Corrections to the Electrical Capacitance of Deformed Lipid Membrane

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The thickness of the lipid membrane is its substantial characteristics. Usually, the thickness of a lipid bilayer is experimentally determined by measuring its electrical capacitance in the approximation of a plane-parallel capacitor. However, membranes formed from a mixture of lipids or containing membrane-deforming inclusions are laterally inhomogeneous, and for them the plane-parallel capacitor approximation generally does not hold. In this work, corrections to the electrical capacitance resulting from deformation of the lipid membrane were numerically calculated. It is shown that the model of a planar capacitor (or their parallel connections), in the general case, does not quantitatively describe these corrections due to the non-zero tangential component of the electric field strength. It is shown that the relative deviation of corrections to the electrical capacitance calculated in various simplified models from the exact solution can reach 50%.

Full Text

Restricted Access

About the authors

O. V. Kondrashov

Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences

Author for correspondence.
Email: akimov_sergey@mail.ru
Russian Federation, Moscow, 119071

S. A. Akimov

Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences

Email: akimov_sergey@mail.ru
Russian Federation, Moscow, 119071

References

  1. Evans E., Heinrich V., Ludwig F., Rawicz W. 2003. Dynamic tension spectroscopy and strength of biomembranes. Biophys. J. 85, 2342–2350.
  2. Evans E., Smith B.A. 2011. Kinetics of hole nucleation in biomembrane rupture. New J. Phys. 13, 095010.
  3. Rawicz W., Olbrich K.C., McIntosh T., Needham D., Evans E. 2000. Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys. J. 79, 328–339.
  4. Akimov S.A., Molotkovsky R.J., Kuzmin P.I., Galimzyanov T.R., Batishchev O.V. 2020. Continuum models of membrane fusion: Evolution of the theory. Int. J. Mol. Sci. 21, 3875.
  5. Карпунин Д.В., Акимов С.А., Фролов В.А. 2005. Формирование пор в плоских липидных мембранах, содержащих лизолипиды и холестерин. Биол. мембраны 22, 429–432.
  6. Golani G., Leikina E., Melikov K., Whitlock J.M., Gamage D.G., Luoma-Overstreet G., Millay D.P., Kozlov M.M., Chernomordik L.V. 2021. Myomerger promotes fusion pore by elastic coupling between proximal membrane leaflets and hemifusion diaphragm. Nature Comm. 12, 495.
  7. Кондрашов О.В., Акимов С.А. 2022. Латеральное взаимодействие цилиндрических трансмембранных пептидов в одномерном приближении. Биол. мембраны 39, 186–194.
  8. Kondrashov O.V., Galimzyanov T.R., Pavlov K.V., Kotova E.A., Antonenko Y.N., Akimov S.A. 2018. Membrane elastic deformations modulate gramicidin A transbilayer dimerization and lateral clustering. Biophys. J. 115, 478–493.
  9. Lundbæk J.A., Andersen O.S. 1999. Spring constants for channel-induced lipid bilayer deformations estimates using gramicidin channels. Biophys. J. 76, 889–895.
  10. Pan J., Tieleman D.P., Nagle J.F., Kučerka N., Tristram-Nagle S. 2009. Alamethicin in lipid bilayers: Combined use of X-ray scattering and MD simulations. Biochim. Biophys. Acta. 1788, 1387–1397.
  11. Сухарев С., Анишкин А. 2023. Механочувствительные каналы: история, многообразие, механизмы. Биол. мембраны 40 (1), 19–42.
  12. Heftberger P., Kollmitzer B., Rieder A.A., Amenitsch H., Pabst G. 2015. In situ determination of structure and fluctuations of coexisting fluid membrane domains. Biophys. J. 108, 854–862.
  13. Pfeffermann J., Eicher B., Boytsov D., Hannesschlaeger C., Galimzyanov T.R., Glasnov T.N., Pabst G., Akimov S.A., Pohl P. 2021. Photoswitching of model ion channels in lipid bilayers. J. Photochem. Photobiol. B224, 112320.
  14. Peng C., Song S., Fort T. 2006. Study of hydration layers near a hydrophilic surface in water through AFM imaging. Surface and Interface Analysis 38, 975–980.
  15. Higgins M.J., Polcik M., Fukuma T., Sader J.E., Nakayama Y., Jarvis S.P. 2006. Structured water layers adjacent to biological membranes. Biophys. J. 91, 2532–2542.
  16. Montal M., Mueller P. 1972. Formation of bimolecular membranes from lipid monolayers and a study of their electrical properties. Proc. Natl. Acad. Sci. USA. 69, 3561–3566.
  17. Benz R., Fröhlich O., Läuger P., Montal M. 1975. Electrical capacity of black lipid films and of lipid bilayers made from monolayers. Biochim. Biophys. Acta. 394, 323–334.
  18. Saitov A., Akimov S.A., Galimzyanov T.R., Glasnov T., Pohl P. 2020. Ordered lipid domains assemble via concerted recruitment of constituents from both membrane leaflets. Phys. Rev. Lett. 124, 108102.
