[en] Proteins are ubiquitous in biological membranes and have a significant impact on their scattering properties. In this contribution, we introduce a general mathematical construction to add proteins to any pre-existing membrane model and to calculate the resulting elastic and/or inelastic scattering cross section. The model is a low-resolution one, which describes the proteins as made up of regions of homogeneous scattering length density that extend through an arbitrary fraction of the membrane and possibly protrude out of it. In this construction, the protein characteristics that are relevant to scattering are their space and time correlation functions in the two-dimensional plane of the membrane. The results are particularized to a static bilayer model and to a Gaussian model of a fluctuating membrane. The models are then applied to the joint analysis of small-angle neutron and X-ray scattering of red blood cell membranes, of which transmembrane proteins constitute 25% of the volume, and to neutron spin-echo data measured on the same systems.
Disciplines :
Physics Chemistry
Author, co-author :
Gommes, Cédric ; Université de Liège - ULiège > Department of Chemical Engineering
Matsarskaia, Olga; Institut Laue-Langevin, 71 Avenue des Martyrs, 38042 Grenoble, France
Pusterla, Julio M; Jülich Centre for Neutron Science JCNS-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
Graf von Westarp, Igor; Jülich Centre for Neutron Science JCNS-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany ; Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52056 Aachen, Germany
Wu, Baohu ; Jülich Centre for Neutron Science at MLZ, Forschungszentrum Jülich GmbH, Lichtenbergstrasse 1, 85747 Garching, Germany
Czakkel, Orsolya; Institut Laue-Langevin, 71 Avenue des Martyrs, 38042 Grenoble, France
Stadler, Andreas M; Jülich Centre for Neutron Science JCNS-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany ; Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52056 Aachen, Germany
Language :
English
Title :
Model for small-angle scattering analysis of membranes with protein-like inclusions.
Publication date :
01 October 2025
Journal title :
Journal of Applied Crystallography
ISSN :
0021-8898
eISSN :
1600-5767
Publisher :
International Union of Crystallography, United States
We gratefully acknowledge beam-time allocation for the neutron scattering experiments on the small-angle diffractometer D22 and on the high-resolution spin\u2013echo spectrometer IN15 at the Institut Laue\u2013Langevin, Grenoble, France, and for X-ray experiments on the KWS-X laboratory beam-line at the Heinz Maier-Leibnitz Zentrum in Garching, Germany. Open access funding enabled and organized by Projekt DEAL. C. J. Gommes is grateful to the Funds for Scientific Research (FRS-FNRS, Belgium) for supporting this work through a Research Associate position.
Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T., Pritzel, A., Ronneberger, O., Willmore, L., Ballard, A. J., Bambrick, J., Bodenstein, S. W., Evans, D. A., Hung, C.-C., O’Neill, M., Reiman, D., Tunyasuvunakool, K., Wu, Z., Žemgulytė, A., Arvaniti, E., Beattie, C., Bertolli, O., Bridgland, A., Cherepanov, A., Congreve, M., Cowen-Rivers, A. I., Cowie, A., Figurnov, M., Fuchs, F. B., Gladman, H., Jain, R., Khan, Y. A., Low, C. M. R., Perlin, K., Potapenko, A., Savy, P., Singh, S., Stecula, A., Thillaisundaram, A., Tong, C., Yakneen, S., Zhong, E. D., Zielinski, M., Žídek, A., Bapst, V., Kohli, P., Jaderberg, M., Hassabis, D. & Jumper, J. M. (2024). Nature 630, 493–500.
Anghel, V. N. P., Bolmatov, D. & Katsaras, J. (2018). Phys. Rev. E 97, 062405.
Aoki, T. (2017). Membranes 7, 56.
Baus, M. & Colot, J.-L. (1986). J. Phys. C Solid State Phys. 19, L643–L648.
Bennett, V. & Baines, A. J. (2001). Physiol. Rev. 81, 1353–1392.
Büldt, G., Gally, H., Seelig, A., Seelig, J. & Zaccai, G. (1978). Nature 271, 182–184.
Chappa, V., Smirnova, Y., Komorowski, K., Müller, M. & Salditt, T. (2021). J. Appl. Cryst. 54, 557–568.
Dewhurst, C. D. (2023). J. Appl. Cryst. 56, 1595–1609.
Doster, W. & Longeville, S. (2007). Biophys. J. 93, 1360–1368.
Dupuy, A. D. & Engelman, D. M. (2008). Proc. Natl Acad. Sci. USA 105, 2848–2852.
Gommes, C. J. (2018). Microporous Mesoporous Mater. 257, 62–78.
Gommes, C. J. (2022). Gels 8, 236.
Gommes, C. J., Dubey, P. S., Stadler, A. M., Wu, B., Czakkel, O., Porcar, L., Jaksch, S., Frielinghaus, H. & Holderer, O. (2024). Phys. Rev. E 110, 034608.
Gommes, C. J., Jaksch, S. & Frielinghaus, H. (2021a). J. Appl. Cryst. 54, 1832–1843.
Gommes, C. J., Zorn, R., Jaksch, S., Frielinghaus, H. & Holderer, O. (2021b). J. Chem. Phys. 155, 024121.
Himbert, S., Alsop, R. J., Rose, M., Hertz, L., Dhaliwal, A., Moran-Mirabal, J. M., Verschoor, C. P., Bowdish, D. M., Kaestner, L., Wagner, C. & Rheinstädter, M. C. (2017). Sci. Rep. 7, 39661.
Himbert, S., D’Alessandro, A., Qadri, S. M., Majcher, M. J., Hoare, T., Sheffield, W. P., Nagao, M., Nagle, J. F. & Rheinstädter, M. C. (2022). PLoS One 17, e0269619.
