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The study of lateral structure of biological and model membranes by neutron scattering
Physica B 180 & 181 (1992) 750-752 North-Holland
The study of lateral structure of biological and model membranes by neutron scattering V.I. Gordeliy Joint Institute for Nuclear Research,
Laboratory of Neutron Physics, 101000, Moscow, Head Post Box 79, USSR
In this paper it has been shown that the difference in neutron amplitudes for isotopes (primarily hydrogen and deuterium) and the large lateral contrast (the difference in scattering amplitude density) of membrane components such as lipids, proteins, DNA, can be used for the study of membrane lateral organization. We have demonstrated the possibility to determine, with the help of elastic thermal neutron scattering, lateral pair correlation functions for membrane component packing and the possibility to study membrane inhomogeneities and aggregation processes. We have also given ratios for the dependences of neutron scattering intensities in the case of fractal distributions of membrane components.
1. Introduction The variation of neutron scattering with substance, primarily a strong dependence of scattering amplitude on isotope composition, determines its effectiveness in the study of the structure of biological objects [ 11. The scattering of thermal neutrons is a direct method of studying membrane structure. It is via this method that the distribution of water and ions in membranes was determined and also practically all molecular groups in membranes of dipalmitoylecithin were shown. Subsequently cholesterol, anesthetics, hexane and other membrane components were studied [2]. And yet all this important information is related to the structural organization of membranes in the direction normal to their planes. It is also becoming evident that many of the properties both of biological and lipid membranes can be explained only if one knows the in-plane organization of the membranes [3]. However, a direct determination of the membrane lateral structure with the help of X-ray and neutron scattering is often a much more difficult problem. The main reason for that is the absence (as usual) of long range order in the lateral packing of membrane components and also a small lateral contrast of amplitude density for X-rays. The aim of this paper is to demonstrate theoretically the unique possibilities of neutron scattering for the study of membrane lateral structure, arising from the amplitude difference of neutron scattering for isotopes and the large scattering contrast for membrane components. Experiments of this kind are possible in the case of highly oriented samples (the technique of their preparation is well developed, especially for lipid membranes [4]) in experiments with the scattering vector directed along the membrane plane. 0921-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
2. Determination of the lateral correlation function of a membrane component In the first Born approximation elastic coherent neutron scattering
the amplitude can be written
of as
151: F(4 = ]PW exp(iqddr 1
(1)
where p(r) is the density of scattering amplitude, q = (47~lh) sin 0 the scattering vector, where 0 is half the scattering angle and A is the radiation wavelength. Suppose q = Q and is directed along the membrane plane and the z axis of the coordinate system is perpendicular to it. Then it follows from eq. (l), that:
F(Q) = 1 P,(R) exp(iQR) dR> where
R is directed
P,(R)=
along
the membrane
(2) plane
I P(X>
Y, 2) d.z
and
(3)
is the scattering amplitude density projected on the membrane plane. The scattered neutron intensity, which is being measured in the experiment, equals [5]
I(Q) = F(Q) * F*(Q) = / S(R) exp(iQR)dR,
(4)
where S(R)= I p,(r + R) p(r) dr is the lateral correlation function of the projection of the scattering amplitude density on the membrane plane. Let us suppose that membranes consist only of two components. As will be made clear further on, the following calculations can be easily expanded to the case of multicomponent membranes. To make it sim-
B.V. All rights
reserved
V.I. Gordeliy
pler let us suppose that membrane components are point ones (which is the equivalent of Q-i + L, where L is the lateral size of each membrane component). Then, if we consider that p,(R) = p,,,(R) + p,,,(R), where indices 1 and 2 are related to the membrane components, it follows from eq. (3), that Z(Q) or S(Q) is equal to
S(Q) = b:S,,(Q) + 2b,b,S,,(Q)
+ b:&,(Q)
7
(5)
where S,,(Q) is the geometrical part of the corresponding pair correlation function and b, is the sum of the scattering amplitudes for the ith membrane component. Supposing we have at our disposal membranes both of the usual type and with deuterium-labeled components, then after carrying out three measurements (on the usual type, with the deuterium-labeled component, and also with the deuterium-labeled second component), one can determine s,;(Q). Indeed according to eq. (5) we shall have a system of three ratios with three unknown values S;;(Q). The matrix of coefficients of the mixed system equals:
