- Email: [email protected]
Extracting order parameters from powder EPR lineshapes for spin-labelled lipids in membranes
SPECTROCHIMICA ACTA PART A
ELSEVIER
Spectrochimica
Acta
Part A 53 (1997)
2235-2240
Letter
Extracting order parameters from powder EPR lineshapes for spin-labelled lipids in membranes Karl Schorn, Derek Marsh * Max-Planck-Institut
fir
biophysikalische
Chemie,
Received
Abteilung
24 April
Spektroskopie,
1997; accepted
Am Fassberg,
28 May
D-37077
Giittingen,
Germany
1997
---Abstract
The correctionsthat must be madeto the spectralseparationsof the hyperfine extrema in the pseudo-powderEPR lineshapesfrom lipid spin labelsin randomly oriented membraneshave beeninvestigatedby spectralsimulationsthat include slow motional components. Using simulation parametersthat are able to describe the corresponding experimentalspectrarather well, it is found that any correction requiredto the outer hyperfmesplitting, 2A,,, is small, but that the correction to the inner splitting, 2Ami,, differs from that obtained previously from motional narrowing theory. Both A,,, and A,, deduced from the simulated spectra are found to vary almost linearly with the molecular-frameorder parameter,S,=.The correctionsto A,, are usedto obtain order parametersfrom the experimental line splittings. Theseare found to be in reasonableagreementwith the order parametersderived from direct spectral simulation.The inclusionof slowmotionalcomponentsin the simulationsrepresentsan improvementover the correction to Aminthat is routinely usedfor membranesystemsand which isbasedon motional narrowing theory. 0 1997Elsevier ScienceB.V. Keywords:Spin label; Order parameter;EPR; Powderlineshape;Hyperfine anisotropy; Lipids; Membranes
1. Introduction Lipids spin-labelled stereospecifically in the hydrocarbon chain with the doxyl (4,4-dimethyloxazolidine-N-oxyl) nitroxide free radical moiety have a molecular configuration that is optimally suited to determining the z-principal component of the ordering tensor of the labelled chain segment. This is because the z-axis of the 14N-
hyperfine tensor lies along the long axis of the all-truns lipid chain. Such nitroxide-labelled lipid spin probes (e.g. fatty acids or phospholipids) have therefore proved especially useful in studying the chain order and mobility of the lipid chains in phospholipid bilayers and biological membranes ([ 11). Anisotropic rotation of the spin-labelled lipid chain segments in the orienting potential experienced within the membrane (specified by an order tensor with principal element, SJ results in
* Corresponding 1386-1425/97/$17.00 PIIS1386-1425(97)00136-4
the following principal elements of the motionally averaged axial hyperfine tensor:
author. 0 1997 Elsevier
Science
B.V.
All rights
reserved.
dA = u. + (2,‘3)AA.S __ ;in L = u,, - (1 i3)AA.S,,
(1)
and
(2)
A,(gauss) = A,,,,, + 0.85
where, with a 14N-hyperfine tensor A = (A,,, A,.,.. A,;). the isotropic hyperfine coupling constant is u. = (1/3)(A,, + Al,. + A,,) and the maximum extent of the axial hyperfine anisotropy is AA = A,; - ( l/2) (A ,..,.+ A,,. 1.
Complications arise in extracting the principal elements of the motionally averaged axial hyperfine tensor from the EPR spectra of nonaligned membrane dispersions because of the statistical distribution of orientations of the membrane normal in such dispersions. The EPR spectra from the spin labels with different angular orientations relative to the spectrometer static magnetic field are superimposed, giving rise to a pseudo-powder spectrum. Analysis of such spectra is of considerable practical importance because of the difficulty in producing perfectly aligned membranes in excess water. The best alignments have been achieved with partly dried samples. In principle, all the required information can be obtained by spectral simulation. However, peaks in the spectra from random membrane dispersions that correspond to turning points in the angular dependence of spectra from aligned samples allow a simpler method of analysis for deriving hyperfine splittings [2,3]. For the fast motional averaging regime of nitroxide EPR spectroscopy, the outer extrema of the first-derivative 9-GHz spectra have the absorption lineshape for an aligned sample with the magnetic field parallel to the director (i.e. membrane normal) and their splitting, 2A,,,, is equal to 2A;,. The separation of the inner extrema, 2Amin, is related to 2A, but requires a correction to allow for spectral overlap in this region of the pseudo-powder spectrum. Corrections obtained from simulations of powder-patterns based on Eq. (1) and Eq. (2) and their equivalents for the g-tensor (which are essentially equivalent to extreme motional narrowing theory) have been given in [3-51. From the simulations given in [4], it is found that [6]: A,(gauss) = Ami, + 1.32 + 1.86 . log,, (1 - S,,,) for S,,, 2 0.45
(3)
for S,,,,, ~10.45
(4)
The first of these where S,,, = (A,,,-A,,l,,)~AA. corrections (Eq. (3), for higher order parameters) corresponds to that given in [4] and the second (Eq. (4). for lower order parameters) is very close to that proposed in [3]. Whereas the lipid spin-label EPR spectra from lamellar soap systems lie in the fast motional regime and can be simulated rather successfully by using motional narrowing perturbation theory [7], this has been found not to be the case for the spectra of spin-labelled lipids in phospholipid bilayers or biological membranes (see e.g. [8]). The latter cannot be simulated adequately by fast motional theories because they contain important contributions from slow motional components and require more comprehensive simulations that are based on the stochastic Liouville equation [9- 111. The purpose of this communication is to present simple empirical corrections for extracting order parameters from the spectra of membrane dispersions that are derived from simulations which incorporate slow motional contributions and are capable of describing the experimental spectra with high precision [12]. This approach is equivalent for the general motional case to that introduced previously by using simulations which correspond to the fast motional narrowing regime (i.e. Eq. (3) and Eq. (4)). These new corrections are more appropriate to lipid spin-label spectra from phospholipid and membrane systems than are those currently available (which are used extensively, in spite of their obvious limitations) and therefore they should find wide application.
