Water distribution function across the curved lipid bilayer: SANS study

Available online at www.sciencedirect.com

Chemical Physics 345 (2008) 185–190 www.elsevier.com/locate/chemphys

Water distribution function across the curved lipid bilayer: SANS study M.A. Kiselev a, E.V. Zemlyanaya b, N.Y. Ryabova a, T. Hauss c, S. Dante c, D. Lombardo

d,*

a

Frank Laboratory of Neutron Physics, JINR, Dubna, Russia Laboratory of Information Technologies, JINR, Dubna, Russia c Hahn-Meither-Institute, Berlin, Germany CNR-IPCF, Istituto per i Processi Chimico Fisici (Sez. Messina), Messina, Italy b

d

Received 23 March 2007; accepted 28 September 2007 Available online 6 October 2007

Abstract The neutron scattering length density across the membrane is simulated on the basis of fluctuated model of lipid bilayer. The use of a separated form factors method has been applied for the identification of the structural features of the polydispersed unilamellar DMPC vesicle system. The hydration of vesicle is described by sigmoid distribution function of the water molecules. The application of the model to the obtained SANS spectra allow the determination of the main parameters of the system, such as the average vesicle radius (and its polydispersity), the membrane thickness, the thickness of hydrocarbon chain region, the number of water molecules located per lipid molecule, and the phospholipid surface area. Moreover the approach allow the calculation of some relevant parameters connected with the water distribution function across the bilayer system. The main features of the obtained results furnish an explanation of why lipid membrane is easily penetrated by the water molecules of the solution.  2007 Elsevier B.V. All rights reserved. Keywords: Neutron scattering; Bilayer; Form factor; Lipid membrane

1. Introduction Research into the structure of phospholipids, the main component of biological membranes, is very important from the viewpoint of structural biology, chemistry and pharmacology. A determination of the internal lipid membrane structure is far beyond the resolution of light microscopy or light scattering. Small angle neutron scattering ˚ provides better (SANS) in the wavelength range of 1–10 A spatial resolution of an internal structure on the scale of Angstroms. It allows to determine the internal membrane structure with reasonable accuracy. Generally, average radius of the vesicle population, vesicle polydispersity, membrane thickness, and internal structure of membrane were defined on the basis of the hollow sphere model (HS) and the Kratky Porod method [1–4]. This approach,

*

Corresponding author. Tel.: +39 090 3974130; fax: +39 090 39762222. E-mail address: [email protected] (D. Lombardo).

0301-0104/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.09.051

on the other hand, present an important limitation: the neutron scattering length density distribution across the bilayer is described by a uniform (i.e. constant) function or a strip function, that can be considered respectively as the zero- and the first-order approximation in the evaluation of the internal membrane structure from SANS. The real scattering density profile from neutron diffraction experiments demonstrates a more complex and smooth distribution [5]. The approach based on the separated form factor method (SFF) allows one to apply any function to simulate the scattering length density of neutrons across the bilayer for the calculation of coherent macroscopic scattering cross-section of vesicle population [7–9]. The parameters of the DMPC vesicle population (average radius, polydispersity, membrane thickness, thickness of hydrophobic part, and number of linear distributed water molecules in the membrane bilayer) were obtained only from the SANS spectra, without additional methods (light scattering, diffraction, etc.) [9]. Water distribution in the hydrophilic part

186

M.A. Kiselev et al. / Chemical Physics 345 (2008) 185–190

of membrane was simulated by linear function [9] and sigmoidal function [8]. The evaluation of water distribution function across the lipid bilayer is important to understand the physical principals of water diffusion through lipid membrane and water penetration through biological membrane of the cell. The second important question is the water penetration depth into the lipid bilayer. For many decades it was a common opinion that water penetrates only into the polar head group region. Recently, the water penetration into the region of hydrocarbon chains was detected experimentally for saturated phospholipids by nuclear magnetic resonance [10], by SANS [8,9] and by neutron diffraction [11]. The Gauss functions has been successfully used by Wiener and White to describe the internal membrane structure from neutron and X-ray diffraction experiment [5]. Later, this approach was further developed for the interpretation of X-ray reflectivity from phospholipid monolayer on water surface [14,15] and for the interpretation of SANS spectra in [8]. It was shown that strip-functions can be correctly applied to describe the reflectivity curve only for ˚ 1. The use of Gauss functions take into proper q < 0.5 A account the circumstance that the molecular groups in phospholipid bilayer (monolayer) fluctuate near its equilibrium position. Any group can be described via two parameters: average group position and the Gauss distribution function around it. According to this approach, the geometrical sense of lipid membrane thickness changes to the distribution function of polar head group position. Structure of flat and curved phospholipids bilayer are different. It was shown by differential thermal calorimetry that phase pretransition temperatures of the flat bilayers of dipalmitoyllecithine are different from its curved bilayer [16]. Recently it was shown by SANS on the dimyristoylphosphatidylcholine (DMPC) [9] and palmitoyloleoylphosphatidylcholine POPC [17] vesicles that membrane thickness and hydration increase at increasing of membrane curvature radius. One of the open questions here concern the correct evaluation of the water distribution function from SANS on the unilamellar vesicles. This work clarify, within the fluctuation bilayer model, the problems connected with water distribution function across the bilayer of the unilamellar DMPC vesicles [8]. 2. Materials and methods Unilamellar dimyristoylphosphatidylcholine vesicles (DMPC) were prepared by extrusion of 15 mM (1% w/w) suspension of DMPC in D2O through filters with a pore ˚ . The SANS spectra from the unilamellar diameter of 500 A vesicle population at T = 30 C were collected at the SANS spectrometer as was described in [9]. Note that the accuracy in the fitting of the vesicle structure strongly depends on the experimentally measured range of the scattering vector. This means that the obtained parameters of the internal membrane structure depend on the value of maximum q measured experimentally. For the system under study,

the experimental conditions allow to collect a scattering ˚ 1 to qmax = curve in the q range from qmin = 0.0033 A 1 ˚ 0.56 A . To fit the SANS data in the framework of SFF model, the Fortran code was developed using the minimizing code DFUMIL from the JINRLIB library (JINR, Dubna). The oriented multilamellar DMPC lipid films on quartz substrate were prepared as described in [6]. DMPC was solved in the chloroform/methanol solution 1/1 (w/w) with 1% concentration. Solution of 1.2 g was spread over 3.2 cm · 6.5 cm area of quartz slide and dried at room temperature. The rest of the organic solvent was removed under vacuum. The sample was heated in horizontal position above 50 C at relative humidity RH=100% to decrease the sample mosaicity. Neutron diffraction patterns from the oriented sample were collected at the V1 diffractometer of the Hahn-Meitner-Institute, Berlin. Fourier synthesis of the neutron scattering length density q(x) was done as described in detail in [6]. 3. Results and discussion We start our analysis with the formulation of the fitting problem for the SFF method. The macroscopic coherent scattering for a monodispersed vesicles population is defined as [18] dR ðqÞ ¼ n  A2 ðqÞ  SðqÞ; dXmon

ð1Þ

where n is a number of vesicles per unit volume, A(q) is the scattering amplitude of vesicle, S(q) is the vesicle structure factor (calculated as in [22,23]); q is the scattering wavevector (q = (4p/k) sin (h/2), with h the scattering angle, k the neutron wavelength). The scattering amplitude in the spherically symmetric case is equal [18] to Z sinðqRÞ 2 AðqÞ ¼ 4p  qðrÞ   r  dr ð2Þ qR Here q = (qC  qD2 O ) is the neutron contrast between the neutron scattering length density of the lipid bilayer (qC) and of D2O (qD2 O = 6.33 · 1010 cm2). Eq. (2) can be rewritten in the following form [7]: Z d m =2 sin½ðR þ xÞ  q 2  ðR þ xÞ  dx qðxÞ  ð3Þ AðqÞ ¼ 4p  ðR þ xÞ  q d m =2 Here R is the radius of vesicle, dm is the membrane thickness. Integration of Eq. (3) with the following assumption R  d/2, R + x  R gives Z d m =2 sinðqRÞ 2 R  ASFF ðqÞ ¼ 4p  qðxÞ  cosðqxÞ  dx ð4Þ qR d m =2 When the inter-particle interaction is negligible (i.e. in case, S(q) = 1), the macroscopic cross-section of the monodispersed population of vesicles can be written as dR ðqÞ ¼ n  F s ðq; RÞ  F b ðq; dÞ; dXmon

ð5Þ

M.A. Kiselev et al. / Chemical Physics 345 (2008) 185–190

while Fb(q,R) is the form factor of the symmetric lipid bilayer !2 Z d m =2 qc ðxÞ  cosðqxÞ  dx ð7Þ F b ðq; dÞ ¼ d m =2

