Gaussian model of fluctuating membrane and its scattering properties.

Analytical expressions; Elastic and inelastic scattering; Fluctuating membrane; Gaussian modeling; Gaussian random fields; Intermediate scattering functions; Scattering data; Scattering property; Theoretical framework; Time dependent; Statistical and Nonlinear Physics; Statistics and Probability; Condensed Matter Physics

Abstract :

[en] A mathematical model is developed to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a nonhomogeneously clipped time-dependent Gaussian random field. This specific approach provides one with general analytical expressions for the intermediate scattering function for any number of sublayers in the membrane and arbitrary contrasts. The model is illustrated with the analysis of small-angle x-ray and neutron scattering as well as with neutron spin-echo data measured on unilamellar vesicles prepared from phospholipids extracted from porcine brain tissues. The parameters fitted on the entire data set are the lengths of the chain and the head of the molecules that make up the membrane, the amplitude and lateral sizes of the bending deformations, the thickness fluctuation, and a single parameter characterizing the dynamics.

Disciplines :

Physics
Biochemistry, biophysics & molecular biology

Author, co-author :

Gommes, Cédric ; Université de Liège - ULiège > Department of Chemical Engineering

Dubey, Purushottam S; Forschungszentrum Jülich GmbH, Jülich Center for Neutron Science at the Heinz Maier Leibnitz Zentrum, Lichtenbergstrasse 1, 85747 Garching, Germany

Stadler, Andreas M ; Forschungszentrum Jülich GmbH, Jülich Center for Neutron Science, 52425 Jülich, Germany ; Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52056 Aachen, Germany

Wu, Baohu ; Forschungszentrum Jülich GmbH, Jülich Center for Neutron Science at the Heinz Maier Leibnitz Zentrum, Lichtenbergstrasse 1, 85747 Garching, Germany

Czakkel, Orsolya ; Institut Laue-Langevin, 71 avenue des Martyrs, 38042 Grenoble Cedex 9, France

Porcar, Lionel; Institut Laue-Langevin, 71 avenue des Martyrs, 38042 Grenoble Cedex 9, France

Jaksch, Sebastian ; Forschungszentrum Jülich GmbH, Jülich Center for Neutron Science at the Heinz Maier Leibnitz Zentrum, Lichtenbergstrasse 1, 85747 Garching, Germany ; European Spallation Source (ESS) ERIC, Partikelgatan 2, 22484 Lund, Sweden

Frielinghaus, Henrich ; Forschungszentrum Jülich GmbH, Jülich Center for Neutron Science at the Heinz Maier Leibnitz Zentrum, Lichtenbergstrasse 1, 85747 Garching, Germany

Holderer, Olaf ; Forschungszentrum Jülich GmbH, Jülich Center for Neutron Science at the Heinz Maier Leibnitz Zentrum, Lichtenbergstrasse 1, 85747 Garching, Germany

Language :

English

Title :

Gaussian model of fluctuating membrane and its scattering properties.

Publication date :

September 2024

Journal title :

Physical Review. E

ISSN :

2470-0045

eISSN :

2470-0053

Publisher :

American Physical Society, United States

Volume :

110

Issue :

3-1

Pages :

