez, C.; Sanchez, G.; Garrigues, T. M.; Merino, V.
Eur. J. Pharm. Sci. 2004, 21, 429-441.
A R T I C L E S
Rezai et al.
14080 J. AM. CHEM. SOC.9VOL. 128, NO. 43, 2006