Eqs. (5)–(7) represent the separated form factor method (SFF) for unilamellar vesicles presented in Fig. 1. The most important features of this approach are mainly connected with the possibility of describing the membrane structure via representation of q(x) with any function. Fig. 1 presents the structure of the unilamellar vesicles and demonstrate difference scale of vesicle size and membrane nanostructure. The macroscopic cross-section dR(q)/dX is described via the convolution of the dR(q)/dXmon with the vesicle distribution function G(R, hRi) (i.e. the non-symmetric Schulz distribution which take into account the vesicle polydispersity [2,20]) by integration over the vesicle radius from ˚ to Rmax = 1000 A ˚ Rmin = 100 A R Rmax dR ðq; R; dÞ  GðR; hRiÞ  dR dR R dX ðqÞ ¼ min RmonRmax ð8Þ dX GðR; hRiÞ  dR Rmin As the resolution function of the spectrometer is not a delta-function, the experimentally measured cross-section I(q) is not exactly equal to the actual macroscopic cross-section Im(q). More specifically the experimental cross-section I(q) can be written as 1 d2 I theor ðq; hRi; dÞ ; IðqÞ ¼ I theor ðq; hRi; dÞ þ  D2  2 dq2

in a single vesicle, while C = 89.17 · 1017 is the number of DMPC molecules in cm3). The volume of the liquid bilayer is V = 4/3[(hRi + dm/2)3  (hRi  dm/2)3] (where d is the membrane thickness), while the volume of molecular DMPC in the liquid phase is given by VDMPC = ˚ 3 – volume of the ‘dry’ V0 + nWV D2 O (where V0 = 1101 A DMPC molecules [13], nW – number of the water molecules ˚ 3 – volume of the per one DMPC molecule, V D2 O = 30 A heavy water molecule). In the present analysis we make the assumption that VDMPC  V0, while the parameter nW is estimated after that all other vesicle parameters have been calculated. The choice of the q(x) function could be done on the basis of the knowledge obtained from neutron diffraction experiment. Neutron diffraction experiment with contrast variation is, in fact, a suitable technique for the determination of q(x) function of partly hydrated multilamellar flat membranes. The evaluation of q(x) function for DMPC flat membrane from neutron diffraction experiment was described in [6]. In Fig. 1, we present the q(x) function of DMPC system measured in the liquid phase: (T = 40 C, relative humidity RH = 96% of water with 8% D2O). Repeat distance of the multilamellar membrane is equal ˚ . Water with 8% D2O has zero scatterto d = 49.1 ± 0.1 A ing length density. Thus, q(x) function presented in Fig. 2 corresponds to the structure of the DMPC membrane. The polar head region could be described by Gauss function as was shown in [6]. This statement is essential for the formulation of Eqs. (11) and (12).

3

ρ( x), a.u.

where Fs(q,R) is the form factor of an infinitely thin sphere with radius R [19]  2 R2  sinðqRÞ F s ðq; RÞ ¼ 4p  ð6Þ qR

187

2

ð9Þ

where D2 is a second moment of the resolution function [21], Im(q) = dR(q)/dX (see Eq. (8). The parameters of the fitting are average vesicle radius hRi, coefficient of polydispersity m, and parameters of function q(x) modelling the neutron scattering length density (note that the incoherent background is also considered as an unknown parameter of the model). The number of vesicles per unit volume are n = C/M (where M = V/VDMPC is the number of DMPC molecules

1

0 -25

-15

-20

-5

5

-10

0 -1

15

10

25

20

x, Å

-2

Fig. 2. Neutron scattering length density of DMPC multilamellar ˚, membrane at T = 40 C, RH = 96% and 8% D2O. d = 49.1 ± 0.1 A liquid phase.

Fig. 1. Unilamellar vesicle in water. Radius of vesicle R is sufficiently larger relative to the bilayer thickness dm. Water molecules (dots) locate in the hydrophilic region of the bilayer according to the water distribution function.

