A Combined NMR and Molecular Dynamics Study of the Transmembrane
Solubility and Diffusion Rate Profile of Dioxygen in Lipid Bilayers†
M. Sameer Al-Abdul-Wahid,‡,§ Ching-Hsing Yu,‡,| Ihor Batruch,§ Ferenc Evanics,§ Re´gis Pome`s,|,⊥ and
R. Scott Prosser*,§
Department of Chemistry, UniVersity of Toronto, UTM, 3359 Mississauga Road, North Mississauga,
Ontario, Canada L5L 1C6, Structural Biology and Biochemistry, Hospital for Sick Children, 555 UniVersity AVenue,
Toronto, Ontario, Canada M5G 1X8, and Department of Biochemistry, UniVersity of Toronto
ReceiVed February 8, 2006; ReVised Manuscript ReceiVed July 5, 2006
ABSTRACT: The transmembrane profile of oxygen solubility and diffusivity in a lipid bilayer was assessed
by 13C NMR of the resident lipids (sn-2-perdeuterio-1-myristelaidoyl-2-myristoyl-sn-glycero-3-phospho-
choline) in combination with molecular dynamics (MD) simulations. At an oxygen partial pressure of 50
atm, distinct chemical shift perturbations of a paramagnetic origin were observed, spanning a factor of
3.2 within the sn-1 chain and an overall factor of 10 from the headgroup to the hydrophobic interior. The
distinguishing feature of the 13C NMR shift perturbation measurements, in comparison to ESR and
fluorescence quenching measurements, is that the local accessibility of oxygen is achieved for nearly all
carbon atoms in a single experiment with atomic resolution and without the use of a probe molecule. MD
simulations of an oxygenated and hydrated lipid bilayer provided an immersion depth distribution of all
carbon nuclei, in addition to the distribution of oxygen concentration and diffusivity with immersion
depth. All oxygen-induced 13C NMR chemical shift perturbations could be reasonably approximated by
simply accounting for the MD-derived immersion depth distribution of oxygen in the bilayer, appropriately
averaged according to the immersion depth distribution of the 13C nuclei. Second-order effects in the
paramagnetic shift are attributed to the collisionally accessible solid angle or to the propensity of the
valence electrons in the vicinity of a given nuclear spin to be polarized or delocalized by oxygen. A
method is presented to measure such effects. The excellent agreement between MD and NMR provides
an important cross-validation of the two techniques.
The transmembrane distribution and associated transport
properties of oxygen are fundamental to cellular respiration
and key to many basic processes in the cell. Slight changes
in the availability of oxygen at certain sites in the cell
membrane are thought to trigger a cascade of responses,
brought about by oxygen-sensing mechanisms (1, 2). Changes
in local oxygen concentrations are also integrally related to
ischemia (3, 4), cellular responses to anesthesia (5, 6),
photodynamic therapy, and radiation. A key issue in the role
of oxygen in many physiological processes is whether its
transbilayer permeation is the limiting step in cellular
respiration, and if not, might existing channel proteins
facilitate oxygen transport. Current understanding of oxygen
transport rates and of the transmembrane distribution of both
concentration and diffusion rates has come largely from
fluorescence (7, 8) and ESR studies (9-11), though transport
can also be effectively measured across lipid monolayers
deposited on a working electrode (12-14). The prevailing
opinion, at least in the case of ESR studies of plasma
membranes, is that oxygen permeation across the membrane
is not the rate-limiting step in respiration (15, 16). The issue
of the relative contribution of passive and facilitated diffusion
is also of current interest to cell physiologists (17, 18). ESR
and fluorescence quenching measurements designed to probe
local oxygen concentration and diffusivity usually rely on a
relatively large spin-label or fluorophore, which can be
attached to either a lipid-like amphiphile or peptide and thus
localized over a range of depths in the membrane. Moreover,
the sensitivity of ESR and fluorescence is such that the probe
molecule can be used at low concentrations. Nevertheless,
the possibility that the oxygen concentration and diffusivity
are disrupted in the vicinity of the probe cannot be
discounted, making it difficult to deduce the precise oxygen
concentration and diffusivity profile of the membrane.
We revisit the problem of the solubility of oxygen with
immersion depth from the perspective of solution state 13C
NMR of the resident bilayer lipids, where we show that
distinct chemical shift perturbations of a paramagnetic origin
can be simultaneously measured for nearly every carbon
nucleus in the lipid without the use of any sterically
perturbing probe. The measured effects span an order of
magnitude from the lipid headgroup to the hydrophobic
interior and a factor of roughly 3 along the length of the
† R.P. thanks CIHR and the Hospital for Sick Children RTC program
for funding. R.P. is a CRCP chairholder. R.S.P. acknowledges support
from the American Chemical Society (PRF AC Grant 376620) and the
Natural Sciences and Engineering Research Council of Canada
(NSERC). R.S. also acknowledges support from the Petroleum Research
Council and NSERC.
* To whom correspondence should be addressed. E-mail: sprosser@
utm.utoronto.ca. Tel: (905) 828-3802. Fax: (905) 828-5425.
‡ The two first authors contributed equally to this work.
§ Department of Chemistry, University of Toronto.
| Hospital for Sick Chidren.
⊥ Department of Biochemistry, University of Toronto.
10719Biochemistry 2006, 45, 10719-10728
10.1021/bi060270f CCC: $33.50 © 2006 American Chemical Society
Published on Web 08/09/2006

sn-1 chain of the lipid. Our results are corroborated by
molecular dynamics (MD) simulations of oxygen in a fully
hydrated lipid bilayer. We discuss herein aspects of the lipid
bilayer model system and associated solution NMR experi-
ments followed by an introduction to the theory related to
paramagnetic shifts from a diffusible paramagnet and a
discussion of the MD simulations.