034608

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevE.110.034608

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 30 January 2025

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Bibliography

H. Watson, Essays Biochem. 59, 43 (2015) 0071-1365 10.1042/bse0590043.
D. E. Discher and A. Eisenberg, Science 297, 967 (2002) 0036-8075 10.1126/science.1074972.
A. Guinart, M. Korpidou, D. Doellerer, G. Pacella, M. C. Stuart, I. A. Dinu, G. Portale, C. Palivan, and B. L. Feringa, Proc. Natl. Acad. Sci. USA 120, e2301279120 (2023) 0027-8424 10.1073/pnas.2301279120.
B. Krugmann, A. Radulescu, M.-S. Appavou, A. Koutsioubas, L. R. Stingaciu, M. Dulle, S. Förster, and A. M. Stadler, Sci. Rep. 10, 16691 (2020) 2045-2322 10.1038/s41598-020-73671-3.
B. Krugmann, A. Koutsioubas, L. Haris, S. Micciulla, D. Lairez, A. Radulescu, S. Förster, and A. M. Stadler, Front. Chem. 9, 631277 (2021) 2296-2646 10.3389/fchem.2021.631277.
G. Büldt, H. Gally, A. Seelig, J. Seelig, and G. Zaccai, Nature (London) 271, 182 (1978) 0028-0836 10.1038/271182a0.
G. Pabst, N. Kucerka, M.-P. Nieh, M. Rheinstädter, and J. Katsaras, Chem. Phys. Lipids 163, 460 (2010) 0009-3084 10.1016/j.chemphyslip.2010.03.010.
C. J. Gommes, S. Jaksch, and H. Frielinghaus, J. Appl. Cryst. 54, 1832 (2021) 1600-5767 10.1107/S1600576721010293.
L. Van Hove, Phys. Rev. 95, 249 (1954) 0031-899X 10.1103/PhysRev.95.249.
D. S. Sivia, Elementary Scattering Theory (Oxford University Press, Oxford, 2011).
G. L. Squires, Introduction to the Theory of Thermal Neutron Scattering, 3rd ed. (Cambridge University Press, Cambridge, 2012).
O. Glatter, Scattering Methods and their Application in Colloid and Interface Science (Elsevier, Amsterdam, 2018).
X. Luo, T. Cui, and X. Chu, Front. Phys. 11, 1279007 (2023) 2296-424X 10.3389/fphy.2023.1279007.
J. S. Pedersen, Adv. Colloid Interface Sci. 70, 171 (1997) 0001-8686 10.1016/S0001-8686(97)00312-6.
D. Svergun, Biophys. J. 76, 2879 (1999) 0006-3495 10.1016/S0006-3495(99)77443-6.
C. J. Gommes, Microp. Mesop. Mater. 257, 62 (2018) 1387-1811 10.1016/j.micromeso.2017.08.009.
M. Kiselev, E. Zemlyanaya, N. Ryabova, T. Hauss, S. Dante, and D. Lombardo, Chem. Phys. 345, 185 (2008) 0301-0104 10.1016/j.chemphys.2007.09.051.
M. A. Kiselev, P. Lesieur, A. M. Kisselev, D. Lombardo, and V. L. Aksenov, Appl. Phys. A 74, s1654 (2002) 0947-8396 10.1007/s003390201837.
J. Pencer, S. Krueger, C. P. Adams, and J. Katsaras, J. Appl. Cryst. 39, 293 (2006) 0021-8898 10.1107/S0021889806005255.
V. Chappa, Y. Smirnova, K. Komorowski, M. Muller, and T. Salditt, J. Appl. Cryst. 54, 557 (2021) 1600-5767 10.1107/S1600576721001461.
C. Monzel and K. Sengupta, J. Phys. D 49, 243002 (2016) 0022-3727 10.1088/0022-3727/49/24/243002.
I. W. Hamley, Soft Matter 18, 711 (2022) 1744-683X 10.1039/D1SM01758F.
H. T. McMahon and J. L. Gallop, Nature (London) 438, 590 (2005) 0028-0836 10.1038/nature04396.
A. Zidovska and E. Sackmann, Phys. Rev. Lett. 96, 048103 (2006) 0031-9007 10.1103/PhysRevLett.96.048103.
R. M. Venable, Y. Zhang, B. J. Hardy, and R. W. Pastor, Science 262, 223 (1993) 0036-8075 10.1126/science.8211140.
A. J. Sodt, M. L. Sandar, K. Gawrisch, R. W. Pastor, and E. Lyman, J. Am. Chem. Soc. 136, 725 (2014) 0002-7863 10.1021/ja4105667.
S. Chakraborty, M. Doktorova, T. R. Molugu, F. A. Heberle, H. L. Scott, B. Dzikovski, M. Nagao, L. Stingaciu, R. F. Standaert, F. N. Barrera, J. Katsaras, G. Khelashvili, M. F. Brown, and R. Ashkar, Proc. Natl. Acad. Sci. USA 117, 21896 (2020) 0027-8424 10.1073/pnas.2004807117.
D. W. Hayward, S. Jaksch, M. Fomina, P. S. Dubey, H. Frielinghaus, O. Holderer, and M. Monkenbusch, Acta Cryst. D 78, 1249 (2022) 2059-7983 10.1107/S2059798322008701.
A. G. Zilman and R. Granek, Phys. Rev. Lett. 77, 4788 (1996) 0031-9007 10.1103/PhysRevLett.77.4788.
