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Nuclear magnetic relaxation dispersion in lecithin bilayers
Volume 62, number 1
NUCLEAR
CHEMICAL
MAGNETIC
RELAXATION
Rainer KIMMICH and Gerhard VOIGT S&Con Ke-sonan~spek~oslcople. Unirersirtir Received I6 October
15 hiarch 1979
PHYSICS LETTERS
DISPERSION
Urn.
IN LECITHIN
BILAYERS
O-79 ulm, Wesr-Ger~~~iz_v
1978
Longitudinal proton relaxation data in the frequency range 10 4 to 108 Hz are presented for dipslmito! I-lecnhin biIs)ers dispersed in DaO. A defect diffusion model is proposed which clllows to desnlbr unconstraintly these data as ~211 as temperature dependent measurements presiously published by Daycock Gt al.
1. Introduction MolecuIar dynamics of lipid studied in various papers. Apart “H [9,10] or 13C [8,1 I], there r,, [ 121, TID [ 131, line-shape
bilayers has been from r, of ‘H [I-S] _
are investigations of parameters such as the second moment 112~or the linewidth [I4-IS] and the order parameter S [ 19,20] _All these methods yielded so far results only at one or a few frequencies or - in the time domain - are sensitive to a limited time scale_ In order to obtain information on the stochastic type of the molecular motion we have therefore carried out proton relaxation measurements in a broad frequency range (I O4 to 1O* Hz) now available even for solids by a field cychng technique_ A problem often arising in the discussion of the relaxation behaviour of anisotropic materials is that the correlation functions turn out to be nonexponenrial. Ibis means that the relevant processes do not obey Poisson statistics. Previously we have derived a series of specified defect diffusion models as a solution of this problem [7,21]_ The common assumption of these models is that the relaxation is due to defects diffusing in one dimension along the ohgomer chains terminated by two reflecting barriers.
2_ EsperimentaI Dipalmitoyl-L-o-lecithin (DPL) was purchased from Fluka_ The sample preparation and control was
as described previously [7] yielding homogeneous multilayer structures. The concentration of the DPL in D,O was 40% by weight. The proton relaxation curves have been found to be exponential at least over one and a haIf decades indicating a negIigibIe portion of residual protons in the DzO ‘[7] _Above 20 MHz a conventional puIse spectrometer (Bruker !XP a-100) has been used. In the Iow frequency range a home built field cycling apparatus [22] enabled us to detect proton signals of 0.2 g of a solid sample_ The results are plotted in fig_ I_
3. Interpretation We assume defects (kinks, torsions) diffusing between both Iayers of polar head groups at the lipid water interface. The diffusion itself is treated as a continuous process so that we can use the foilowing theoretical expressions for spins I/Z I/7-; = ~~4n’(~,/4ir)‘[a”)1,,(W)
+ o(z)z,,(2fJ)]_
(Ia) (Ib)
(FO are the dipoiar interaction functions. I,,(w) is the normalized intensity function)_ Indicating with p the a p%rI probability that a nucleus is influenced by a defect and assuming a two state mcdei for simplicity leads to 121,231 o(I) = (I - p)plF(I)(I)
- F(I)(3)lZ
= 0.25 o(2)_
(2)
181
Volume 67, number 1
15 March 1979
CHEMKAL PHYSICS LJZTTERS
(Tile bar refers to a powder average_) For I,,(U) the following Iirnits hold for continuous diffusion [21] or for stepwise diffusion at frequencies below the step rate [7]_
40%
DPL
in
D,O
-
18
106
105
loa
107
0% V/Hz
I& l_ Frequency dependenceof the longitudinal proton relaxation time in a dispersion of 405 DPL in DtO. The lipid bihyers hake an “onion Skin” arrangement. The solid
Iinrs arc thcorcticalcurvescalcuhtcd with the parameters giwn in the tea The xrows indicate the positions we& = 1.
i = r. esp(E‘JR T). The distance rl between the pofar head groop !ayers acting as reflecting barriers is d = 38 .%_The length of a defect b is assumed to cover the projection of t\\o n~etbyIene groups as one would estimate for a UtFsequence. For such a “kink” one also derives a 35 diffusion step Ien;tb C= b = 2-54 A_ Thus we have ‘;I 1ib = 217_ The appxen: activation energy [?a] should correspond to that of the y-process of amorphous polycthyIene, i.e. E = 6.65 kc;lI/moI = 27-M kJ/nioI [36.27 j _ The pre-esponential factor is infiuenced by the so-called free volume [27--391 so that a jumpwise reduction is expected at the gel to Iiqtrid cc st.11transition in company with x stepwise increase in the specific volume [30.3 I] _ The folIowing values lead to a satisfying description of the results: r. = I_7 X IO- I4 s below the transition temperJturc and it, = 5.9 X IO-” s rtbote this tenperature. (Amorphous polyethylene shows with r0 = x9 x IO-” s [25] ZIvalue which corresponds to ZIfree vohnne J little bit higher tImn for liquid crystdline DPL.) These data xe in reasonable xcordance with tile specific volume changes at the phase transitions [30,3 I] _ Eq_ (I) diows to describe unconstraintly the frequency dependence (tk~_ I) as \\elI as the ternper&ure IS2
is
3-O
I-?%_2. Tcmpcra:ure
I
. Oaycock
:
“=‘a0
et
as
drpcndrnce
I
aI_
MHZ
4.0
4’5
lOOOK/
T
of thr longitudinal proton
rthution time in a dispersion of 60% DPL in D,O. The experimental data hair been taken from ref. [II. The solid Iines zre theoretical curres calculated with the same p-metersas used for the theoretical CUN~S in fig_ I_
dependence (rig. 2) of the Iongitudinal proton relaxation times. The solid lines in both figures have been calculated with the data given above and by assuming ~r4fi’(JIo/4ii) ’ (3(I) = 5.8 X IO’_ (This value would b,compatible with an estimation based on structural data for kink [23] and a kink concentration of less than 4% in the gel phase_)
-+. Discussion The experimental data have so far been described
Volume 62, number I
CHEMICAL PHYSICS LETTERS
by a defect diffusion model which appears to be appropriate in the medium frequency/temperature range. At the lowest frequencies the over-all biiayer ttimbling becomes visible in the liquid crystalline phase (fig_ I), whde in the geI phase at 0°C no Tl dispersion due to this process could be detected down to IO4 Hz. This picture is compatible with M,data [IS] I The decrease of &I2 in the gel phase with increasing temperature corresponds IO4 to 10’ Hz_ As solid DPL shows quite simdar Al,-vaIues, overaJ1 tumbling cannot be responsible for this reduction process_ The absolute values of M, are moreover compatibie with the defect diffusion GodeI [3X] _ At the lowest temperatures the influence of methyl group rotation obviously becomes visible (fig_ 2). Daycock et al. [I] could experimentaIIy verify this interpretation by investigatmg the perdeuterated analogue. The superposition of the methyi group reIaxation couId - on the other hand - iead to a Tl minimum (fig. 2) at a slightly lower temperature than would be expected for the alkane phase alone_ Methy group rotation is however too fast to have any influence in the temperature/frequency range of the data in fig. I. so that no correction is necessary. Previous relaxation studies [I] indicated that no dramatic Tl effect occurred at the gel to liquid crystalline please transition. The low-frequency data and the mode1 presented in this paper yield a complete explanation of this at the first sight unexpected fact: At the high frequencies to which previous studies have been restricted, the expected jump of the absoIute vaIue of T, is compensated by a shift of the dispersion curve due to shorter time constants_ Merely at low frequencies a T, -jump can actually be observed (fig_ I).