Atomic Resolution of Lipid Bilayers. Phospholipids present
a significant challenge to the NMR spectroscopist due to line
broadening and severe overlap of methylene resonances,
particularly in multilamellar lipid bilayer aggregates which
form spontaneously upon addition of excess water. An
alternative model membrane system is the isotropic or fast
tumbling bicelle. Bicelles consist of both long-chain phos-
pholipids, which spontaneously form a stable lipid bilayer,
and short-chain phospholipids, designed to coat the hydro-
phobic edges of the disk-shaped bilayer domain, resulting
in an aggregate which is considerably smaller than a multi-
or unilamellar vesicle. The small aggregate size facilitates
rapid tumbling of the bicelle in solution, giving rise to
relatively narrow line widths in the associated NMR spectra
(19, 20). To further eliminate the overlap of methylene
resonances, we have made use of an unsaturated phospho-
lipid, sn-2-perdeuterio-1-myristelaidoyl-2-myristoyl-sn-glyc-
ero-3-phosphocholine (MLMPC).1 The double bond in the
sn-1 chain of MLMPC improves chemical shift dispersion,
and deuteration of the sn-2 chain simplifies the resulting
spectra, which show peaks resulting only from the sn-1 chain.
When MLMPC is combined with equimolar amounts of a
short-chain lipid (DHPC-d22), the above fast-tumbling bi-
1 Abbreviations: MLMPC, sn-2-perdeuterio-1-myristelaidoyl-2-
myristoyl-sn-glycero-3-phosphocholine; DHPC, 1,2-dihexanoyl-sn-glyc-
ero-3-phosphocholine; DMPC, 1,2-dimyristoyl-sn-glycero-3-phospho-
choline; DOPC, 1,2-dioleoyl-sn-glycero-3-phosphocholine; DOPM, 1,2-
dioleoyl-sn-glycero-3-phosphomethanol; MLEV, Malcolm Levitt’s
composite pulse decoupling; DEPT, distortionless enhancement by
polarization transfer; INEPT, insensitive nuclei enhanced by polarization
transfer; HSQC, heteronuclear single-quantum correlation; HMBC,
heteronuclear multiple-bond correlation.
FIGURE 1: Structural formula of MLMPC with corresponding 1H and 13C DEPT NMR spectra at 45 °C. The 1H spectrum is that of MLMPC
in 1:1 deuterated methanol/chloroform, while the 13C spectrum is obtained from a 25% (w/w) q ) 0.8 bicelle mixture of chain-perdeuterated
DHPC-d22 and MLMPC. 1H and 13C NMR assignments, shown in the figure, were based on literature values and on 1H,13C HSQC and
two-bond 1H,13C HMBC experiments.
10720 Biochemistry, Vol. 45, No. 35, 2006 Al-Abdul-Wahid et al.

celles spontaneously form (19, 20). The structure and
assigned 1H and 13C NMR spectra of the long-chain lipid,
MLMPC, are shown in Figure 1.
Paramagnetic Effects. Paramagnetic effects of oxygen may
include local spin-lattice relaxation (T1), line broadening
(T2), and chemical shift perturbations. The majority of NMR
studies involving oxygen as a paramagnetic probe have
utilized T1 or T2 effects on 1H nuclei to study protein topology
and protein-protein interactions (21-27). The paramagnetic
influence of oxygen on T1 and T2 is relatively easy to
interpret, in part because the oxygen electronic spin relaxation
times are sufficiently short (on the order of picoseconds) to
render the effective correlation time associated with modula-
tion of the dipolar interaction constant (28). A second
consequence of the short electronic relaxation time is that
line broadening is relatively weak at partial pressures where
significant paramagnetic spin-lattice relaxation rates and
chemical shift perturbations are observed (i.e., 20-50 atm).
This paper focuses on oxygen-induced paramagnetic shifts,
rather than spin-lattice relaxation effects, to study perme-
ation of oxygen in lipid bilayers. This approach has the
advantage that the effects are directly related to local oxygen
concentrations, while one need not be concerned with
deuteration levels and the effects of spin diffusion, which
often complicate 1H relaxation rate analyses, particularly in
membranes and micelles. Small 1H chemical shift perturba-
tions from oxygen have been previously reported in protein
studies (23), and sizable oxygen-induced 19F chemical shift
perturbations have been reported and used to study membrane
immersion depth (29) and protein topology (30). In the latter
study, a site-directed spin-labeling approach was taken, in
which a cysteine-specific fluorinated substituent was em-
ployed so that relative differences in oxygen-induced para-
magnetic shifts could be interpreted in terms of membrane
protein structure and environment. In the present case, our
goal is to directly measure local effects of oxygen in a lipid
bilayer without the use of any probe molecule. We observe
that modest partial pressures (50 atm) are sufficient to
observe significant 13C NMR paramagnetic shifts, which we
attribute to a contact mechanism (31). Contact shifts, which
arise from unpaired electron spin density at the resonant
nucleus, are typically awkward to compute or interpret in
terms of structural information (32, 33). Contact shifts arising
from a freely diffusible paramagnet might be expected to
be even more complicated. However, here we adopt a very
empirical approach and assume the paramagnet does not
undergo strong binding at or near the nucleus of interest (i.e.,
does not coordinate with a specific geometry), in which case
the key variables may simply involve the local oxygen
concentration, [O2], and the depth distribution function of
the probe nucleus, Fi. This situation is distinct from either
ESR or fluorescence spectroscopy, where the collisional
frequency of oxygen, which involves both [O2] and the local
diffusion coefficient, DO2, dictates the magnitude of quench-
ing. The characteristic frequency associated with a diffusional
jump is much faster than the NMR time scale, in which case
the chemical shift perturbations should be determined by the
average time an oxygen molecule is associated with a given
carbon nucleus. In other words, we expect that the para-
magnetic shifts should relate to the local oxygen concentra-
tion rather than the product of the concentration and oxygen-
carbon collision frequency. For the moment we consider both
cases: (1) the strong collision limit, in which the contact
shift depends on the collisional frequency of the paramagnet
with the 13C atom (i.e., the product of the oxygen concentra-
tion and diffusion coefficient, DO2) (9), and (2) the weak
collision limit where the paramagnetic shifts will depend on
the local oxygen concentration in the membrane. Under the
assumption of the strong collision limit, we express the 13C
contact shift, ¢äi, acting on nucleus i, resulting from
nonspecific collisional accessibility of oxygen, as
where k is simply a proportionality constant and the integral
accounts for the variation of the local oxygen concentration,
[O2(z)], and diffusion coefficient, DO2(z), with immersion
depth, z, weighted by the depth-dependent distribution
function of the ith nucleus, Fi(z). Here we approximate the
collisional frequency by the product of the oxygen concen-
tration and diffusion coefficient, and we neglect any con-
tribution from lipid diffusion or translational excursions
resulting from acyl chain isomerizations. The alternative
description of the contact shift neglects diffusion as discussed
above, in which case we define an appropriate proportionality
constant, k′, and we write
In either case, to deconvolve the above contributions, we
have performed an all-atom molecular dynamics (MD)
simulation of a hydrated lipid bilayer, involving the lipid
MLMPC, in the presence of oxygen and under conditions
approximating those used in our experiment. The MD
simulations provide an independent assessment of Fi(z), [O2-
(z)], and DO2(z), leaving only the global proportionality
constant, k′, as an adjustable parameter in the fitting of the
paramagnetic shift profile for the entire membrane.
MATERIALS AND METHODS
Sample Preparation. sn-2-Perdeuterio-1-myristelaidoyl-2-
myristoyl-sn-glycero-3-phosphocholine (MLMPC) and chain-
perdeuterated 1,2-dihexanoyl-sn-glycero-3-phosphocholine
(DHPC-d22) were obtained as powders from Avanti Polar
Lipids (Alabaster, AL). Bicelles in which the long-chain to
short-chain lipid molar ratio, q, was 0.8 were prepared by
first combining dry MLMPC to a stock solution of 25% (w/
w) DHPC-d22 in D2O, maintained at pH 7.0 with 100 mM
phosphate buffer. An appropriate amount of buffer was
subsequently added to obtain a 25% (w/w) dispersion. A few
minutes of gentle vortexing was sufficient to obtain a clear
mixture. In the study of lipid shift perturbations below the
critical concentration for aggregation, approximately 25 mg
of MLMPC was solubilized in 700 íL of a 1:1 (molar ratio)
deuterated methanol/chloroform solution.
NMR Experiments. All NMR experiments were performed
on a 600 MHz Varian Inova spectrometer and a standard
HX broad-band probe. In the case of oxygen paramagnetic
rate measurements, the sample was usually pressurized in a
5 mm o.d. sapphire NMR tube (Saphikon, NH) to 50-70
atm of oxygen partial pressure for 2 days to speed up
equilibration rates and then equilibrated in the magnet while
maintaining the desired final pressure of 50 atm. Spectra were
¢äi ) ksFi(z)[O2(z)]DO2(z) dz (1a)
¢äi ) k′sFi(z)[O2(z)] dz (1b)
NMR/MD of O2 Solubility/Diffusion in Lipid Bilayers Biochemistry, Vol. 45, No. 35, 2006 10721

compared to those obtained under equivalent partial pressures
of N2 to factor out any pressure-induced shifts. Absolute
referencing of the chemical shift was established through
the Varian “setref” macro which establishes a 13C chemical
shift based on the lock signal; identical transmitter frequen-
cies were used in both the oxygenated and unoxygenated
samples in order to obtain an absolute change in chemical
shift from oxygen. Typical 13C and 1H (decoupling) pulse
lengths were 7 and 10 ís, respectively, while most spectra
were obtained using 500-1200 scans and a repetition time
of either 8.2 or 1.4 s, for either ambient or oxygenated
membranes. All 13C natural abundance NMR spectra were
obtained using a DEPT sequence, which simply converts
proton magnetization to transverse 13C magnetization, through
two INEPT periods, thereby discriminating between CH,
CH2, and CH3 groups, while filtering out 13C resonances
directly associated with deuterated moieties. Thus, only 13C
NMR aliphatic signals from the sn-1 chain of the long-chain
lipid are observed in a 1H-coupled 13C NMR experiment.
To optimize resolution, while minimizing local heating due
to decoupling, 13C acquisition times were usually 140 ms,
under 2500 Hz B1 decoupling fields and using broad-band
MLEV decoupling. Spectral analysis and peak deconvolution
were performed using Varian software.
13C Chemical Shift Assignments. Returning to the 13C NMR
DEPT spectrum of MLMPC in Figure 1, note that the lipid
headgroup resonances arise from both MLMPC and chain-
perdeuterated DHPC-d22, since both possess identical phos-
phatidylcholines. The aliphatic signal arises purely from the
long-chain lipid with the exception of the residual signal from
the C2 carbon of DHPC-d22, which is not fully deuterated
at this position. The headgroup and glycerol backbone
resonances are well established for both 1H and 13C NMR.