with the resolution
b:, b: The ratio K,, = (b;,lb,)’ has the important characteristic of “placing” the ith membrane component, measuring the increased contribution to the neutron scattering intensity from the corresponding deuteriumlabelled component. To demonstrate the effectiveness of the proposed method K,,, values for totally deuterated membrane components are shown (table 1). In conclusion it is necessary to make two remarks. First, in the general case [5] bi values should be replaced by corresponding formfactors of membrane components J(Q), equaling:
P,.~@)exp(iQR) dR ,
where p,,,(R) is the projection of the scattering amplitude density for the ith component and the integration is done over its cross-section. Second, the transition from scattering intensities Z(Q) to correlation functions in the general case demands deconvolution
“Component”
(7)
3. The study of lateral defects and membrane components structure scattering (SANS)
via small angle neutron
It follows from the general theory of small angle scattering that the scattering intensity of an inhomogeneity is proportional to the square of the so-called contrast [6]: lN(P
-P,)’
(8)
1
where p is the average density of the scattering amplitude from membrane inhomogeneities and p, the average scattering amplitude density of the solvent (i.e. the matrix of the membrane). In this, p, and p depend both on the type of radiation used and the substance. As shown previously, it can be shown, that for the geometry of the experiment in question: (9)
Table 2 illustrates the effectiveness with which SANS is used to detect defects in lipid membranes. It can be seen from table 2 that in the case of defects in the hydrocarbon region of the bilayer, filled with heavy water, the contrast using neutrons is more than 30 times as large as that in the case of X-rays. This property was used in ref. [7] for testing the cluster model of lipid bilayers. Table 3 contains contrasts for X-ray and neutrons in the lipid matrix. This table shows the effectiveness of using small angle neutron scattering for the study of the lateral structure of such membrane components as proteins and DNA. The above evaluation makes it possible to consider that this method can be used for the study of membrane component aggregation with sizes from about 10 to lo4 A and also for the study of the membrane lateral structure in the region of phase transitions.
Table 2 The calculated ratio fects in lipid bilayers
of the scattering intensities by the defor neutrons and X-rays [7].
Defect filling
(p - p,)(lO~*” cm-“) neutron
for totally
deuterated
type
Hydrogen chains of lipids Choline groups of polar head Cholesterol
membrane
X-rays
components. K,.. 580 424 1289
R(Q) as
~(Q)=s(Q)*NQ).
Medium Table 1 K,,, values
function of the instrument
[51:
lot (P, - P,.J2 .
b:
r;(Q)=/A
751
I Lateral structure of biological and model membranes
Hydrocarbon chains Polar head groups
D,O empty D,O empty
45.2 0.116 20.8 3.24
1.44 67.0 12.9 169.0
Ratio of intensities neutrons/ X-rays 31.4 1.7 x lo-’ 1.62 1.9 x 1o-2
V.I. Gordeliy
752 Table Ratio
3 of scattering
I Lareral slructure of biological and model membranes
intensities
of X-rays
and neutrons
for membrane
components
in lipid
matrix.
Type of membrane component
(p - ~,)‘(lO-~~‘crn-~) Neutron
Protein
- usual - deuterated
28.5 99.0
DNA - usual - deuterated Lipids with deuterated
4.
20.0 56.0 chains
62.0
Neutron scattering in the case of fractal structure distribution of membrane components In refs. [S, 91 it has been shown that at non-equihb-
rium phase transitions in lipid monolayers and membranes, fractal structure of various phases can be observed. There is also, in a number of cases, fractal organization of membrane components [lo]. As in ref. [ll], it can be shown that for the two-dimensional analogue of a volume fractal the scattering law is r(Q)x
Q-l’ ,
(10)
where a = d..,.. and d..,.. is the “volume” fractal dimension, and for a two-dimensional analogue of a surface fractal (i.e. fractal structure of the domain boundary) it is
GQ)m Q-” ,
(11)
where a = 4 - d, and d, is the boundary fractal dimension. Ratios (10) and (11) can be used to identify the lateral distribution of membrane components.
X-rays 4.0 4.0 -4.0 -4.0 0.0
Ratio of intensities neutron/X-rays 4.5 25.0 5.0 14.0 2
References [I] B. Jacrot, Rep. Prog. Phys. 39 (1976) 911-953. [2] A.E. Blaurock, in: Progress in Protein-Lipid Interactions (Elsevier Science Publishers, Amsterdam, 1986) pp. I-43. [3] M.K. Jain, in: Membrane Fluidity in Biology, Vol. 1, ed. R.C. Aloin (Academic Press, New York, 1983). [4] L. Powers and P.S. Pershan, Biophys. J. 20 (1977) 137. [S] J. Kauly, Physics of Diffraction (1975). [6] A. Guinier and G. Fournet, Small-angle Scattering of X-rays (Wiley, New York, 1955). [7] V.I. Gordehy, V.G. Ivkov, Yu.M. Ostanevich and L.S. Yaguzhinskiy, Biochim. Biophys. Acta 1061 (1991) 39. [S] A. Miller and H. Mohwald, J. Chem. Phys. 86 (1987) 4258. 19) M.J. Zuckermann and O.G. Mouritsen, Eur. Biophys. J. 15 (1987) 77. [IO] T.F. Monnenmacher, Eur. Biophys. J. 16 (1989) 375. [ll] S.H. Liu, Solid State Phys. 39 (1986) 207.