  19. Сойбельман Я.С. 1984. Асимптотика емкости конденсатора с пластинами произвольной формы. Сибирск. математ. журн. 25, 167–181.
  20. Семахин А.Н., Шнеерсон Г.А. 1990. К расчету главной части поправки к конденсаторной емкости между двумя проводниками, разделенными малым зазором. Журн. технич. физики 60, 5–12.
  21. Cherepanov D.A., Feniouk B.A., Junge W., Mulkidjanian A.Y. 2003. Low dielectric permittivity of water at the membrane interface: Effect on the energy coupling mechanism in biological membranes. Biophys. J. 85, 1307–1316.
  22. Merla C., Liberti M., Apollonio F., d’Inzeo G. 2009. Quantitative assessment of dielectric parameters for membrane lipid bi‐layers from RF permittivity measurements. Bioelectromagnetics 30, 286–298.
  23. Beaven A.H., Maer A.M., Sodt A.J., Rui H., Pastor R.W., Andersen O.S., Im W. 2017. Gramicidin A channel formation induces local lipid redistribution I: Experiment and simulation. Biophys. J. 112, 1185–1197.
  24. García-Sáez A.J., Chiantia S., Schwille P. 2007. Effect of line tension on the lateral organization of lipid membranes. J. Biol. Chem. 282, 33537–33544.
  25. Sodt A.J., Venable R.M., Lyman E., Pastor R.W. 2016. Nonadditive compositional curvature energetics of lipid bilayers. Phys. Rev. Lett. 117, 138104.
  26. Leikin S., Kozlov M.M., Fuller N.L., Rand R.P. 1996. Measured effects of diacylglycerol on structural and elastic properties of phospholipid membranes. Biophys. J. 71, 2623–2632.
  27. Reddy A.S., Warshaviak D.T., Chachisvilis M. 2012. Effect of membrane tension on the physical properties of DOPC lipid bilayer membrane. Biochim. Biophys. Acta. 1818, 2271–2281.
  28. Rinia H.A., Snel M.M., van der Eerden J.P., de Kruijff B. 2001. Visualizing detergent resistant domains in model membranes with atomic force microscopy. FEBS Lett. 501, 92–96.
  29. Saslowsky D.E., Lawrence J., Ren X., Brown D.A., Henderson R.M., Edwardson J.M. 2002. Placental alkaline phosphatase is efficiently targeted to rafts in supported lipid bilayers. J. Biol. Chem. 277, 26966–26970.
  30. Kim T., Lee K.I., Morris P., Pastor R.W., Andersen O.S., Im W. 2012. Influence of hydrophobic mismatch on structures and dynamics of gramicidin A and lipid bilayers. Biophys. J. 102, 1551–1560.
  31. Huang H.W. 1986. Deformation free energy of bilayer membrane and its effect on gramicidin channel lifetime. Biophys. J. 50, 1061–1070.
  32. Лаврентьев М.А., Шабат Б.В. 1987. Методы теории функции комплексной переменной. М.: Наука.
  33. Кондрашов О.В., Акимов С.А. 2022. Латеральное взаимодействие цилиндрических трансмембранных пептидов в одномерном приближении. Биол. мембраны 39, 186–194.
  34. Кондрашов О.В., Акимов С.А. 2022. Возможность формирования пор в липидных мембранах несколькими молекулами амфипатических пептидов. Биол. мембраны 39, 384–397.
  35. Pinigin K.V., Kondrashov O.V., Jiménez-Munguía I., Alexandrova V.V., Batishchev O.V., Galimzyanov T.R., Akimov S.A. 202. Elastic deformations mediate interaction of the raft boundary with membrane inclusions leading to their effective lateral sorting. Sci. Rep. 10, 4087.
  36. Bohinc K., Kralj-Iglič V., May S. 2003. Interaction between two cylindrical inclusions in a symmetric lipid bilayer. J. Chem. Phys. 119, 7435–7444.
  37. Zemel A., Ben-Shaul A., May S. 2005. Perturbation of a lipid membrane by amphipathic peptides and its role in pore formation. Eur. Biophys. J. 34, 230–242.
  38. Nielsen C., Goulian M., Andersen O.S. 1998. Energetics of inclusion-induced bilayer deformations. Biophys. J. 74, 1966–1983.

Supplementary files

Supplementary Files
Action
1. JATS XML
2. Fig. 1. Dependence of the normalized electric potential u/u0 on the spatial coordinates r, z in the cylindrical coordinate system at Δh = 0.5 nm, σ = 1 nm. The black contour bordering the white fields at the top and bottom of the figure corresponds to the shape of the surfaces of the upper and lower monolayers of the membrane determined by relations (3).

Download (206KB)
3. Fig. 2. Dependence on Δh, σ of the corrections to the electrical capacitance arising due to membrane deformations described by equation (3): a - exact solution ∆C; b - approximate solution ∆C1 (average thickness approximation (6)); c - approximate solution ∆C2 (average inverse thickness approximation (7)).

Download (445KB)
4. Fig. 3. Relative error of approximations: a - averaged thickness approximation (6); b - averaged inverse thickness approximation (7). The white straight line Δh = 0 denotes the discontinuity of the first kind resulting from the fact that in the undeformed membrane (Δh = 0) the capacitance correction is zero (ΔC = 0).

Download (268KB)

Copyright (c) 2024 The Russian Academy of Sciences

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies