Correlation functions for lipid membrane dynamics obtained from NMR spectroscopy
Alexander A. Nevzorov,
1
Theodore P. Trouard,
2
and Michael F. Brown
1,
*
1
Department of Chemistry, University of Arizona, Tucson, Arizona 85721
2
Department of Radiology, University of Arizona, Tucson, Arizona 85724
Received 15 October 1996
Nuclear magnetic resonance NMR studies of the spin relaxation of lipid membranes provide a powerful
tool for investigating the dynamics of these important biological structural elements. Here spectral densities of
motion for various dynamical models have been fitted to
2
H spin-lattice relaxation rates ( R
1Z
) measured for
vesicles for 1,2-dimyristoyl-sn-glycero-3-phosphocholine, in the liquid-crystalline state, over a broad fre-
quency range 2.50–95.3 MHz; total of 15 magnetic-field strengths. Moreover, the corresponding
13
C R
1Z
values predicted from the models have been compared to experiment from 15.0 to 151 MHz, thereby enabling
unification of the NMR relaxation data for bilayer lipids. A molecular diffusion model or alternatively a
three-dimensional collective fluctuation model describes best the
2
H and
13
C R
1Z
data. To emphasize the
universality of this approach, the models have also been fitted to
13
C R
1Z
data for vesicles of 1,2-dipalmitoyl-
sn-glycero-3-phosphocholine 15.0–151 MHz; eight magnetic field strengths, and the
2
H R
1Z
values for the
corresponding multilamellar dispersions theoretically predicted. Correlation functions have been calculated for
the lipid reorientations from the analysis of NMR relaxation data. The results suggest that slower motions are
predominant in the low to mid megahertz range due to noncollective molecular motions or thermal collective
excitations, whereas the bilayer interior corresponds to liquid hydrocarbon. The reorientational correlation
functions derived from NMR spectroscopy are compared to recent molecular-dynamics simulations of bilayer
lipids in the fluid phase. S1063-651X9707803-3
PACS numbers: 87.22.Bt, 71.45.Gm, 87.64.Hd, 76.60.-k
I. INTRODUCTION
Lipid bilayers, an essential structural element of biologi-
cal membranes, represent an example of soft matter having a
broad dynamic hierarchy with fast local motions and slow,
noncollective, and possibly collective motions 1. Extensive
NMR experimental studies of lipid bilayers have been car-
ried out in the past 1–9 and are amenable to further analy-
sis and theoretical interpretation. Examples of models for the
reorientational dynamics of bilayer lipids in the liquid-
crystalline state include discrete jumps 10, rotational diffu-
sion 9,11, or collective excitations treated as director fluc-
tuations 6,12,13. As a rule it is necessary to distinguish
between fast motions, which modulate the static coupling
tensor arising from the quadrupolar and dipolar nuclear spin
interactions, and slow motions, which further modulate the
residual coupling. Most workers agree 6,8,14,15 that the
nuclear spin relaxation of liquid-crystalline bilayers in the
megahertz regime predominantly manifests fluctuations in
the local ordering rather than faster segmental motions of the
chains; further testing of this hypothesis is needed. In addi-
tion, there is the open question of whether the relatively slow
order fluctuations are due to noncollective molecular motions
6,8,9,14 or, alternatively, to collective excitations of the
bilayer 6,9. Herein the authors have tested various dynami-
cal models in closed form for their ability to describe simul-
taneously the
2
H and
13
C R
1 Z
relaxation rates correspond-
ing to the same C-H bond segment of the bilayer lipids. A
comparison of theory with experiment suggests that order
fluctuations are detectable with NMR relaxation techniques
and that the local bilayer viscosity corresponds to liquid hy-
drocarbon. Correlation functions for these stochastic motions
are calculated and compared with the results of recent
molecular-dynamics MD simulations of lipid bilayers in
the fluid state.
II. THEORETICAL MODELS FOR DYNAMICS
OF LIPID BILAYERS
We discuss here diffusional models and models consider-
ing thermal excitations in membranes as a continuous me-
dium. In developing a model aiming to describe reorienta-
tions in lipids, one has as the ultimate goal an analytical
expression for the irreducible correlation functions of the
various segments. For second-rank interactions these are de-
fined as
G
m
= D
0 m
2
PL
, t + - D
0 m
2
PL
*
D
0 m
2
PL
, t - D
0 m
2
PL
, 1
where m =0, 1, or 2 is the projection index; an axially
symmetric coupling tensor is assumed. Here D
(2)
indicates
the second-rank Wigner rotation matrix, where the Euler
angles
PL
describe the orientation of the principal axis sys-
tem PAS associated with the C-H bond segment relative
to the main magnetic field and contain the time dependence.
By introducing closure, the rotation matrix for the overall
rotation
PL
can be expanded in terms of various interme-
diate motional frames 6,9; cf. Fig. 1. The corresponding
spectral densities are given by Fourier transformation of
Eq. 1.
*Also at Division of Physical Chemistry 1, Center for Chemistry
and Chemical Engineering, Lund University, S-221 00 Lund,
Sweden.
PHYSICAL REVIEW E MARCH 1997 VOLUME 55, NUMBER 3
55 1063-651X/97/553/32767/$10.00 3276 © 1997 The American Physical Society