Acknowledgement The financial support received from Deutsche Forschungsgemeinschaft is gratefulI)- acknowledged. We wish to thank A_ Peters and E. Neff for assistance during the experiments. References
[ 11 J-T_ Daycock, A. Dxkr and D- Ctip~n. Lipids 6 (1971) 205.
Chem- Phbs-
-1.5 March :979
[3] S.I. Ghan. G-N’. reigenson and ChA. Seiter, Nature 231 (1971) 1:o. [3] G-W. Feigenson and ‘21. Chan, J. Am. Chem. Sot. 96 (1974) 1312. [4] AC_ JIcLaughlin, F. Podo and J.K. Blssie, Biochim. Biophys. Xcta 330 (1973) 109. 1.51 E. Old&Id. J. \farsden and D. Chapman, Chsm_ Ph>s. Lipids 7 (1971) 1. [6] X-F_ Horwltz. WJ. Horsley znd M-P. Klein. Proc. Nstl. Aud. Sci. US 69 (1972) 590. [71 R. Kimmich and A. Peters, J. S&n. Rrson. 19 (197.5) 14+. [81 Z!.P_X_ Gent and J-H. Prestegzrd, J. Jfagn. Reson. 25 (1977) 243. (91 E. Oldfield, D. Chapman and U’\‘.Derbyshire_ Chem. Phys. Llpids 9 (1972) 69. [IO] J.H. Dais, K.R. Jeffrey and .\1. Bloom. J. Wgn Reson 19 (1978) 191. [ 1 I j Y.K. Lerinc, N_I_M_Bird&l_ =\_G. Lee 2r.d I C_ Maslfe. Biochemistr> 1 I (I 9721 1416. [ 121 N-l. Salabur>, D. Chapman and G P. Jones, Trans. I=araday SOC. 66 (1970) IS%%_ [ 131 H. Gtlbon. Chem. Ph) s_ Letters 40 f 1976) 49. [ I4 J NJ. S&bun and D. Chapman. Biochmx Biophrs. Acw
163 (196s) 314. [ 15 J Z. Vcksh, NJ. Salsburl and D. Chapman, Biocbim. Bioph> s. Acta 183 (I 969) 434. [ 16 1 A.F. Horwxtz, D. Wchaeison and X1.P. KIcm, Biochtm. Biophls. Acta 29s (19?3) 1. [I 7 J XX_Bloom, E.L. BurnelI, \l.I. Valic and G. Weeks. Chem. Phys. Lipids 14 (1975) 107. [ 181 A. Peters and R. Kimmlch, Biophvs. Struct. \Iechanism
4 (1978) 67. [ 191 X. See& and J. Seehg. Biochemisiry
13 (1971) 4839. [?O] J.H. Davis and K R. Jeffrey. Chem. ?h_rs. Lipids 10 (1977) 87. [?I 1 R. Ki-nmxh, 2. Naturforsch. 31s (1976) 693 122 J G Voigt and R. Kimmich. Proceedings of the European Conference on NMR of Mxromolscu!es. ‘&sari (1978)_ [73J R. Kimmich. Colloid Polymer SC?. 752 (1971) 786_
[24 J J. KoppeImzmn, KoIiold-Z.Z. Pof m+re II 6/217 (1967) 6. [ 25J G. Voigt and R. Kimmich, Chem Ph>s Lctrers 56 (1978) 275. [ 261 U. Hxberlen, Kollold-Z.Z. PO&mere 225 (I 968) 15. [27J
11-H. Cohen and D. Turnbull, J. Chem. Ph\-s. 31 (1959)
[18J
D. TurnbuII and KH. Cohen. J. Chem. Phls. 34 (I961) .
116-l.
_
170
F. Bueche, J. Chem. Ph) s 36 (1962) 2910. H. Tr;iubIe and D.H. HA) nes. Chem. Phys. Lipids 7 (1971) 32-l. D-L. Meichior and H.J. Morowitz, Siochemisrrl 11 (1972) 4558. I;. Schmauder. R. Kimmlch 2nd G. Vogt, fo be published.
183
NUCLEAR
CHEMICAL
MAGNETIC
RELAXATION
Rainer KIMMICH and Gerhard VOIGT S&Con Ke-sonan~spek~oslcople. Unirersirtir Received I6 October
15 hiarch 1979
PHYSICS LETTERS
DISPERSION
Urn.
IN LECITHIN
BILAYERS
O-79 ulm, Wesr-Ger~~~iz_v
1978
Longitudinal proton relaxation data in the frequency range 10 4 to 108 Hz are presented for dipslmito! I-lecnhin biIs)ers dispersed in DaO. A defect diffusion model is proposed which clllows to desnlbr unconstraintly these data as ~211 as temperature dependent measurements presiously published by Daycock Gt al.
1. Introduction MolecuIar dynamics of lipid studied in various papers. Apart “H [9,10] or 13C [8,1 I], there r,, [ 121, TID [ 131, line-shape
bilayers has been from r, of ‘H [I-S] _
are investigations of parameters such as the second moment 112~or the linewidth [I4-IS] and the order parameter S [ 19,20] _All these methods yielded so far results only at one or a few frequencies or - in the time domain - are sensitive to a limited time scale_ In order to obtain information on the stochastic type of the molecular motion we have therefore carried out proton relaxation measurements in a broad frequency range (I O4 to 1O* Hz) now available even for solids by a field cychng technique_ A problem often arising in the discussion of the relaxation behaviour of anisotropic materials is that the correlation functions turn out to be nonexponenrial. Ibis means that the relevant processes do not obey Poisson statistics. Previously we have derived a series of specified defect diffusion models as a solution of this problem [7,21]_ The common assumption of these models is that the relaxation is due to defects diffusing in one dimension along the ohgomer chains terminated by two reflecting barriers.
2_ EsperimentaI Dipalmitoyl-L-o-lecithin (DPL) was purchased from Fluka_ The sample preparation and control was
as described previously [7] yielding homogeneous multilayer structures. The concentration of the DPL in D,O was 40% by weight. The proton relaxation curves have been found to be exponential at least over one and a haIf decades indicating a negIigibIe portion of residual protons in the DzO ‘[7] _Above 20 MHz a conventional puIse spectrometer (Bruker !XP a-100) has been used. In the Iow frequency range a home built field cycling apparatus [22] enabled us to detect proton signals of 0.2 g of a solid sample_ The results are plotted in fig_ I_
3. Interpretation We assume defects (kinks, torsions) diffusing between both Iayers of polar head groups at the lipid water interface. The diffusion itself is treated as a continuous process so that we can use the foilowing theoretical expressions for spins I/Z I/7-; = ~~4n’(~,/4ir)‘[a”)1,,(W)
+ o(z)z,,(2fJ)]_
(Ia) (Ib)
(FO are the dipoiar interaction functions. I,,(w) is the normalized intensity function)_ Indicating with p the a p%rI probability that a nucleus is influenced by a defect and assuming a two state mcdei for simplicity leads to 121,231 o(I) = (I - p)plF(I)(I)
- F(I)(3)lZ
= 0.25 o(2)_
(2)
181
Volume 67, number 1
15 March 1979
CHEMKAL PHYSICS LJZTTERS
(Tile bar refers to a powder average_) For I,,(U) the following Iirnits hold for continuous diffusion [21] or for stepwise diffusion at frequencies below the step rate [7]_
40%
DPL
in
D,O
-
18
106
105
loa
107
0% V/Hz
I& l_ Frequency dependenceof the longitudinal proton relaxation time in a dispersion of 405 DPL in DtO. The lipid bihyers hake an “onion Skin” arrangement. The solid
Iinrs arc thcorcticalcurvescalcuhtcd with the parameters giwn in the tea The xrows indicate the positions we& = 1.
i = r. esp(E‘JR T). The distance rl between the pofar head groop !ayers acting as reflecting barriers is d = 38 .%_The length of a defect b is assumed to cover the projection of t\\o n~etbyIene groups as one would estimate for a UtFsequence. For such a “kink” one also derives a 35 diffusion step Ien;tb C= b = 2-54 A_ Thus we have ‘;I 1ib = 217_ The appxen: activation energy [?a] should correspond to that of the y-process of amorphous polycthyIene, i.e. E = 6.65 kc;lI/moI = 27-M kJ/nioI [36.27 j _ The pre-esponential factor is infiuenced by the so-called free volume [27--391 so that a jumpwise reduction is expected at the gel to Iiqtrid cc st.11transition in company with x stepwise increase in the specific volume [30.3 I] _ The folIowing values lead to a satisfying description of the results: r. = I_7 X IO- I4 s below the transition temperJturc and it, = 5.9 X IO-” s rtbote this tenperature. (Amorphous polyethylene shows with r0 = x9 x IO-” s [25] ZIvalue which corresponds to ZIfree vohnne J little bit higher tImn for liquid crystdline DPL.) These data xe in reasonable xcordance with tile specific volume changes at the phase transitions [30,3 I] _ Eq_ (I) diows to describe unconstraintly the frequency dependence (tk~_ I) as \\elI as the ternper&ure IS2
is
3-O
I-?%_2. Tcmpcra:ure
I
. Oaycock
:
“=‘a0
et
as
drpcndrnce
I
aI_
MHZ
4.0
4’5
lOOOK/
T
of thr longitudinal proton
rthution time in a dispersion of 60% DPL in D,O. The experimental data hair been taken from ref. [II. The solid Iines zre theoretical curres calculated with the same p-metersas used for the theoretical CUN~S in fig_ I_
dependence (rig. 2) of the Iongitudinal proton relaxation times. The solid lines in both figures have been calculated with the data given above and by assuming ~r4fi’(JIo/4ii) ’ (3(I) = 5.8 X IO’_ (This value would b,compatible with an estimation based on structural data for kink [23] and a kink concentration of less than 4% in the gel phase_)
-+. Discussion The experimental data have so far been described
Volume 62, number I
CHEMICAL PHYSICS LETTERS
by a defect diffusion model which appears to be appropriate in the medium frequency/temperature range. At the lowest frequencies the over-all biiayer ttimbling becomes visible in the liquid crystalline phase (fig_ I), whde in the geI phase at 0°C no Tl dispersion due to this process could be detected down to IO4 Hz. This picture is compatible with M,data [IS] I The decrease of &I2 in the gel phase with increasing temperature corresponds IO4 to 10’ Hz_ As solid DPL shows quite simdar Al,-vaIues, overaJ1 tumbling cannot be responsible for this reduction process_ The absolute values of M, are moreover compatibie with the defect diffusion GodeI [3X] _ At the lowest temperatures the influence of methyl group rotation obviously becomes visible (fig_ 2). Daycock et al. [I] could experimentaIIy verify this interpretation by investigatmg the perdeuterated analogue. The superposition of the methyi group reIaxation couId - on the other hand - iead to a Tl minimum (fig. 2) at a slightly lower temperature than would be expected for the alkane phase alone_ Methy group rotation is however too fast to have any influence in the temperature/frequency range of the data in fig. I. so that no correction is necessary. Previous relaxation studies [I] indicated that no dramatic Tl effect occurred at the gel to liquid crystalline please transition. The low-frequency data and the mode1 presented in this paper yield a complete explanation of this at the first sight unexpected fact: At the high frequencies to which previous studies have been restricted, the expected jump of the absoIute vaIue of T, is compensated by a shift of the dispersion curve due to shorter time constants_ Merely at low frequencies a T, -jump can actually be observed (fig_ I).
Acknowledgement The financial support received from Deutsche Forschungsgemeinschaft is gratefulI)- acknowledged. We wish to thank A_ Peters and E. Neff for assistance during the experiments. References
[ 11 J-T_ Daycock, A. Dxkr and D- Ctip~n. Lipids 6 (1971) 205.
Chem- Phbs-
-1.5 March :979
[3] S.I. Ghan. G-N’. reigenson and ChA. Seiter, Nature 231 (1971) 1:o. [3] G-W. Feigenson and ‘21. Chan, J. Am. Chem. Sot. 96 (1974) 1312. [4] AC_ JIcLaughlin, F. Podo and J.K. Blssie, Biochim. Biophys. Xcta 330 (1973) 109. 1.51 E. Old&Id. J. \farsden and D. Chapman, Chsm_ Ph>s. Lipids 7 (1971) 1. [6] X-F_ Horwltz. WJ. Horsley znd M-P. Klein. Proc. Nstl. Aud. Sci. US 69 (1972) 590. [71 R. Kimmich and A. Peters, J. S&n. Rrson. 19 (197.5) 14+. [81 Z!.P_X_ Gent and J-H. Prestegzrd, J. Jfagn. Reson. 25 (1977) 243. (91 E. Oldfield, D. Chapman and U’\‘.Derbyshire_ Chem. Phys. Llpids 9 (1972) 69. [IO] J.H. Dais, K.R. Jeffrey and .\1. Bloom. J. Wgn Reson 19 (1978) 191. [ 1 I j Y.K. Lerinc, N_I_M_Bird&l_ =\_G. Lee 2r.d I C_ Maslfe. Biochemistr> 1 I (I 9721 1416. [ 121 N-l. Salabur>, D. Chapman and G P. Jones, Trans. I=araday SOC. 66 (1970) IS%%_ [ 131 H. Gtlbon. Chem. Ph) s_ Letters 40 f 1976) 49. [ I4 J NJ. S&bun and D. Chapman. Biochmx Biophrs. Acw
163 (196s) 314. [ 15 J Z. Vcksh, NJ. Salsburl and D. Chapman, Biocbim. Bioph> s. Acta 183 (I 969) 434. [ 16 1 A.F. Horwxtz, D. Wchaeison and X1.P. KIcm, Biochtm. Biophls. Acta 29s (19?3) 1. [I 7 J XX_Bloom, E.L. BurnelI, \l.I. Valic and G. Weeks. Chem. Phys. Lipids 14 (1975) 107. [ 181 A. Peters and R. Kimmlch, Biophvs. Struct. \Iechanism
4 (1978) 67. [ 191 X. See& and J. Seehg. Biochemisiry
13 (1971) 4839. [?O] J.H. Davis and K R. Jeffrey. Chem. ?h_rs. Lipids 10 (1977) 87. [?I 1 R. Ki-nmxh, 2. Naturforsch. 31s (1976) 693 122 J G Voigt and R. Kimmich. Proceedings of the European Conference on NMR of Mxromolscu!es. ‘&sari (1978)_ [73J R. Kimmich. Colloid Polymer SC?. 752 (1971) 786_
[24 J J. KoppeImzmn, KoIiold-Z.Z. Pof m+re II 6/217 (1967) 6. [ 25J G. Voigt and R. Kimmich, Chem Ph>s Lctrers 56 (1978) 275. [ 261 U. Hxberlen, Kollold-Z.Z. PO&mere 225 (I 968) 15. [27J
11-H. Cohen and D. Turnbull, J. Chem. Ph\-s. 31 (1959)
[18J
D. TurnbuII and KH. Cohen. J. Chem. Phls. 34 (I961) .
116-l.
_
170
F. Bueche, J. Chem. Ph) s 36 (1962) 2910. H. Tr;iubIe and D.H. HA) nes. Chem. Phys. Lipids 7 (1971) 32-l. D-L. Meichior and H.J. Morowitz, Siochemisrrl 11 (1972) 4558. I;. Schmauder. R. Kimmlch 2nd G. Vogt, fo be published.
183