2. Methods The method used for simulation is the so-called very anisotropic reorientation (VAR) model [ 131, in which the order parameter, S,,, is specified by a fixed effective tilt angle, pefr, of the nitroxide z-axis with respect to the z-principal diffusion axis about which the rotation rate, R,,, is faster than that (R,) about the orthogonal x- and y-diffusion axes. The latter is chosen to lie well into
K. Schorn,
D. Marsh
/Spectrochimica
the slow motional regime (i.e. R, I 5 x lo6 s- ‘) and, in addition to modelling slow off-axial rotational components, ensures that a spectrum corresponding to a random distribution of director orientations is obtained for axially symmetric systems. (In principle, the formulation is valid for all values of the rotational rate, R,,.) Strictly speaking, this model applies to the very anisotropic rotation of labelled macromolecules undergoing slow Brownian diffusion but it is found to simulate experimental 9 GHz-spectra obtained from a wide range of different chain-labelled lipid spin probes in membrane dispersions, with a high degree of precision 1121. Further refinement of the model is not justified by the relatively low resolution obtained in experimental spectra from macroscopically disordered membrane dispersions, which tends to preclude an unambiguous parameterization of more exact slow motional models. For the latter, the higher resolution spectra that are obtained from oriented samples allow a more tractable analysis [&lo].
Acta Part
A 53 (1997)
2235-2240
7237
plicitly in the model (see [10,12]). For order parameters S,, 5 0.6, the spectra correspond very closely to those of different positional isomers (n = 4- 16) of the n-PCSL labels in fluid phospholipid bilayers and the only parameter that has been varied appreciably is the effective angular orientation Peff that determines the order parameter. For the higher order parameters, suitable experimental spectra are not available for a reliable comparison, but the dynamic parameters have been chosen such that the spectra at high order approximate those found in lipid gel phases (see [12]). In practice, it is found that experimental spectra from random membrane dispersions which have very large outer splittings normally
3. Results and discussion Spectra appropriate to 14N-nitroxide spin labels at a microwave frequency of 9.0 GHz have been simulated for the full range of molecular order parameters, SZZEE(l/2)(3 co? Peff - 1) = 0 to 1, and are given in Fig. 1. The parameters used in the simulations are given in Table 1 and have been chosen to reproduce typical experimental spectra of chain-labelled lipids (e.g. 1-acyl-2-[n(4,4 - dimethyloxazolidine - 1 - oxyl)stearoyl] -sn - gly cero-3-phosphocholine, n-PCSL) in lipid membranes [12]. The slow motional spectral simulation programme used is that of [14]. It will be recognised immediately that the spectra in Fig. 1 correspond more closely to the spectra obtained from lipid membranes than do those of [4,5] for which slow rotational dynamics is not taken into account (cf. e.g. [15,16]). The g-tensor used differs slightly from the single-crystal value for a doxyl spin label because it has reduced non-axiality to account in part for some of the effects of rapid tvans-gauche isomerism that are not included ex-
Fig. 1. Slow motional simulations of axial r4N-nitroxide spin label spectra for various values of the order parameter, Szz, obtained using the programme of [14]. The order parameter is varied by adjusting the angular orientation of the nitroxide z-axis with respect to the principal diffusion axis (i.e. membrane normal). Simulation parameters are listed in Table 1 and are chosen to correspond to representative experimental spectra of different positional isomers of doxyl chain-labelled lipids in phospholipid bilayers. The positions of the peaks defining the outer and inner hyperfine splittings are indicated by vertical lines for the spectrum corresponding to Szz = 0.5. Total scan width = 100 G; field centre = 3210 G; microwave frequency = 9.0 GHz.