The study of lateral structure of biological and model membranes by neutron scattering V.I. Gordeliy Joint Institute for Nuclear Research,
Laboratory of Neutron Physics, 101000, Moscow, Head Post Box 79, USSR
In this paper it has been shown that the difference in neutron amplitudes for isotopes (primarily hydrogen and deuterium) and the large lateral contrast (the difference in scattering amplitude density) of membrane components such as lipids, proteins, DNA, can be used for the study of membrane lateral organization. We have demonstrated the possibility to determine, with the help of elastic thermal neutron scattering, lateral pair correlation functions for membrane component packing and the possibility to study membrane inhomogeneities and aggregation processes. We have also given ratios for the dependences of neutron scattering intensities in the case of fractal distributions of membrane components.
1. Introduction The variation of neutron scattering with substance, primarily a strong dependence of scattering amplitude on isotope composition, determines its effectiveness in the study of the structure of biological objects [ 11. The scattering of thermal neutrons is a direct method of studying membrane structure. It is via this method that the distribution of water and ions in membranes was determined and also practically all molecular groups in membranes of dipalmitoylecithin were shown. Subsequently cholesterol, anesthetics, hexane and other membrane components were studied [2]. And yet all this important information is related to the structural organization of membranes in the direction normal to their planes. It is also becoming evident that many of the properties both of biological and lipid membranes can be explained only if one knows the in-plane organization of the membranes [3]. However, a direct determination of the membrane lateral structure with the help of X-ray and neutron scattering is often a much more difficult problem. The main reason for that is the absence (as usual) of long range order in the lateral packing of membrane components and also a small lateral contrast of amplitude density for X-rays. The aim of this paper is to demonstrate theoretically the unique possibilities of neutron scattering for the study of membrane lateral structure, arising from the amplitude difference of neutron scattering for isotopes and the large scattering contrast for membrane components. Experiments of this kind are possible in the case of highly oriented samples (the technique of their preparation is well developed, especially for lipid membranes [4]) in experiments with the scattering vector directed along the membrane plane. 0921-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
2. Determination of the lateral correlation function of a membrane component In the first Born approximation elastic coherent neutron scattering
the amplitude can be written
of as
151: F(4 = ]PW exp(iqddr 1
(1)
where p(r) is the density of scattering amplitude, q = (47~lh) sin 0 the scattering vector, where 0 is half the scattering angle and A is the radiation wavelength. Suppose q = Q and is directed along the membrane plane and the z axis of the coordinate system is perpendicular to it. Then it follows from eq. (l), that:
F(Q) = 1 P,(R) exp(iQR) dR> where
R is directed
P,(R)=
along
the membrane
(2) plane
I P(X>
Y, 2) d.z
and
(3)
is the scattering amplitude density projected on the membrane plane. The scattered neutron intensity, which is being measured in the experiment, equals [5]
I(Q) = F(Q) * F*(Q) = / S(R) exp(iQR)dR,
(4)
where S(R)= I p,(r + R) p(r) dr is the lateral correlation function of the projection of the scattering amplitude density on the membrane plane. Let us suppose that membranes consist only of two components. As will be made clear further on, the following calculations can be easily expanded to the case of multicomponent membranes. To make it sim-
B.V. All rights
reserved
V.I. Gordeliy
pler let us suppose that membrane components are point ones (which is the equivalent of Q-i + L, where L is the lateral size of each membrane component). Then, if we consider that p,(R) = p,,,(R) + p,,,(R), where indices 1 and 2 are related to the membrane components, it follows from eq. (3), that Z(Q) or S(Q) is equal to
S(Q) = b:S,,(Q) + 2b,b,S,,(Q)
+ b:&,(Q)
7
(5)
where S,,(Q) is the geometrical part of the corresponding pair correlation function and b, is the sum of the scattering amplitudes for the ith membrane component. Supposing we have at our disposal membranes both of the usual type and with deuterium-labeled components, then after carrying out three measurements (on the usual type, with the deuterium-labeled component, and also with the deuterium-labeled second component), one can determine s,;(Q). Indeed according to eq. (5) we shall have a system of three ratios with three unknown values S;;(Q). The matrix of coefficients of the mixed system equals:
with the resolution
b:, b: The ratio K,, = (b;,lb,)’ has the important characteristic of “placing” the ith membrane component, measuring the increased contribution to the neutron scattering intensity from the corresponding deuteriumlabelled component. To demonstrate the effectiveness of the proposed method K,,, values for totally deuterated membrane components are shown (table 1). In conclusion it is necessary to make two remarks. First, in the general case [5] bi values should be replaced by corresponding formfactors of membrane components J(Q), equaling:
P,.~@)exp(iQR) dR ,
where p,,,(R) is the projection of the scattering amplitude density for the ith component and the integration is done over its cross-section. Second, the transition from scattering intensities Z(Q) to correlation functions in the general case demands deconvolution
“Component”
(7)
3. The study of lateral defects and membrane components structure scattering (SANS)
via small angle neutron
It follows from the general theory of small angle scattering that the scattering intensity of an inhomogeneity is proportional to the square of the so-called contrast [6]: lN(P
-P,)’
(8)
1
where p is the average density of the scattering amplitude from membrane inhomogeneities and p, the average scattering amplitude density of the solvent (i.e. the matrix of the membrane). In this, p, and p depend both on the type of radiation used and the substance. As shown previously, it can be shown, that for the geometry of the experiment in question: (9)
Table 2 illustrates the effectiveness with which SANS is used to detect defects in lipid membranes. It can be seen from table 2 that in the case of defects in the hydrocarbon region of the bilayer, filled with heavy water, the contrast using neutrons is more than 30 times as large as that in the case of X-rays. This property was used in ref. [7] for testing the cluster model of lipid bilayers. Table 3 contains contrasts for X-ray and neutrons in the lipid matrix. This table shows the effectiveness of using small angle neutron scattering for the study of the lateral structure of such membrane components as proteins and DNA. The above evaluation makes it possible to consider that this method can be used for the study of membrane component aggregation with sizes from about 10 to lo4 A and also for the study of the membrane lateral structure in the region of phase transitions.
Table 2 The calculated ratio fects in lipid bilayers
of the scattering intensities by the defor neutrons and X-rays [7].
Defect filling
(p - p,)(lO~*” cm-“) neutron
for totally
deuterated
type
Hydrogen chains of lipids Choline groups of polar head Cholesterol
membrane
X-rays
components. K,.. 580 424 1289
R(Q) as
~(Q)=s(Q)*NQ).
Medium Table 1 K,,, values
function of the instrument
[51:
lot (P, - P,.J2 .
b:
r;(Q)=/A
751
I Lateral structure of biological and model membranes
Hydrocarbon chains Polar head groups
D,O empty D,O empty
45.2 0.116 20.8 3.24
1.44 67.0 12.9 169.0
Ratio of intensities neutrons/ X-rays 31.4 1.7 x lo-’ 1.62 1.9 x 1o-2
V.I. Gordeliy
752 Table Ratio
3 of scattering
I Lareral slructure of biological and model membranes
intensities
of X-rays
and neutrons
for membrane
components
in lipid
matrix.
Type of membrane component
(p - ~,)‘(lO-~~‘crn-~) Neutron
Protein
- usual - deuterated
28.5 99.0
DNA - usual - deuterated Lipids with deuterated
4.
20.0 56.0 chains
62.0
Neutron scattering in the case of fractal structure distribution of membrane components In refs. [S, 91 it has been shown that at non-equihb-
rium phase transitions in lipid monolayers and membranes, fractal structure of various phases can be observed. There is also, in a number of cases, fractal organization of membrane components [lo]. As in ref. [ll], it can be shown that for the two-dimensional analogue of a volume fractal the scattering law is r(Q)x
Q-l’ ,
(10)
where a = d..,.. and d..,.. is the “volume” fractal dimension, and for a two-dimensional analogue of a surface fractal (i.e. fractal structure of the domain boundary) it is
GQ)m Q-” ,
(11)
where a = 4 - d, and d, is the boundary fractal dimension. Ratios (10) and (11) can be used to identify the lateral distribution of membrane components.
X-rays 4.0 4.0 -4.0 -4.0 0.0
Ratio of intensities neutron/X-rays 4.5 25.0 5.0 14.0 2
References [I] B. Jacrot, Rep. Prog. Phys. 39 (1976) 911-953. [2] A.E. Blaurock, in: Progress in Protein-Lipid Interactions (Elsevier Science Publishers, Amsterdam, 1986) pp. I-43. [3] M.K. Jain, in: Membrane Fluidity in Biology, Vol. 1, ed. R.C. Aloin (Academic Press, New York, 1983). [4] L. Powers and P.S. Pershan, Biophys. J. 20 (1977) 137. [S] J. Kauly, Physics of Diffraction (1975). [6] A. Guinier and G. Fournet, Small-angle Scattering of X-rays (Wiley, New York, 1955). [7] V.I. Gordehy, V.G. Ivkov, Yu.M. Ostanevich and L.S. Yaguzhinskiy, Biochim. Biophys. Acta 1061 (1991) 39. [S] A. Miller and H. Mohwald, J. Chem. Phys. 86 (1987) 4258. 19) M.J. Zuckermann and O.G. Mouritsen, Eur. Biophys. J. 15 (1987) 77. [IO] T.F. Monnenmacher, Eur. Biophys. J. 16 (1989) 375. [ll] S.H. Liu, Solid State Phys. 39 (1986) 207.