However, the majority of aliphatic resonances of the sn-1
chain of MLMPC are also resolvable in the 13C spectrum,
due to the fact that the 9,10 trans double bond causes
additional chemical shift dispersion in the so-called plateau
region of the lipid chain and in part to relatively long T2
relaxation times of this model system. The sn-2 chain is
perdeuterated and, thus, not observed. Assignments were
obtained by a combination of 1H,13C HSQC and HMBC
experiments where both one- and two-bond scalar couplings
(i.e., 1JCH and 2JCH couplings of 145 and 10 Hz) were utilized.
Molecular Dynamics Simulations. The CHARMM pro-
gram (34), version 27, was used for the simulations of oxygen
diffusion in MLMPC bilayers. The CHARMM22 force field
(35, 36), TIP3P water potential (37), and Lennard-Jones
dioxygen potential (38) were used to model the system.
Calculations were carried out under experimental conditions,
i.e., 318 K and 1 atm and, upon bilayer equilibration, constant
N, PN, ç, and T, which denote the number of particles, normal
pressure, surface tension, and temperature of the ensemble,
respectively. At the early stage of bilayer equilibration,
elevated temperatures and N, PN, A, T (where A denotes
constant surface area) were used. The Langevin piston
algorithm (36) was used to maintain the pressure and surface
tension using a piston mass of 500 amu, a collision frequency
of 10 ps-1, and a surface tension of 10 dyn/cm (see below).
Temperature was maintained using the Hoover thermostat
(39). Periodic boundary conditions and tetragonal symmetry
were applied to the lipid systems. The particle-mesh Ewald
(PME) method (40) was employed to calculate the electro-
static interactions with a  value of 0.3 and a grid spacing
of approximately 1 Å for the three-dimensional fast Fourier
transform. Nonbonded pair lists were updated heuristically
with a cutoff of 14 Å for the real-space portion of the Ewald
sum and the Lennard-Jones potential, which was smoothly
switched off to zero over the range of 10-12 Å. The SHAKE
algorithm (41) was used to fix the length of all covalent
bonds involving hydrogen. The time step for the integration
of the equations of motion was 2 fs.
The initial MLMPC bilayer was constructed from 32 all-
trans lipids (16 per monolayer) placed on a regular grid; 1152
water molecules were then added to the system, yielding a
stoichiometry of 36 water molecules per lipid. This system
was then subjected to several hundred picoseconds of N, PN,
A, T simulations with a surface area per lipid set to either
62.3 or 68.5 Å2 and with temperatures ranging from 318 to
500 K. The resulting preequilibrated bilayers were then
inspected, and three systems were separately chosen for
replication to a full 128 lipid model system. Each of these
three bilayer systems was subjected to further equilibration
for at least 500 ps, followed by 2 ns of N, PN, ç, T simulation
at 318 K with a surface tension of 10 dyn/cm; 128 oxygen
molecules were then introduced to the middle of the water
layer (64 per side) on a regular grid. Each model system
was then subjected to a final 8 ns N, PN, ç, T calculation.
The last 2 ns of these trajectories was used for analysis. A
separate 5 ns simulation of a neat bilayer was performed as
a reference.
The optimal value of the applied surface tension was
determined from simulations at three different strengths, 10,
15, and 20 dyn/cm. Recent work by Sankararamakrishnan
and Weinstein (42) suggested that a value of 25-30 dyn/
cm should be used for a system of 90 DMPC lipid molecules.
In this study, a surface tension of 10 dyn/cm was chosen
because it led to a surface area per lipid of 63.3 ( 1.3 Å2 at
318 K (average of 2 ns simulations) in good agreement with
experimental DMPC bilayer measurements of 60.0 and 65.4
Å2 at 303 and 323 K, respectively (43). The equilibration of
the lipid systems was further verified on the basis of bilayer
thickness and order parameters, which are in good agreement
with experimental and MD results (42, 43). The partitioning
of O2 from the water layer to the bilayer interior required
over 4 ns of simulation time. Equilibration was assumed once
the number of O2 molecules within the hydrophobic interior
of the bilayer reached a steady state (i.e., the numbers of O2
molecules entering and exiting the bilayer over a period of
100 ps became approximately equal).
Calculating Oxygen Concentrations and Diffusion Coef-
ficients. The distribution of oxygen concentration (with
respect to immersion depth) was evaluated from the simula-
tions as the number of oxygen molecules in the local volume
of a 2 Å slice along the bilayer normal. To obtain reliable
statistics, the distributions were determined by sampling 600
conformations from 60 trajectories at 10 ps intervals. The
local diffusion coefficients of O2 in the bilayer plane, Dxy,
with respect to immersion depth were calculated through the
slope of the mean-square displacement (MSD):
where [r(t) - r(0)]2 is the displacement in the bilayer xy
plane at time t.
Dxy(z) ) 14t limtf∞ 〈jr(t) - r(0)j
2〉 (2)
10722 Biochemistry, Vol. 45, No. 35, 2006 Al-Abdul-Wahid et al.

A slab of 2 Å was used for the evaluation, and the slabs
were moved along the z-axis in 1 Å increments to obtain
the coefficients at different depths. To improve statistics, the
time origin, t ) 0, was assigned independently for each O2
molecule when it entered the slab. Due to the nature of
oxygen diffusion, it is not possible to calculate the diffusion
coefficients in a finite slab over an infinite time. In this study,
the choice of relatively thin slabs forced the calculation of
diffusion coefficients over short time intervals of 1-1.6 ps.
Longer time intervals (44, 45) could be attained by using
thicker slabs. However, this would yield less localized values.