Himbert, S., Qadri, S. M., Sheffield, W. P., Schubert, P., D’Alessandro, A. & Rheinstädter, M. C. (2021). PLoS One 16, e0259267.
Himbert, S. & Rheinstädter, M. C. (2022). Front. Physiol. 13, 953257.
Jeulin, D. (2000). Stat. Comput. 10, 121–132.
Kienzle, P. (2025). Neutron activation and scattering calculator, https://www.ncnr.nist.gov/resources/activation/.
Kinnun, J. J., Scott, H. L., Bolmatov, D., Collier, C. P., Charlton, T. R. & Katsaras, J. (2023). Biophys. J. 122, 931–949.
Kiselev, M. A., Lesieur, P., Kisselev, A. M., Lombardo, D. & Aksenov, V. L. (2002). Appl. Phys. A 74(Suppl. II), S1654–S1656.
Kiselev, M., Zemlyanaya, E., Ryabova, N., Hauss, T., Dante, S. & Lombardo, D. (2008). Chem. Phys. 345, 185–190.
Krueger, S., Chen, S. H., Hofrichter, J. & Nossal, R. (1990). Biophys. J. 58, 745–757.
Krueger, S. & Nossal, R. (1988). Biophys. J. 53, 97–105.
Krugmann, B., Koutsioubas, A., Haris, L., Micciulla, S., Lairez, D., Radulescu, A., Förster, S. & Stadler, A. M. (2021). Front. Chem. 9, 631277.
Krugmann, B., Radulescu, A., Appavou, M.-S., Koutsioubas, A., Stingaciu, L. R., Dulle, M., Förster, S. & Stadler, A. M. (2020). Sci. Rep. 10, 16691.
Kučerka, N., Nagle, J. F., Feller, S. E. & Balgavý, P. (2004). Phys. Rev. E 69, 051903.
Levental, I. & Lyman, E. (2023). Nat. Rev. Mol. Cell Biol. 24, 107–122.
Longeville, S. & Stingaciu, L.-R. (2017). Sci. Rep. 7, 10448.
Matsarskaia, O., Czakkel, O., Graf von Westarp, I., Pusterla, J. M. & Stadler, A. M. (2023). The role of red blood cells in long Covid: a SANS and NSE study, https://doi.ill.fr/10.5291/ILL-DATA.8-03-1061.
Mohandas, N. & Gallagher, P. G. (2008). Blood 112, 3939–3948.
Monzel, C. & Sengupta, K. (2016). J. Phys. D Appl. Phys. 49, 243002.
Nickels, J. D., Smith, J. C. & Cheng, X. (2015). Chem. Phys. Lipids 192, 87–99.
Pedersen, J. S. (1997). Adv. Colloid Interface Sci. 70, 171–210.
Poole, J. (2000). Blood Rev. 14, 31–43.
Pusterla, J. M., Schneck, E., Funari, S. S., Démé, B., Tanaka, M. & Oliveira, R. G. (2017). PLoS One 12, e0184881.
Pusterla, J. M., Schneck, E. & Oliveira, R. G. (2020). Cells 9, 670.
Schrödinger LLC (2015). The PyMOL molecular graphics system. Version 1.8. https://www.pymol.org/.
Shou, K., Sarter, M., de Souza, N. R., de Campo, L., Whitten, A. E., Kuchel, P. W., Garvey, C. J. & Stadler, A. M. (2020). R. Soc. Open Sci. 7, 201507.
Sivia, D. S. (2011). Elementary scattering theory. Oxford University Press.
Sonntag, U., Stoyan, D. & Hermann, H. (1981). Phys. Status Solidi A 68, 281–288.
Spinozzi, F., Alcaraz, J.-P., Ortore, M. G., Gayet, L., Radulescu, A., Martin, D. K. & Maccarini, M. (2022). Langmuir 38, 15026–15037.
Spinozzi, F., Barbosa, L. R. S., Corucci, G., Mariani, P. & Itri, R. (2023). J. Appl. Cryst. 56, 1348–1360.
Squires, G. L. (2012). Introduction to the theory of thermal neutron scattering, 3rd ed. Cambridge University Press.
Stadler, A., Digel, I., Artmann, G., Embs, J., Zaccai, G. & Büldt, G. (2008a). Biophys. J. 95, 5449–5461.
Stadler, A. M., Embs, J. P., Digel, I., Artmann, G. M., Unruh, T., Büldt, G. & Zaccai, G. (2008b). J. Am. Chem. Soc. 130, 16852–16853.
Stadler, A. M., Garvey, C. J., Bocahut, A., Sacquin-Mora, S., Digel, I., Schneider, G. J., Natali, F., Artmann, G. M. & Zaccai, G. (2012). J. R. Soc. Interface 9, 2845–2855.
Stadler, A. M., Garvey, C. J., Embs, J. P., Koza, M., Unruh, T., Artmann, G. & Zaccai, G. (2014). Biochim. Biophys. Acta 1840, 2989–2999.
Stadler, A. M., van Eijck, L., Demmel, F. & Artmann, G. (2011). J. R. Soc. Interface 8, 590–600.
Studart, N., Da Silveira, H. V. & De Freitas, U. (1996). Mod. Phys. Lett. B 10, 393–400.
Van Hove, L. (1954). Phys. Rev. 95, 249–262.
von Heijne, G. (2006). Nat. Rev. Mol. Cell Biol. 7, 909–918.
Watson, H. (2015). Essays Biochem. 59, 43–69.
Xia, X., Liu, S. & Zhou, Z. H. (2022). Nat. Struct. Mol. Biol. 29, 698–705.
Zhang, B.-K., Li, H.-S., Tian, W.-D., Chen, K. & Ma, Y.-Q. (2014). J. Chem. Phys. 140, 094506.