2238
K. &horn,
D. Marsh
,; Specfrochirnica
Table 1 Parameters used in the spectral simulations of Fig. 1 sz,
P,fF (“)
R, (s-‘1
AH, (G)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
54.74 50.77 46.91 43.09 39.23 35.26 3 I .09 26.57 21.42 14.96 0
3.3 x 106 3.3 x 106 3.3 x 106 3.3 x 106 3.3 x 106 3.3 x 106 2.5 x lo6 1.5x 106 9x 105 3x 10s 1 x 105
0.4 0.4 0.4 0.5 0.7 0.9 1.2 1.5 1.8 2.2 2.5
For all cases, the hyperhne and g-tensors are (A,,, A,. A,) = (5.9, 5.4, 32.9 G) and (g,,, g ?-,,,g,,)=(2.0076, 2.0072, 2.0021), respectively, and the principal element of the rotational diffusion tensor is RI, = 5.8 x IO8 SC’. R. ,, R, are the principal elements of the rotational diffusion tensor; pen is the effective angle between the nitroxide z-axis and the R,,, diffusion axis; AH, is the intrinsic linewidth.
also lie well into the slow motional regime for all rotational components and are therefore rather difficult to distinguish from those with slow isotropic motion. The simulations for very high order are thus only included for the sake of completeness and should be treated with considerable caution if used for extracting order parameters. The splittings between the outer peaks (2A,,,) and between the inner peaks (2A,,) in the simulated spectra have been measured (as is the common practice for experimental spectra) and are plotted in Fig. 2 as a function of the order parameters used for the simulations. The measured values of 2A,,, vary linearly with SZZfrom 2A,,, z 2~2,for S,, = 0 (Berr = 54.74”) to 2A,,, z 2A,; for SZZ= 1 (Peff = O”), as predicted from motional narrowing theory by Eq. (1). This is neither an obvious nor a trivial result for spectra that contain contributions from slow motions and arises from a balance of the effects of the different rotational diffusion tensor elements, R,, and R,, on the spectral line positions. Although somewhat fortuitous, this simple result is that which corresponds best to experimental spectra and means that the relationship A,, = A,,, which is normally employed may be retained as a reasonable ap-
Acra
Part
A 53 (1997)
2235 -7730
proximation. This is the most conservative approach and may not be exactly the case for more complex motional models, for which (as already mentioned) an unambiguous parameterization from the spectra of unoriented samples may not be possible. The measured values of ZA,, do not correspond to Eq. (2), nor to those obtained by fast motional narrowing simulations. The dependence on the order parameter, S=,. is linear over a range at least from S,, = 0.05-0.8, and implies the following relation for the A, motionally averaged tensor element: A,(gauss) = Amin + 1.29 - 1.75 . S,
(5)
This correction is similar to that introduced previously based on simulations for fast motional averaging [5], except that in the latter case both
G? 2 m 0 i2
aE cu .c
aE cu
101 0.0
0.2
0.4
0.6
S
0.8
1.0
22
Fig. 2. Outer (2A,,) and inner (2A,,) apparent hyperfine splittings measured from the separation of the peaks in the simulated spectra of Fig. 1. Splittings are plotted as a function of the order parameter, S,,, used in the simulations. The upper and lower full lines correspond to linear regressions for 2A,,, and 2A,,, respectively. Dashed lines are the dependence of 2A,, (upper) and 2A, (lower) on XZ, as given by Eq. (1) and Eq. (2), respectively.
K. &horn, D. Marsh/Spectrochimiea
numerical terms had a value of 1.4 G. The differences in 2A, between these calibrations and those from motional-narrowing simulations given by Eq. (3) or Eq. (4) range from + 0.5 to - 1.3 G for order parameters up to Sz, = 0.6. This discrepancy could have a considerable influence on effective environmental polarities deduced from the isotropic hyperfine coupling constant, a,. Finally, the order parameter may then be expressed in terms of the experimentally accessible quantity, Sapp, by using Eq. (l), Eq. (2) and Eq. (5) with A;, = A,,,: &=
1.069 . S&, - 0.051
(6)
The differences between this calibration and those of Eq. (3) and Eq. (4) from motional-narrowing simulations amount to AS,, z rt 0.015, depending on the range of order parameters. In some ways, this result partly justifies a postiori the relative popularity of the previously proposed corrections, at least as regards order parameters and to the extent that slow motional contributions do not also necessitate a correction to A,,,. Eq. (6) allows immediate estimation of Szz by using values of A,,, and Amin measured from the experimental spectra. If necessary, additional corrections may be applied to account for the difference in polarity of the spin label environment, relative to that corresponding to the hyperfine tensor values, by using the ratio of the isotropic hyperfine coupling constants as in [3-S]. The hyperfine tensor used for the simulations and corrections presented here corresponds to a value of a, = 14.7 G that is reasonably representative of the values for doxyl spin labels in the hydrocarbon chain regions of lipid membranes. Allowance for the polarity correction, in principle gives rise to a quadratic equation for S,=, the solution for which is approximated by: S,= = i (A,,, + 2A,iJ -
k (A,,, + 2A,iJ
Ami,) + J1
0.6
where A,,,
1
* - 0.46(A,,, -
and Amin are in gauss.
(7)
Acta Part A 53 (1997) 2235-2240
2239
Table 2
Comparison of molecular order parameters deduced from experimental ESR spectra of phosphatidylcholine spin probes (n-PCSL) with the spin label on C-n of the m-2 chain in fluid lipid bilayer membranes, by simulation using the VAR model, Sz,(p,& with those obtained from calibration of the line separationsby using Eq. (6) and Eq. (7), S,; Eq. (6) and X, Eq. (7), respectively. --Spin Label* S,; Eq. (6) S,, Eq. (7) L &f) __~__ 5-PCSL 0.406 0.410 0.398 6-PCSL 0.367 0.371 0.359 7-PCSL 0.315 0.322 0.314 8-PCSL 0.250 0.241 0.237 9-PCSL 0.211 0.228 0.225 IO-PCSL 0.107 0.100 0.101 * The experimental spectra are for dimyristoyl phosphatidylcholine/dimyristoyl glycerol (58:42 mol/mol) bilayers at 60°C and, together with the spectral simulations, are from [12].
In Table 2, order parameters obtained by direct simulation using the VAR slow-motion model are compared with those calculated from the experimental line separations by using the corrections given in Eq. (6) or Eq. (7). The experimental spectra and simulations are taken from Fig. 3 in [12]. They refer to different chain positional isomers of a phosphatidylcholine spin probe (nFCSL) in dimyristoyl phosphatidylchoiine/ dimyristoyl glycerol (58:32 mol/mol) bilayer membranes, in the fluid phase at 60°C. The dynamic simulation parameters are R,: = 5.5 x lo* s- ’ and R, = 3.3 x 10” SK’, with AH, = 0.4 G. The different positional isomers cover much of the range of spectral anisotropy expected for such spin probes in fluid membranes. It can be seen that the order parameters obtained from the corrected line splittings agree reasonably well with those obtained by simulation of the complete spectrum. The isotropic hyperfine coupling constants obtained from the corrected splittings range from a, = 15.0 G for 5-PCSL to a0 = 14.4 G for lo-PCSL. As regards S..., the motional narrowing calibrations also perform reasonably well, for this particular dataset. Significant deviations of the calculated values presented in Table 2 from the true order parameters are found only in the case of S-PCSL, for which the simulation agreed less well with the line splittings in the experimental spectrum.
2740
K. &horn.
D. Marsh,
Spectrochinticu
Values for the order parameter obtained by using the calibrations given here therefore agree quite well with those obtained by direct simulation of the experimental spectra by using the VAR model. They represent an improvement over the correction that is usually applied to the experimental values determined for Amin that is based solely on motional narrowing theory. Further refinement is only possible by using more complex and more realistic slow motional treatments than the VAR model, but this would require extensive experimental data from macroscopically aligned samples.
Acru Purt
A 53 (19Y7)
2235
‘710
W.L. Hubbell, H.M. McConnell, J. Am. Chem. Sot 93 (1971) 314. [41 O.H. Griffith. P.C. Jost. In: L.J. Berliner (Ed.,. Spin Labeling. Theory and Applications. Academic Press. New York. 1976. p. 453. [51 B.J. Gaffney, in: L.J. Berliner (Ed.), Spin Labeling. Theory and Applications. Academic Press, New York, 1976. p. 567. Y31D. Marsh, in: P.M. Bayley, R.E. Dale (Eds.), Spectroscopy and the Dynamics of Molecular Biological Systems, Academic Press, London, 1985, p. 209. [71 H. Schindler, J. Seelig, J. Chem. Phys. 59 (1973) 1841. PI A. Lange, D. Marsh, K.-H. Wassmer. P. Meier, G. Kothe, Biochemistry 24 (1985) 4383. [91 J.H. Freed, in: L.J. Berliner (Ed.), Spin Labeling. Theory and Applications, Academic Press, New York. 1976. p. 131
53,
UOI M. Moser, D. Marsh, P. Meier, K.-H. Wassmer, G. Kothe, Biophys. J. 55 (1989) 111.
IIll M. Ge, D.E. Budil, J.H. Freed, Biophys. J. 66 ( 1994)
Acknowledgements
1515.
This work was supported in part Deutsche Forschungsgemeinschaft.
by the
References [l] D. Marsh, in: E. Grell (Ed.), Membrane Spectroscopy, Springer, Berlin, 1981, p. 51. [2] J.A. Weil, H.G. Hecht, J. Chem. Phys. 38 (1963) 281.
[W K. Schorn, D. Marsh, Chem. Phys. Lipids 82 (1996) 7.
E. Meirovitch, A. Nayeem, J.H. Freed, J. Phys. Chem. 88 (1984) 3454. [I41 D. Schneider, J.H. Freed, in: L.J. Berliner, J. Reuben (Eds.), Spin Labeling. Theory and Applications. Biological Magnetic Resonance. vol. 8, Plenum, New York, 1989, p. 1. PSI P. Fretten, S.J. Morris, A. Watts, D. Marsh, Biochim. Biophys. Acta 598 (1980) 247. U61 Y.V.S. Rama Khrishna, D. Marsh, Biochim. Biophys. Acta 1024 (1990) 89. [I31
ELSEVIER
Spectrochimica
Acta
Part A 53 (1997)
2235-2240
Letter
Extracting order parameters from powder EPR lineshapes for spin-labelled lipids in membranes Karl Schorn, Derek Marsh * Max-Planck-Institut
fir
biophysikalische
Chemie,
Received
Abteilung
24 April
Spektroskopie,
1997; accepted
Am Fassberg,
28 May
D-37077
Giittingen,
Germany
1997
---Abstract
The correctionsthat must be madeto the spectralseparationsof the hyperfine extrema in the pseudo-powderEPR lineshapesfrom lipid spin labelsin randomly oriented membraneshave beeninvestigatedby spectralsimulationsthat include slow motional components. Using simulation parametersthat are able to describe the corresponding experimentalspectrarather well, it is found that any correction requiredto the outer hyperfmesplitting, 2A,,, is small, but that the correction to the inner splitting, 2Ami,, differs from that obtained previously from motional narrowing theory. Both A,,, and A,, deduced from the simulated spectra are found to vary almost linearly with the molecular-frameorder parameter,S,=.The correctionsto A,, are usedto obtain order parametersfrom the experimental line splittings. Theseare found to be in reasonableagreementwith the order parametersderived from direct spectral simulation.The inclusionof slowmotionalcomponentsin the simulationsrepresentsan improvementover the correction to Aminthat is routinely usedfor membranesystemsand which isbasedon motional narrowing theory. 0 1997Elsevier ScienceB.V. Keywords:Spin label; Order parameter;EPR; Powderlineshape;Hyperfine anisotropy; Lipids; Membranes
1. Introduction Lipids spin-labelled stereospecifically in the hydrocarbon chain with the doxyl (4,4-dimethyloxazolidine-N-oxyl) nitroxide free radical moiety have a molecular configuration that is optimally suited to determining the z-principal component of the ordering tensor of the labelled chain segment. This is because the z-axis of the 14N-
hyperfine tensor lies along the long axis of the all-truns lipid chain. Such nitroxide-labelled lipid spin probes (e.g. fatty acids or phospholipids) have therefore proved especially useful in studying the chain order and mobility of the lipid chains in phospholipid bilayers and biological membranes ([ 11). Anisotropic rotation of the spin-labelled lipid chain segments in the orienting potential experienced within the membrane (specified by an order tensor with principal element, SJ results in
* Corresponding 1386-1425/97/$17.00 PIIS1386-1425(97)00136-4
the following principal elements of the motionally averaged axial hyperfine tensor:
author. 0 1997 Elsevier
Science
B.V.
All rights
reserved.
dA = u. + (2,‘3)AA.S __ ;in L = u,, - (1 i3)AA.S,,
(1)
and
(2)
A,(gauss) = A,,,,, + 0.85
where, with a 14N-hyperfine tensor A = (A,,, A,.,.. A,;). the isotropic hyperfine coupling constant is u. = (1/3)(A,, + Al,. + A,,) and the maximum extent of the axial hyperfine anisotropy is AA = A,; - ( l/2) (A ,..,.+ A,,. 1.
Complications arise in extracting the principal elements of the motionally averaged axial hyperfine tensor from the EPR spectra of nonaligned membrane dispersions because of the statistical distribution of orientations of the membrane normal in such dispersions. The EPR spectra from the spin labels with different angular orientations relative to the spectrometer static magnetic field are superimposed, giving rise to a pseudo-powder spectrum. Analysis of such spectra is of considerable practical importance because of the difficulty in producing perfectly aligned membranes in excess water. The best alignments have been achieved with partly dried samples. In principle, all the required information can be obtained by spectral simulation. However, peaks in the spectra from random membrane dispersions that correspond to turning points in the angular dependence of spectra from aligned samples allow a simpler method of analysis for deriving hyperfine splittings [2,3]. For the fast motional averaging regime of nitroxide EPR spectroscopy, the outer extrema of the first-derivative 9-GHz spectra have the absorption lineshape for an aligned sample with the magnetic field parallel to the director (i.e. membrane normal) and their splitting, 2A,,,, is equal to 2A;,. The separation of the inner extrema, 2Amin, is related to 2A, but requires a correction to allow for spectral overlap in this region of the pseudo-powder spectrum. Corrections obtained from simulations of powder-patterns based on Eq. (1) and Eq. (2) and their equivalents for the g-tensor (which are essentially equivalent to extreme motional narrowing theory) have been given in [3-51. From the simulations given in [4], it is found that [6]: A,(gauss) = Ami, + 1.32 + 1.86 . log,, (1 - S,,,) for S,,, 2 0.45
(3)
for S,,,,, ~10.45
(4)
The first of these where S,,, = (A,,,-A,,l,,)~AA. corrections (Eq. (3), for higher order parameters) corresponds to that given in [4] and the second (Eq. (4). for lower order parameters) is very close to that proposed in [3]. Whereas the lipid spin-label EPR spectra from lamellar soap systems lie in the fast motional regime and can be simulated rather successfully by using motional narrowing perturbation theory [7], this has been found not to be the case for the spectra of spin-labelled lipids in phospholipid bilayers or biological membranes (see e.g. [8]). The latter cannot be simulated adequately by fast motional theories because they contain important contributions from slow motional components and require more comprehensive simulations that are based on the stochastic Liouville equation [9- 111. The purpose of this communication is to present simple empirical corrections for extracting order parameters from the spectra of membrane dispersions that are derived from simulations which incorporate slow motional contributions and are capable of describing the experimental spectra with high precision [12]. This approach is equivalent for the general motional case to that introduced previously by using simulations which correspond to the fast motional narrowing regime (i.e. Eq. (3) and Eq. (4)). These new corrections are more appropriate to lipid spin-label spectra from phospholipid and membrane systems than are those currently available (which are used extensively, in spite of their obvious limitations) and therefore they should find wide application.