Another method to calculate the diffusion coefficients is
to use the force autocorrelation function of O2 molecules
(43-45). However, this method would require additional
simulations with spatial restraints on oxygen positions. Since
the primary objective of the MD simulations is to compute
the local oxygen concentration and diffusion solubility
product, [O2(z)]  DO2(z), the MSD approach, which involves
a large number of unconstrained O2 molecules, offers the
advantage of simultaneously yielding the two quantities of
interest, [O2(z)] and DO2(z).
RESULTS AND DISCUSSION
Transmembrane 13C Paramagnetic Shift Effects from
Oxygen. Figure 2 depicts the oxygen-induced 13C chemical
shift perturbations for nuclei spanning the entire bilayer (i.e.,
headgroup and hydrophobic domain) at a partial pressure of
50 atm. Shift perturbations, ¢äi, were determined by
subtracting the chemical shifts of the assigned 13C NMR
DEPT spectrum of MLMPC under nitrogen from those under
the equivalent pressure of oxygen. Note that resonances
assigned to carbon nuclei 4, 5, and 6 overlap, and therefore
only an average shift perturbation can be determined for these
three nuclei. Overall, the paramagnetic shifts span an order
of magnitude across the entire bilayer, while the shifts
associated with the sn-1 chain span a factor of 3.2 from
carbon 2 to the terminal methyl carbon. Dashed and solid
lines represent fits based upon eqs 1a and 1b (vide infra).
We consider next the various contributions to the paramag-
netic shifts based on a thorough MD analysis of the identical
lipid bilayer.
Calculations of the Solubility and DiffusiVity from Mo-
lecular Dynamics Simulations. Figure 3 displays the immer-
sion depth distribution functions of carbon nuclei belonging
to the sn-1 chain of MLMPC, obtained from the MD
simulations of the lipid bilayer at 318 K. The instantaneous
depths of each nucleus are referenced to the plane associated
with the hydrophobic center of the bilayer. Therefore, out-
of-plane dynamics and intramolecular motions both contrib-
ute to the observed distribution of immersion depths. The
small magnitude of asymmetry of each distribution with
respect to z ) 0 indicates that statistical convergence is
adequate. Note that the glycerol carbons are relatively closely
packed and serve to anchor the lipid acyl chains at one end,
while the gauche-trans isomerizations of the acyl chain give
rise to a prominent disorder gradient along the immersion
depth axis (46). This disorder is manifested in an increasingly
broader distribution of immersion depth toward the methyl
terminus of the lipid chain. Similar positional distributions
have been measured in oriented lipid bilayers, by a combina-
tion of low-angle X-ray and neutron scattering (47). As
discussed below, the MD-derived immersion depth distribu-
tions of the probe (carbon) nuclei must be combined with
depth-specific oxygen concentration before the oxygen-
induced shift profile can be predicted, using eq 1b.
Figure 4A displays both the oxygen distribution function,
[O2(z)], and diffusion coefficient profile, DO2(z), determined
from the MD simulation. Note that the oxygen concentration
is normalized so that the local concentration in the bulk water
region roughly agrees with that expected for water in the
FIGURE 2: Oxygen-induced 13C chemical shift perturbations, ¢äi,
of MLMPC in a q ) 0.8 bicellar mixture at 45 °C. Shift
perturbations were determined by subtracting the chemical shifts
of the assigned 13C NMR DEPT spectrum of MLMPC under oxygen
from the equivalent spectrum under nitrogen. Note that resonances
assigned to carbon nuclei 4-6 overlap. Therefore, only an average
shift perturbation can be determined for these three resonances.
Two fits to ¢äi in the lipid bilayer are shown: one based on an
MD average involving ¢äi ) k′sFi(z)[O2(z)] dz, shown by the solid
line, and the other based on MD incorporating the oxygen diffusion
rate, ¢äi ) ksFi(z)[O2(z)]DO2(z) dz, shown by the dashed line.
FIGURE 3: Immersion depth distribution profile of carbon nuclei
from the sn-1 chain of MLMPC, resulting from a 5 ns molecular
dynamics simulation involving 128 lipids, 4608 water molecules,
and 128 oxygen molecules. Distributions are vertically displaced
for clarity, and z ) 0 is defined to represent the hydrophobic center
of the bilayer.
NMR/MD of O2 Solubility/Diffusion in Lipid Bilayers Biochemistry, Vol. 45, No. 35, 2006 10723

presence of 100 mM salt, assuming an oxygen partial
pressure (PO2) of 1.0 atm (i.e., 800 íM). Since oxygen
solubility in the membrane/water system depends linearly
on pressure, at least below oxygen partial pressures of 50
atm (48), the local concentration can be estimated in this
pressure range by multiplying the appropriate value in Figure
4A by the applied oxygen partial pressure. Local oxygen
solubility is dictated by hydrophobicity and accessible free
volume. As such, it is not surprising that the MD simulation
predicts a significant variation in oxygen solubility with
immersion depth, since a gradient of accessible free volume
is known to exist (44). Comparing the difference between
the maximum oxygen concentration at z ) 0 Å (the bilayer
center) and that in bulk water, we estimate the excess free
energy to be -5.8 kJ/mol, while the average membrane
oxygen concentration resulting from the MD simulation
translates into an excess free energy of -3.0 kJ/mol at 45
°C. This value is less than the average excess free energy of
oxygen in the membrane of -4.5 kJ/mol, computed by
Marrink and Berendsen (44), although the latter calculation
was performed with a saturated lipid at a considerably higher
temperature (77 °C). Classic oil/water partitioning experi-
ments of oxygen have suggested an excess free energy on
the order of -3.7 kJ/mol (49).
The above MD-derived profile of oxygen solubility may
be contrasted with that predicted by simple thermodynamic
partitioning theory, in which a two-phase distribution
between membrane regions with z < z0 and z > z0 is
established as a result of the difference in free energy
between oxygen in water and in the hydrophobic interior of
the membrane (50). The Boltzmann sigmoidal distribution,
extending from bulk water (z ) -30 Å) to the bilayer center
(z ) 0 Å) is expressed as
where oxygen concentrations range from a minimum in bulk
water, [O2]water, to a maximum, [O2]max, in the hydrophobic
bilayer center. z0 designates an immersion depth where the
oxygen gradient is greatest, while ì characterizes the effective
width of the distribution function. The dashed line in Figure
4A represents a fit of eq 3 to the solubility profile determined
by MD simulations. In our case, the fitted oxygen concentra-
tions range from [O2]water ) 520 ( 100 íM to a maximum
concentration of 7.1 mM in the bilayer center, while ì and
z0 are estimated to be ì ) 3.0 ( 0.25 Å and z0 ) -6.11 (
0.27 Å. ESR studies have made use of spin-labeled phos-
pholipid analogues to assess the collisional accessibility of
oxygen for the majority of sites, at least in the membrane
hydrophobic interior (9-11, 50, 51). These studies reveal a
similar value for z0 although ì is slightly lower than that
determined in our case.
Since our focus in this study is to assess the oxygen
solubility and diffusivity across the entire bilayer and in the
absence of any external probe, we will rely heavily on the
MD simulations to connect the solubility profile and carbon
depth distribution functions with the resulting paramagnetic
chemical shift profile. Examining Figure 4A, a comparison
of the MD [O2] profile (solid squares) to the sigmoidal
approximation (dotted line) shows that the MD profile is
different in several respects from that predicted by partition
theory. For example, oxygen concentrations and mobilities
in the vicinity of the glycerol headgroup are observed to be
lower than that in bulk water (Figure 4A), and the depth-
dependent oxygen concentration profile exhibits a slight
inflection in the vicinity of the (trans) double bond. Such
subtleties are no doubt a result of local density effects, void
volumes, and local lipid dynamics, all of which are incor-
porated in the MD approach.
Figure 4A also displays the MD-derived oxygen diffusion
coefficients as a function of average immersion depth (solid
circles), where the diffusion coefficient is predicted to
increase in the hydrophobic interior by a factor of 5 compared
to that in the bulk water phase, with an average diffusion
coefficient of 3.7  10-5 cm2 s-1 (at 318 K). This result
compares favorably with the average diffusion coefficient
predicted by Marrink and Berendsen for a DPPC lipid bilayer
at 350 K (44), which may be extrapolated to be 4  10-5
cm2 s-1 at 318 K, assuming Arrhenius behavior and an
activation energy of 4.4 kJ/mol. Moreover, experimental
estimates of oxygen diffusion coefficients in tetradecane are
on the order of 3.4  10-5 cm2 s-1 at 296 K (52). Clearly,
FIGURE 4: (A) Oxygen concentration, [O2(z)], and diffusion rate,
DO2(z), as a function of immersion depth, based on MD simulations
of an MLMPC lipid bilayer at 315 K. Note that the concentration,
[O2(z)], is normalized to that expected at an oxygen partial pressure
(PO2) of 1 atm. The dashed line associated with the oxygen solubility
data is a fit to a Boltzmann sigmoidal expression, which describes
a simple two-phase distribution of oxygen between water and the
membrane interior. (B) The product of the oxygen concentration
and diffusion rate versus immersion depth, based on the above MD
simulation.
[O2(z)]sim )
[O2]water - [O2]max
1 + exp[(z - z0)/ì]
+ [O2]max (3)
10724 Biochemistry, Vol. 45, No. 35, 2006 Al-Abdul-Wahid et al.

accurate estimations of both the concentration and diffusion
coefficient of oxygen with atomic resolution are necessary
to predict the oxygen collisional frequency with the probe
species. At issue is the nature of the effect of oxygen on the
13C chemical shifts; in the event that the oxygen encounters
are in the strong collision limit, the chemical shift perturba-
tions should depend on the product of the diffusion coef-
ficient and concentration, shown in Figure 4B. On the other
hand, as discussed earlier, in the weak collision limit the
paramagnetic gradient should depend on the oxygen con-
centration profile, as shown in Figure 4A. To assess the
validity of the predicted oxygen concentration profile and
collisional frequency profile, we must next consider the
motions and exact distribution of immersion depth of each
of the carbon nuclei in the lipid, as introduced in eqs 1a and
1b.
EValuating the Oxygen-Induced Chemical Shift Perturba-
tion Profile. We now revisit the paramagnetic shift perturba-
tions shown in Figure 2 in an attempt to explain the data on
the basis of the above MD analysis. The dashed line
represents theoretical contact shifts calculated using eq 1a
[which incorporates the carbon immersion depth distribution,
oxygen concentration profile, and oxygen diffusion coef-
ficient profile, i.e., ¢äi ) ksFi(z)[O2(z)]DO2(z) dz], while the
solid line represents theoretical shifts calculated using eq 1b,
which assumes that the shifts are determined solely by the
oxygen concentration profile and carbon immersion depth
distribution, i.e., ¢äi ) k′sFi(z)[O2(z)] dz. In either case, only
a single adjustable parameter (k or k′) is used to fit the entire
chemical shift perturbation profile. Clearly, the solid line
associated with eq 1b reproduces the observed paramagnetic
shifts remarkably, confirming that the oxygen diffusion
profile does not play a significant role in affecting the 13C
NMR paramagnetic shift trend.