188

M.A. Kiselev et al. / Chemical Physics 345 (2008) 185–190

Increase of the D2O content in water sensitively influence the q(x) function evaluated from neutron diffraction experiment. As shown in Fig. 3, the scattering length density increases in the region of polar head groups for DMPC multilamellar membrane (at T = 37 C, RH = 57% and 100% D2O). This increase is results of D2O penetration in the hydrophilic region of the membrane. This result is important for SANS study of vesicles in D2O. The q(x) function of the lipid bilayer of the unilamellar vesicles could not be so far from that presented in Fig. 3. Second advantage of the diffraction experiment consists in the possibility to calculate the water distribution function as the difference between q(x) functions, measured at different content of D2O [6]. The water distribution function of DMPC in gel phase is presented in Fig. 4. As seen this function could be approximated by a sigmoid function. This is the reason why the sigmoid function (14) is used in the SANS experiment to describe the water distribution function. We used results obtained from the Fourier analysis of diffraction experiment to construct the approximation of q(x) for SANS experiment on the unilamellar vesicles. The internal structure of the lipid bilayer q(x) is reproduced as the superposition of the functions qph(x) (i.e. the scattering length density of ‘dry’ phospholipids) and

8

qW(x) (i.e. the water distribution inside the vesicle). More specifically we used the strip and Gauss function to model the ‘dry’ lipid as shown in Fig. 5. Hydration of vesicle was simulated by sigmoid function [15]. The background for the introduction of sigmoid function is the water distribution function evaluated from neutron diffraction experiment as presented in Fig. 4. The distribution shown in Fig. 5, is defined by the following formulas: qC ðxÞ ¼ qph ðxÞ þ qch ðxÞ þ qW ðxÞ

ð10Þ

The scattering length density of the dry phospholipids bilayer qph(x) can be expressed as a function of the Gauss distribution f(x) (Fig. 5) as f ðxÞ  lph A ! 2 1 ðx  x0 Þ f ðxÞ ¼ pffiffiffiffiffiffiffiffi exp  2R2 2pr

qph ¼

ð11Þ ð12Þ

where lph = 6.008 · 1012 cm (scattering length of the ‘‘dry’’ phospholipid). As the bilayer (membrane) thickness is defined in this case as dm = 2x0, the surface area of the DMPC molecule is given by A = 2 Æ VDMPC/dm. The scattering length density of the hydrocarbon chain qch(x) is determined as  lch  2=½D  A; D=2 < x < D=2 qch ðxÞ ¼ ð13Þ 0 D=2 < jxj < d=2

7

ρ( x), a.u.

6 5 4 3 2 1 0 -30

-20

-10

10

-1 0 -2

30

20

where D is the thickness of hydrocarbon chain region, while lch =  3.24 · 1012 cm is the value of its scattering length. Finally the scattering length density of internal water qW(x) is defined as qD2 O qD2 O  þ   qW ðxÞ ¼ ð14Þ xW x 1 þ exp rW 1 þ exp xWrWþx

x, Å

-3

Fig. 3. Neutron scattering length density of DMPC multilamellar ˚, membrane at T = 37 C, RH = 57% and 100% D2O. d = (54.7 ± 0.1) A gel phase.

ρ(x), a.u.

0.6

0.4

0.2

0 -25

-20

-15

-10

-5

0

5

10

15

25

20

x, Å

Fig. 4. Water distribution function of DMPC multilamellar membrane at ˚ , gel phase. T = 37 C, RH = 57%. d = 54.7 ± 0.1 A

Fig. 5. Neutron scattering length density across the bilayer (fluctuation model). The upper dash-dots lines demarcate the scattering length density qph(x) of the ‘dry’ phospholipids bilayer. The lower dash-dots represents the sigmoid function which simulate the water distribution qW(x). The solid lines show the total neutron scattering length density across the bilayer q(x).

M.A. Kiselev et al. / Chemical Physics 345 (2008) 185–190

where qD2 O = 6.33 · 1010 cm is the scattering length density of the heavy water. In Fig. 6 and Table 1 are reported the results of the fitting procedures for the SANS spectra. In this calculation, the structure factor was taken into account as in [22,23]. The thickness of the membrane can be estimated as 2 Æ x0 = 50.6 ± 0.8. This result is in good agreement with ˚ obtained using the linear the result of d = 48.9 ± 0.2 A water distribution [9]. The membrane thickness of curved ˚ is larger relative to bilayer with radius of curvature 272 A ˚ the thickness of flat membrane 44.2 A [12]. Kratky Porod model on the other hand give dm = 44.5 ± 0.3 in [4]. The number of water molecules per one DMPC molecule can be calculated as Z d=2 A  qW ðxÞ dx; ð15Þ nW ¼ lD 2 O 0

dΣ /d Ω . cm

-1

where the surface area of the DMPC molecule is given by ˚ 2. The obtained number of water A = (2V0/d) = 43.5 A molecules located in the hydrophilic region nW = 12.6 ± 1.1 is in good agreement with data published in [9] (nW = 12.8 ± 0.3). The number of water molecules in the region of hydrocarbon chains (obtained by the integration of Eq. (15) from 0 to D/2) corresponds to the value 2.2. This result clearly indicate that the fluctuation model detects a small penetration of water molecules inside the region of hydrocarbon chains. On the other hand it is well 10