2. Methods The method used for simulation is the so-called very anisotropic reorientation (VAR) model [ 131, in which the order parameter, S,,, is specified by a fixed effective tilt angle, pefr, of the nitroxide z-axis with respect to the z-principal diffusion axis about which the rotation rate, R,,, is faster than that (R,) about the orthogonal x- and y-diffusion axes. The latter is chosen to lie well into
K. Schorn,
D. Marsh
/Spectrochimica
the slow motional regime (i.e. R, I 5 x lo6 s- ‘) and, in addition to modelling slow off-axial rotational components, ensures that a spectrum corresponding to a random distribution of director orientations is obtained for axially symmetric systems. (In principle, the formulation is valid for all values of the rotational rate, R,,.) Strictly speaking, this model applies to the very anisotropic rotation of labelled macromolecules undergoing slow Brownian diffusion but it is found to simulate experimental 9 GHz-spectra obtained from a wide range of different chain-labelled lipid spin probes in membrane dispersions, with a high degree of precision 1121. Further refinement of the model is not justified by the relatively low resolution obtained in experimental spectra from macroscopically disordered membrane dispersions, which tends to preclude an unambiguous parameterization of more exact slow motional models. For the latter, the higher resolution spectra that are obtained from oriented samples allow a more tractable analysis [&lo].
Acta Part
A 53 (1997)
2235-2240
7237
plicitly in the model (see [10,12]). For order parameters S,, 5 0.6, the spectra correspond very closely to those of different positional isomers (n = 4- 16) of the n-PCSL labels in fluid phospholipid bilayers and the only parameter that has been varied appreciably is the effective angular orientation Peff that determines the order parameter. For the higher order parameters, suitable experimental spectra are not available for a reliable comparison, but the dynamic parameters have been chosen such that the spectra at high order approximate those found in lipid gel phases (see [12]). In practice, it is found that experimental spectra from random membrane dispersions which have very large outer splittings normally
3. Results and discussion Spectra appropriate to 14N-nitroxide spin labels at a microwave frequency of 9.0 GHz have been simulated for the full range of molecular order parameters, SZZEE(l/2)(3 co? Peff - 1) = 0 to 1, and are given in Fig. 1. The parameters used in the simulations are given in Table 1 and have been chosen to reproduce typical experimental spectra of chain-labelled lipids (e.g. 1-acyl-2-[n(4,4 - dimethyloxazolidine - 1 - oxyl)stearoyl] -sn - gly cero-3-phosphocholine, n-PCSL) in lipid membranes [12]. The slow motional spectral simulation programme used is that of [14]. It will be recognised immediately that the spectra in Fig. 1 correspond more closely to the spectra obtained from lipid membranes than do those of [4,5] for which slow rotational dynamics is not taken into account (cf. e.g. [15,16]). The g-tensor used differs slightly from the single-crystal value for a doxyl spin label because it has reduced non-axiality to account in part for some of the effects of rapid tvans-gauche isomerism that are not included ex-
Fig. 1. Slow motional simulations of axial r4N-nitroxide spin label spectra for various values of the order parameter, Szz, obtained using the programme of [14]. The order parameter is varied by adjusting the angular orientation of the nitroxide z-axis with respect to the principal diffusion axis (i.e. membrane normal). Simulation parameters are listed in Table 1 and are chosen to correspond to representative experimental spectra of different positional isomers of doxyl chain-labelled lipids in phospholipid bilayers. The positions of the peaks defining the outer and inner hyperfine splittings are indicated by vertical lines for the spectrum corresponding to Szz = 0.5. Total scan width = 100 G; field centre = 3210 G; microwave frequency = 9.0 GHz.
2238
K. &horn,
D. Marsh
,; Specfrochirnica
Table 1 Parameters used in the spectral simulations of Fig. 1 sz,
P,fF (“)
R, (s-‘1
AH, (G)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
54.74 50.77 46.91 43.09 39.23 35.26 3 I .09 26.57 21.42 14.96 0
3.3 x 106 3.3 x 106 3.3 x 106 3.3 x 106 3.3 x 106 3.3 x 106 2.5 x lo6 1.5x 106 9x 105 3x 10s 1 x 105
0.4 0.4 0.4 0.5 0.7 0.9 1.2 1.5 1.8 2.2 2.5
For all cases, the hyperhne and g-tensors are (A,,, A,. A,) = (5.9, 5.4, 32.9 G) and (g,,, g ?-,,,g,,)=(2.0076, 2.0072, 2.0021), respectively, and the principal element of the rotational diffusion tensor is RI, = 5.8 x IO8 SC’. R. ,, R, are the principal elements of the rotational diffusion tensor; pen is the effective angle between the nitroxide z-axis and the R,,, diffusion axis; AH, is the intrinsic linewidth.
also lie well into the slow motional regime for all rotational components and are therefore rather difficult to distinguish from those with slow isotropic motion. The simulations for very high order are thus only included for the sake of completeness and should be treated with considerable caution if used for extracting order parameters. The splittings between the outer peaks (2A,,,) and between the inner peaks (2A,,) in the simulated spectra have been measured (as is the common practice for experimental spectra) and are plotted in Fig. 2 as a function of the order parameters used for the simulations. The measured values of 2A,,, vary linearly with SZZfrom 2A,,, z 2~2,for S,, = 0 (Berr = 54.74”) to 2A,,, z 2A,; for SZZ= 1 (Peff = O”), as predicted from motional narrowing theory by Eq. (1). This is neither an obvious nor a trivial result for spectra that contain contributions from slow motions and arises from a balance of the effects of the different rotational diffusion tensor elements, R,, and R,, on the spectral line positions. Although somewhat fortuitous, this simple result is that which corresponds best to experimental spectra and means that the relationship A,, = A,,, which is normally employed may be retained as a reasonable ap-
Acra
Part
A 53 (1997)
2235 -7730
proximation. This is the most conservative approach and may not be exactly the case for more complex motional models, for which (as already mentioned) an unambiguous parameterization from the spectra of unoriented samples may not be possible. The measured values of ZA,, do not correspond to Eq. (2), nor to those obtained by fast motional narrowing simulations. The dependence on the order parameter, S=,. is linear over a range at least from S,, = 0.05-0.8, and implies the following relation for the A, motionally averaged tensor element: A,(gauss) = Amin + 1.29 - 1.75 . S,
(5)
This correction is similar to that introduced previously based on simulations for fast motional averaging [5], except that in the latter case both
G? 2 m 0 i2
aE cu .c
aE cu
101 0.0
0.2
0.4
0.6
S
0.8
1.0
22
Fig. 2. Outer (2A,,) and inner (2A,,) apparent hyperfine splittings measured from the separation of the peaks in the simulated spectra of Fig. 1. Splittings are plotted as a function of the order parameter, S,,, used in the simulations. The upper and lower full lines correspond to linear regressions for 2A,,, and 2A,,, respectively. Dashed lines are the dependence of 2A,, (upper) and 2A, (lower) on XZ, as given by Eq. (1) and Eq. (2), respectively.
K. &horn, D. Marsh/Spectrochimiea
numerical terms had a value of 1.4 G. The differences in 2A, between these calibrations and those from motional-narrowing simulations given by Eq. (3) or Eq. (4) range from + 0.5 to - 1.3 G for order parameters up to Sz, = 0.6. This discrepancy could have a considerable influence on effective environmental polarities deduced from the isotropic hyperfine coupling constant, a,. Finally, the order parameter may then be expressed in terms of the experimentally accessible quantity, Sapp, by using Eq. (l), Eq. (2) and Eq. (5) with A;, = A,,,: &=
1.069 . S&, - 0.051
(6)
The differences between this calibration and those of Eq. (3) and Eq. (4) from motional-narrowing simulations amount to AS,, z rt 0.015, depending on the range of order parameters. In some ways, this result partly justifies a postiori the relative popularity of the previously proposed corrections, at least as regards order parameters and to the extent that slow motional contributions do not also necessitate a correction to A,,,. Eq. (6) allows immediate estimation of Szz by using values of A,,, and Amin measured from the experimental spectra. If necessary, additional corrections may be applied to account for the difference in polarity of the spin label environment, relative to that corresponding to the hyperfine tensor values, by using the ratio of the isotropic hyperfine coupling constants as in [3-S]. The hyperfine tensor used for the simulations and corrections presented here corresponds to a value of a, = 14.7 G that is reasonably representative of the values for doxyl spin labels in the hydrocarbon chain regions of lipid membranes. Allowance for the polarity correction, in principle gives rise to a quadratic equation for S,=, the solution for which is approximated by: S,= = i (A,,, + 2A,iJ -
k (A,,, + 2A,iJ
Ami,) + J1
0.6
where A,,,
1
* - 0.46(A,,, -
and Amin are in gauss.