Second-Order Effects. Although the paramagnetic shifts
seem to be well represented by ¢äi ) k′sFi(z)[O2(z)] dz, we
consider next whether slight departures from the curve might
arise due to second-order effects. We consider two effects:
a polarizing correction factor, Ri, associated with the
propensity of the local valence electrons to be delocalized
or polarized, and a steric term, which we express as the
correction factor associated with the average collisionally
accessible solid angle at the nucleus of interest, 〈¿i〉.
Due to differences in delocalization and polarizability, we
expect a difference in response to a diffusible paramagnet
acting on sp1-, sp2-, or sp3-bonded carbon nuclei (53), which
we incorporate into Ri. For example, the sp3 orbitals of the
aliphatic carbons of the sn-1 chain all extend further from
the nucleus, owing to higher p-orbital content, than those of
the sp2 orbitals of carbon atoms 9 and 10, (the trans double
bond). Curiously, ¢äi does indeed appear to fall below the
predicted line for C9 and C10, associated with the sp2
orbitals, as shown in Figure 2. This “susceptibility” effect,
which we refer to as Ri, could be assessed if an experiment
could be performed under conditions where the lipid was
exposed to a uniform oxygen profile. Such an experiment
was attempted by first dissolving the lipid in a 1:1 methanol/
chloroform solution, below the critical micelle concentration.
Oxygen-induced chemical shift perturbations were then
measured in a manner identical to that performed in bicelles
(included in Supporting Information), and shifts associated
with C9 and C10 were observed to be approximately 20%
less than those of the carbons in the immediate vicinity of
the double bond, C8 and C11. Such a correction (i.e., R9 )
R10 ) 1.2) would indeed place the paramagnetic shifts very
near the fitted (solid) line in Figure 2. We have recently taken
a similar approach in a separate study of solvent accessibility
by dioxygen-induced 13C chemical shift perturbations of a
soluble protein, observed via 1H,13C HSQC spectra (54). In
this case, the observed paramagnetic shift for each 13C species
in the protein was divided by the shift observed for the
equivalent 13C atom from the free amino acid. Thus, potential
variations in the sensitivity of 13C paramagnetic shifts due
to delocalization or polarizability effects from nearby oxygen
can be accounted for.
Another potential source of second-order effects might
arise from steric protection, which we express in terms of a
collisionally accessible solid angle correction factor, 〈¿i〉.
For example, the penultimate carbon may experience ad-
ditional protection from the bulky terminal methyl group,
giving rise to a slightly lower shift perturbation, ¢ä13, as is
seen in Figure 2. Indeed, the shift of the penultimate carbon
is also about 20% lower than ¢ä12 or ¢ä14 in the methanol/
chloroform sample, suggesting a correction factor of 〈¿13〉
) 1.2.
Combining both of these second-order effects with eq 1b
provides the following equation for the theoretical paramag-
netic shift:
where Ri and 〈¿i〉 are determined from experiments where
[O2(z)] is constant for all z.
Note that eq 4 is intended to apply only to a freely
diffusing paramagnet, such as oxygen, in which we envisage
the polarizing factor, Ri, to be an isotropic average. Similarly,
the collisionally accessible solid angle is assumed to be
weakly correlated with the various lipid conformations such
that it may be separately considered from the integral in eq
4. Finally, a key assumption is that the local oxygen solubility
does not depend on the instantaneous lipid conformation. In
principle, the MD simulations could provide the solubility
profile associated with each member of the ensemble of lipid
conformers, thereby avoiding this assumption. However,
encounters with molecular oxygen for certain nuclei are quite
rare. Consequently, very long MD trajectories would be
necessary to sample a statistically meaningful average of
oxygen distributions for each carbon nucleus within the vast
ensemble of lipid conformations. The above notwithstanding,
the quality of the fit of the solid line in Figure 2 suggests
that these assumptions are reasonable and that the corrections
introduced by considering second-order effects are relatively
small.
CaVeats in the Bicelle Model. A bicelle membrane model
was necessary to achieve the requisite resolution in this study.
The morphology of the isotropic bicelle has been carefully
considered by neutron scattering, light scattering, and 31P
NMR (55). This and other studies have confirmed that the
combination of a 14-C and 6-C phosphatidylcholine (i.e.,
DMPC and DHPC, respectively) formed an aggregate in
which the two lipids were demixed (i.e., a bicelle rather than
a mixed micelle), for long-chain to short-chain lipid molar
ratios (q) between 0.25 and 1.0. On the basis of these results
we can estimate that, for a q ) 0.8 bicelle, the radius, R, of
¢äi ) k′′Ri〈¿i〉sFi(z)[O2(z)] dz (4)
NMR/MD of O2 Solubility/Diffusion in Lipid Bilayers Biochemistry, Vol. 45, No. 35, 2006 10725

the bilayer “disk” in the plane of the membrane is no more
than 70 Å (55, 56). This dimension implies that a given
bicelle aggregate consists of not more than 500 MLMPC
molecules, where we would expect a significant fraction to
be in contact with the DHPC interface. Therefore, extrapola-
tion of the present results to an infinite bilayer devoid of
DHPC must be viewed with caution until the effect of the
DHPC boundary lipids can be considered in greater detail.
More recently, we have studied the distribution of oxygen-
induced paramagnetic shifts of MLMPC in small unilamellar
vesicles (unpublished results). In this case, the oxygen
paramagnetic shift trend is similar. In general, the ESR results
portray a comparable paramagnetic gradient across the
hydrophobic region of the membrane. Dzikovski et al.
recently observed ESR line shapes and oxygen-induced
changes in line width and T1e of spin-labeled lipid analogues,
spanning a factor of 2 in DMPC bilayers at 30 °C (11). Using
a spin-labeled R-helical peptide, Nielsen et al. reported
electronic spin-lattice relaxation times, T1e, to span a factor
of 2.3 and 2.6 across the hydrophobic domain of DOPC and
DOPM bilayers, respectively (57). However, it should be
pointed out that their conclusion regarding the oxygen
diffusion coefficient profile is considerably different than the
result obtained in our simulations, which predict that oxygen
diffuses significantly faster in the hydrophobic interior, in
comparison to water. Conflicting results on relative oxygen
diffusion coefficients in the hydrophobic interior have been
reported (44, 45). This discrepancy is due at least in part to
systematic errors in the estimates of diffusion rates in bulk
water. Systematic differences between various models of
water yield self-diffusion coefficients that differ by a factor
of 2.
CONCLUSION AND FINAL REMARKS
In this study we have revisited the oxygen accessibility
profile in a lipid bilayer, previously studied in detail by ESR
and fluorescence quenching experiments, via 13C solution
NMR, where we have demonstrated that atomic resolution
can be achieved and the local accessibility of oxygen can
be measured without the use of bulky or sterically perturbing
probes. MD simulations of the identical MLMPC lipid
bilayer provided an estimation of the transmembrane distri-
butions of the carbon nuclei of interest, Fi(z), the local oxygen
concentration profile, [O2(z)], and the local oxygen diffusion
coefficient profile, DO2(z). An equation was proposed to
quantitatively explain the observed paramagnetic shifts for
a diffusible uncharged paramagnet. To first order, this
equation proposes that the shift perturbation, ¢äi, may be
approximated by the integral involving the oxygen concen-
tration, weighted by the transmembrane distribution function
of the probe nucleus. The MD-derived integral, sFi(z)[O2-
(z)] dz, was found to be in excellent agreement with the
observed 13C shift perturbations across the entire bilayer.
Moreover, by comparing simulations which assumed that the
paramagnetic shift was due either to the concentration of
oxygen or to the collisional frequency [O2(z)]  DO2(z), we
confirmed that, in the case of 13C NMR, oxygen interactions
are essentially in the weak collision limit and that variations
in the diffusion rate may be neglected. Second-order cor-
rections involving both the propensity of a given nuclear spin
to be delocalized and/or polarized, Ri, in addition to
corrections associated with differences in the collisionally
accessible solid angle at the nucleus of interest, 〈¿i〉, were
considered. By preparing the lipid in a solvent in which it
did not aggregate, and where the oxygen concentration was
assumed to be homogeneous, it was noted that the paramag-
netic shifts associated with the two sp2-hybrized carbon
nuclei, C9 and C10, were less than the shifts of the
neighboring sp3-hybridized C8 and C11 nuclei. This was
attributed to the property that valence electrons of C9 and
C10 are less easily delocalized by oxygen, although it is
possible that oxygen accessibility is also slightly lower in
the vicinity of the olefinic carbon nuclei, due perhaps to
lower void volume in the vicinity of the trans double bond.
It was also noted that the shift associated with the penultimate
carbon, C13, was slightly lower than that of C12 or C14,
possibly due to the protective effect of the C14 methyl group.
Corrections associated with C9, C10, and C13, based on
measurements obtained from MLMPC in 1:1 methanol/
chloroform solution, were noted to bring these data points
essentially along the fitted solid line shown in Figure 2. It is
important to emphasize that the MD simulations were
accomplished independently from the NMR experiments, in
order that both approaches might be evaluated according to
the degree to which they provided a consistent description
of the oxygen solubility profile. Remarkably, this excellent
agreement provides an important cross-validation of the two
techniques and demonstrates that the approximations inherent
in the theoretical model (eq 1b) as well as those in the
molecular mechanics force field and the methodology of the
simulations of hydrated bilayers are essentially correct.
The study of oxygen permeation in lipid bilayers and cells
has been significantly advanced by both fluorescence quench-
ing and ESR studies using labels attached to amphiphiles at
various immersion depths. The distinct advantage of the
current 13C NMR study is that the oxygen-induced contact
shifts are simultaneously observed on all resolvable 13C
nuclei, in complete absence of any sterically perturbing
external probe. This is particularly important in the vicinity
of the glycerol carbons where the oxygen concentration is
determined to be lowest, and therefore diffusion in this region
is the rate-limiting step for overall passive oxygen transport.
Measurements by either fluorescence or ESR in this region
of the membrane are impossible since lipid packing would
be disrupted by the reporter group. Given the considerable
variation in oxygen concentration and diffusion rates, due
presumably to somewhat subtle changes in free volume and
hydrophobicity, some caution is warranted in interpreting
quenching effects from a bulky reporter group.
Thus far, oxygen-induced paramagnetic shifts have been
reported for 15N, 1H, 19F, and 13C NMR, though only for the
case of 13C and 19F NMR are the shifts of sufficient
magnitude to be of practical utility. One might envisage a
similar approach to the study of oxygen-induced 13C chemical
shift perturbations in proteins for purposes of studying
collisionally accessible surface area and hydrophobicity. In
the case of proteins or polymers, which generally possess a
distinct, well-packed hydrophobic core, shifts would be
anticipated to strongly depend on collisionally accessible
solid angles.
ACKNOWLEDGMENT
Our sincere thanks to Prof. Robert G. Bryant for insightful
comments.
10726 Biochemistry, Vol. 45, No. 35, 2006 Al-Abdul-Wahid et al.

SUPPORTING INFORMATION AVAILABLE
13C paramagnetic shifts of MLMPC in a 1:1 chloroform/
methanol solution. This material is available free of charge
via the Internet at http://pubs.acs.org.
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10728 Biochemistry, Vol. 45, No. 35, 2006 Al-Abdul-Wahid et al.