3

10

2

10

1

10

0

10

-1

10

-2

0.1

0.01

0.1

0.2

0.3

0.4

0.5

0.6

0.01

0.1

1

-1

q, Å

Fig. 6. Fitting results of the DMPC vesicle spectrum relative to the model of the internal structure of the lipid bilayer given in Fig. 5. The points are the experimental data, the solid lines show results of the fitting. The inset shows in detail the curves for large q.

189

known that water molecules easily penetrate through bilayer [24]. In this respect we can state that our SANS results on the basis of the fluctuated model clearly support this experimental fact via calculation of water distribution function across the bilayer. We can make a correction of the DMPC surface area, taking into account that water molecules increase the volume occupied by one DMPC molecule. The use, in fact, ˚ 2 corresponds in fact to of the estimation of A = 43.5 A the area of membrane surface occupied by a dry DMPC molecule. Taking into account the DMPC ‘‘swelling’’ by water, we obtain the effective value of the surface area of ˚2 the DMPC molecule AW = (2VDMPC/d) = 58.5 ± 2 A (where we used the corrected value of VDMPC = V0 + ˚ 3 = 1480 A ˚ 3). This obtained value for AW is close nW Æ 30 A ˚ obtained by Nagle and co-workers [13], to the value 59.6 A ˚ 2 obtained in [9], and also close to the value of 58.9 ± 0.8 A 2 ˚ obtained in [12]. Full width and the value of 58.8 ± 0.5 A at half height of the distribution function of polar head ˚ can be used to estimate the groups 2.36 Æ R = 8.0 ± 1.7 A region of polar head group location. The obtained value ˚ thickness of of polar head group location is near the 9 A polar head groups obtained from the X-ray diffraction [12,13]. It is worth noticing that the thickness of hydrocar˚ obtained in the present work bon chains D = 21.4 ± 2.6 A ˚ is not in contradiction with Nagle’s result of 26.2 A obtained via the strip-function approximation of electron density profile [12]. The precise definition of this boundary is, in fact, not so simple to provide. More specifically the hydrophobic/hydrophilic boundary represent some ‘‘broad ˚ , which region’’ near the value (xW  rW)=11.4 ± 0.8 A reasonably corresponds to the end of the hydrocarbon ˚ ). It is important to note that chains (i.e. D/2=10.7 ± 1.3 A three parameters: xW, rW, and D are independent parameters. An important result of our study is the explanation of the differences in the evaluation of membrane thickness between the case in which q(x) = const and for q(x) as step-function. The calculation of the DMPC membrane thickness on the basis of q(x) = const model gives in fact ˚ , which a value of membrane thickness 36.7 ± 0.1 A ˚ at the application increases up to the value of 42.1 ± 0.4 A of strip-function model of q(x). The total neutron scattering length density across the bilayer obtained in our study (see Fig. 5) clearly demonstrate that modelling of q(x) via box model with q(x) = const inside the bilayer leads to decreasing of the membrane thickness to the value about ˚ . The underestimation of the membrane thickness is 34 A the result of deep D2O penetration inside the bilayer.

Table 1 Parameters of the DMPC vesicles (T = 30 C) calculated in the framework of SFF method for the scattering length density of neutrons across the lipid bilayer presented in Fig. 1a ˚) ˚) hRi (A Polydispersity D (A xW rW x0 R IB (cm1) 272.3 ± 0.4

27%

21.4 ± 2.6

18.3 ± 0.6

6.91 ± 0.2

25.3 ± 0.4

3.43 ± 0.7

6.05 · 103

IB: incoherent background. a hRi: average vesicle radius; D: thickness of hydrophobic region; xW: critical point of the water distribution function (with rW characteristic width of the distribution); x0: half thickness of the membrane; R: characteristic width of the distribution function of polar head groups.