(7)
Acta Part A 53 (1997) 2235-2240
2239
Table 2
Comparison of molecular order parameters deduced from experimental ESR spectra of phosphatidylcholine spin probes (n-PCSL) with the spin label on C-n of the m-2 chain in fluid lipid bilayer membranes, by simulation using the VAR model, Sz,(p,& with those obtained from calibration of the line separationsby using Eq. (6) and Eq. (7), S,; Eq. (6) and X, Eq. (7), respectively. --Spin Label* S,; Eq. (6) S,, Eq. (7) L &f) __~__ 5-PCSL 0.406 0.410 0.398 6-PCSL 0.367 0.371 0.359 7-PCSL 0.315 0.322 0.314 8-PCSL 0.250 0.241 0.237 9-PCSL 0.211 0.228 0.225 IO-PCSL 0.107 0.100 0.101 * The experimental spectra are for dimyristoyl phosphatidylcholine/dimyristoyl glycerol (58:42 mol/mol) bilayers at 60°C and, together with the spectral simulations, are from [12].
In Table 2, order parameters obtained by direct simulation using the VAR slow-motion model are compared with those calculated from the experimental line separations by using the corrections given in Eq. (6) or Eq. (7). The experimental spectra and simulations are taken from Fig. 3 in [12]. They refer to different chain positional isomers of a phosphatidylcholine spin probe (nFCSL) in dimyristoyl phosphatidylchoiine/ dimyristoyl glycerol (58:32 mol/mol) bilayer membranes, in the fluid phase at 60°C. The dynamic simulation parameters are R,: = 5.5 x lo* s- ’ and R, = 3.3 x 10” SK’, with AH, = 0.4 G. The different positional isomers cover much of the range of spectral anisotropy expected for such spin probes in fluid membranes. It can be seen that the order parameters obtained from the corrected line splittings agree reasonably well with those obtained by simulation of the complete spectrum. The isotropic hyperfine coupling constants obtained from the corrected splittings range from a, = 15.0 G for 5-PCSL to a0 = 14.4 G for lo-PCSL. As regards S..., the motional narrowing calibrations also perform reasonably well, for this particular dataset. Significant deviations of the calculated values presented in Table 2 from the true order parameters are found only in the case of S-PCSL, for which the simulation agreed less well with the line splittings in the experimental spectrum.
2740
K. &horn.
D. Marsh,
Spectrochinticu
Values for the order parameter obtained by using the calibrations given here therefore agree quite well with those obtained by direct simulation of the experimental spectra by using the VAR model. They represent an improvement over the correction that is usually applied to the experimental values determined for Amin that is based solely on motional narrowing theory. Further refinement is only possible by using more complex and more realistic slow motional treatments than the VAR model, but this would require extensive experimental data from macroscopically aligned samples.
Acru Purt
A 53 (19Y7)
2235
‘710
W.L. Hubbell, H.M. McConnell, J. Am. Chem. Sot 93 (1971) 314. [41 O.H. Griffith. P.C. Jost. In: L.J. Berliner (Ed.,. Spin Labeling. Theory and Applications. Academic Press. New York. 1976. p. 453. [51 B.J. Gaffney, in: L.J. Berliner (Ed.), Spin Labeling. Theory and Applications. Academic Press, New York, 1976. p. 567. Y31D. Marsh, in: P.M. Bayley, R.E. Dale (Eds.), Spectroscopy and the Dynamics of Molecular Biological Systems, Academic Press, London, 1985, p. 209. [71 H. Schindler, J. Seelig, J. Chem. Phys. 59 (1973) 1841. PI A. Lange, D. Marsh, K.-H. Wassmer. P. Meier, G. Kothe, Biochemistry 24 (1985) 4383. [91 J.H. Freed, in: L.J. Berliner (Ed.), Spin Labeling. Theory and Applications, Academic Press, New York. 1976. p. 131
53,
UOI M. Moser, D. Marsh, P. Meier, K.-H. Wassmer, G. Kothe, Biophys. J. 55 (1989) 111.
IIll M. Ge, D.E. Budil, J.H. Freed, Biophys. J. 66 ( 1994)
Acknowledgements
1515.
This work was supported in part Deutsche Forschungsgemeinschaft.
by the
References [l] D. Marsh, in: E. Grell (Ed.), Membrane Spectroscopy, Springer, Berlin, 1981, p. 51. [2] J.A. Weil, H.G. Hecht, J. Chem. Phys. 38 (1963) 281.
[W K. Schorn, D. Marsh, Chem. Phys. Lipids 82 (1996) 7.
E. Meirovitch, A. Nayeem, J.H. Freed, J. Phys. Chem. 88 (1984) 3454. [I41 D. Schneider, J.H. Freed, in: L.J. Berliner, J. Reuben (Eds.), Spin Labeling. Theory and Applications. Biological Magnetic Resonance. vol. 8, Plenum, New York, 1989, p. 1. PSI P. Fretten, S.J. Morris, A. Watts, D. Marsh, Biochim. Biophys. Acta 598 (1980) 247. U61 Y.V.S. Rama Khrishna, D. Marsh, Biochim. Biophys. Acta 1024 (1990) 89. [I31