A. G. Zilman and R. Granek, Chem. Phys. 284, 195 (2002) 0301-0104 10.1016/S0301-0104(02)00548-7.
M. Nagao and H. Seto, Biophys. Rev. 4, 021306 (2023) 2688-4089 10.1063/5.0144544.
R. Granek, I. Hoffmann, E. G. Kelley, M. Nagao, P. M. Vlahovska, and A. Zilman, Eur. Phys. J. E 47, 12 (2024) 1292-8941 10.1140/epje/s10189-023-00400-9.
M. Nagao, Phys. Rev. E 80, 031606 (2009) 1539-3755 10.1103/PhysRevE.80.031606.
A. C. Woodka, P. D. Butler, L. Porcar, B. Farago, and M. Nagao, Phys. Rev. Lett. 109, 058102 (2012) 0031-9007 10.1103/PhysRevLett.109.058102.
M. Nagao, E. G. Kelley, R. Ashkar, R. Bradbury, and P. D. Butler, J. Phys. Chem. Lett. 8, 4679 (2017) 1948-7185 10.1021/acs.jpclett.7b01830.
N. Berk, Phys. Rev. Lett. 58, 2718 (1987) 0031-9007 10.1103/PhysRevLett.58.2718.
N. F. Berk, Phys. Rev. A 44, 5069 (1991) 1050-2947 10.1103/PhysRevA.44.5069.
M. Teubner, Europhys. Lett. 14, 403 (1991) 0295-5075 10.1209/0295-5075/14/5/003.
S. H. Chen, D. D. Lee, K. Kimishima, H. Jinnai, and T. Hashimoto, Phys. Rev. E 54, 6526 (1996) 1063-651X 10.1103/PhysRevE.54.6526.
A. P. Roberts, Phys. Rev. E 55, R1286 (1997) 1063-651X 10.1103/PhysRevE.55.R1286.
C. J. Gommes and A. P. Roberts, Phys. Rev. E 77, 041409 (2008) 1539-3755 10.1103/PhysRevE.77.041409.
P. Levitz, Adv. Colloid Interface Sci. 76-77, 71 (1998) 0001-8686 10.1016/S0001-8686(98)00042-6.
C. J. Gommes, J. Appl. Cryst. 46, 493 (2013) 0021-8898 10.1107/S0021889813003816.
C. Prehal, C. Koczwara, N. Jäckel, A. Schreiber, M. Burian, H. Amenitsch, M. A. Hartmann, V. Presser, and O. Paris, Nat. Energy 2, 16215 (2017) 2058-7546 10.1038/nenergy.2016.215.
C. J. Gommes and J. P. Pirard, Phys. Rev. E 80, 061401 (2009) 1539-3755 10.1103/PhysRevE.80.061401.
C. J. Gommes, R. Chattot, and J. Drnec, J. Appl. Cryst. 53, 811 (2020) 1600-5767 10.1107/S1600576720005464.
C. J. Gommes, R. Zorn, S. Jaksch, H. Frielinghaus, and O. Holderer, J. Chem. Phys. 155, 024121 (2021) 0021-9606 10.1063/5.0053446.
C. J. Gommes, Gels 8, 236 (2022) 2310-2861 10.3390/gels8040236.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.110.034608 for the calculation of the surface area of the deformed membrane and for the derivation of Eq. (26).
J. Folch, I. Ascoli, M. Lees, J. Meath, and F. LeBaron, J. Biol. Chem. 191, 833 (1951) 0021-9258 10.1016/S0021-9258(18)55987-1.
P. S. Dubey, O. Czakkel, H. Frielinghaus, I. Hoffmann, O. Holderer, S. Jaksch, O. Matsarskaia, J. Ollivier, S. Prevost, and D. Saha (2023), doi: 10.5291/ILL-DATA.9-13-1040.
J. A. Quiblier, J. Colloid Interface Sci. 98, 84 (1984) 0021-9797 10.1016/0021-9797(84)90481-8.
C. Lantuéjoul, Geostatistical Simulations (Springer, Berlin, 2002).
C. J. Gommes and A. P. Roberts, Phys. Chem. Chem. Phys. 20, 13646 (2018) 1463-9076 10.1039/C8CP01628C.
A. Lewis-Laurent, M. Doktorova, F. A. Heberle, and D. Marquardt, Biophys. J. 120, 4639 (2021) 0006-3495 10.1016/j.bpj.2021.09.018.
J. Lemmich, K. Mortensen, J. H. Ipsen, T. Honger, R. Bauer, and O. G. Mouritsen, Phys. Rev. E 53, 5169 (1996) 1063-651X 10.1103/PhysRevE.53.5169.
S. Maiti, H. Frielinghaus, D. Grässel, M. Dulle, M. Axer, and S. Förster, Sci. Rep. 11, 17306 (2021 10.1038/s41598-021-92995-2.
C. Lantuejoul, J. Microsc. 161, 387 (1991) 0022-2720 10.1111/j.1365-2818.1991.tb03099.x.
M. J. Lighthill, An Introduction to Fourier Analysis and Generalised Functions, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 1958).
A. E. Gelfand, P. Diggle, P. Guttorp, and M. Fuentes, Handbook of Spatial Statistics (CRC Press, Boca Raton, FL, 2010).
H. Berg, Random Walks in Biology, 2nd ed. (Princeton University Press, Princeton, NJ, 1993).
G. Pabst, M. Rappolt, H. Amenitsch, and P. Laggner, Phys. Rev. E 62, 4000 (2000) 1063-651X 10.1103/PhysRevE.62.4000.
F. A. Heberle, R. S. Petruzielo, J. Pan, P. Drazba, N. Kuerka, R. F. Standaert, G. W. Feigenson, and J. Katsaras, J. Am. Chem. Soc. 135, 6853 (2013) 0002-7863 10.1021/ja3113615.