190

M.A. Kiselev et al. / Chemical Physics 345 (2008) 185–190

4. Conclusions The use of a separated form factors (SFF) model has been applied for the identification of the structural features of the polydispersed unilamellar DMPC vesicle system. The neutron scattering length density across the internal structure of phospholipid bilayer is simulated on the basis of fluctuated model of lipid bilayer. The hydration of vesicle is described by sigmoid distribution function of the water molecules. The application of the model to the obtained SANS spectra allow the determination of the main parameters of the system (such as vesicle radius, membrane thickness, thickness of hydrocarbon chain region, number of water molecules per lipid molecule, phospholipid surface area). Moreover the approach allow the calculation of some relevant parameters connected with the water distribution function across the bilayer system. The penetration of water molecules through the bilayer is proved via direct calculation of water distribution function across the bilayer. This approach furnish an interesting method for the characterisation of the vesicle based drug delivery systems at the nanometre scale [25]. Acknowledgement The work was supported by Russian Federal Agency of Science and Innovation. References [1] J. Pencer, R. Hallett, Phys. Rev. E 61 (2000) 3003. [2] H. Schmiedel, P. Joerchel, M. Kiselev, G. Klose, J. Phys. Chem. B 105 (2001) 111. [3] P. Balgavy, M. Dubnickova´, N. Kucerka, M.A. Kiselev, S.P. Yaradaikin, D. Uhrikova, Biochim. Biophys. Acta 1521 (2001) 40. [4] N. Kucerka, M. Kiselev, P. Balgavy, Eur. Biophys. J. 33 (2004) 328.

[5] M.C. Wiener, S.H. White, Biophys. J. 59 (1981) 162. [6] M.A. Kiselev, N.Yu. Ryabova, A.M. Balagurov, S. Dante, T. Hauss, J. Zbytovska, S. Wartewig, R.H.H. Neubert, Eur. Biophys. J. 34 (2005) 1030. [7] M.A. Kiselev, P. Lesieur, A.M. Kisselev, D. Lombardo, V.L. Aksenov, J. Appl. Phys. A 74 (2002) S1654. [8] M.A. Kiselev, E.V. Zemlyanaya, V.K. Aswal, Crystallogr. Rep. 49 (Suppl. 1) (2004) s136. [9] M.A. Kiselev, E.V. Zemlyanaya, V.K. Aswal, R.H.H. Neubert, Eur. Biophys. J. 35 (2006) 477. [10] N. Tokutake, B. Jing, S.L. Regen, Langmuir 20 (2004) 8958. [11] M.A. Kiselev, N.Y. Ryabova, A.M. Balagurov, D. Otto, S. Dante, T. Hauss, S. Wartewig, R.H.H. Neubert, Surf. X-ray Synchrotron Neutron Res. 6 (2006) 30 (in Russian). [12] J.F. Nagle, S. Tristram-Nagle, Biochim. Biophys. Acta 1469 (2000) 159. [13] H.I. Petrache, S.E. Feeler, J.F. Nagle, Biophys. J. 72 (1997) 2237. [14] M. Schalke, M. Losche, Adv. Colloid Interf. Sci. 88 (2000) 243. [15] M. Schalke, P. Kruger, M. Weygand, M. Losche, Biochim. Biophys. Acta 1464 (2000) 113. [16] V.A. Tverdislov, The Physical Mechanism of the Biological Membranes Functionality, Moscow University, Moscow, 1987 (in Russian). [17] H. Schmiedel, L. Almasy, G. Klose, Eur. Biophys. J. 35 (2006) 181. [18] L.A. Feigin, D.I. Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Publishing Corporation, New York, 1987. [19] P. Lesieur, M.A. Kiselev, L.I. Barsukov, D. Lombardo, J. Appl. Crystallogr. 33 (2000) 623. [20] F.R. Hallet, J. Watton, P. Krygsman, Biophys. J. 59 (1991) 357. [21] Y.M. Ostanevich, Makromol. Chem. Macromol. Symp. 15 (1988) 91. [22] M.A. Kiselev, P. Lesieur, A.M. Kisselev, D. Lombardo, M. Killany, S. Lesieur, M. Ollivon, Nucl. Instrum. Meth. Phys. Res. A 470 (2001) 409. [23] M.A. Kiselev, D. Lombardo, A.M. Kisselev, P. Lesieur, V.L. Aksenov, Surf. X-ray Synchrotron Neutron Res. 11 (2003) 20. [24] M.A. Kiselev, P. Lesieur, A.M. Kisselev, M. Ollivon, Nucl. Instrum. Meth. Phys. Res. A 448 (2000) 255. [25] J. Pencer, S. Krueger, C.P. Adams, J. Katsaras, J. Appl. Crystallogr. 39 (2006) 293.