Abstract
Biological cells are almost never truly spherical, even in the absence of an obvious cause that disrupts the cell’s symmetry. Using rather simple energy considerations, we show that even though all real biological cells are subject to a completely radial electric field along the cell membrane, the spherical shape is unstable under most practical situations. This simple result appears to have been overlooked in the literature.
Issue Section:
Research Papers
Keywords:
constitutive modeling of materials
References
1.
Alberts
, B.
, Johnson
, A.
, Lewis
, J.
, Raff
, M.
, Roberts
, K.
, and Walter
, P.
, 2002
, Molecular Biology of the Cell
, Garland
, New York
.2.
McCormick
, D. A.
, 2014
, “Membrane Potential and Action Potential,” From Molecules to Networks
, 3rd ed., Academic Press
, Boston, MA
, pp. 351
–376
.3.
Rivlin
, R.
, 1948
, “Large Elastic Deformations of Isotropic Materials. II. Some Uniqueness Theorems for Pure, Homogeneous Deformation
,” Philos. Trans. R. Soc. Lond. A
, 240
(822
), pp. 491
–508
. 4.
Liu
, L.
, and Sharma
, P.
, 2013
, “Flexoelectricity and Thermal Fluctuations of Lipid Bilayer Membranes: Renormalization of Flexoelectric, Dielectric, and Elastic Properties
,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
, 87
(3
), p. 032715
. 5.
Torbati
, M.
, Mozaffari
, K.
, Liu
, L.
, and Sharma
, P.
, 2022
, “Coupling of Mechanical Deformation and Electromagnetic Fields in Biological Cells
,” Rev. Mod. Phys.
, 94
(2
), p. 025003
. 6.
Helfrich
, W.
, 1973
, “Lipid Bilayer Spheres: Deformation and Birefringence in Magnetic Fields
,” Phys. Lett. A
, 43
(5
), pp. 409
–410
. 7.
Helfrich
, W.
, 1973
, “Elastic Properties of Lipid Bilayers: Theory and Possible Experiments
,” Z. für Naturforschung C
, 28
(11–12
), pp. 693
–703
. 8.
Krichen
, S.
, and Alameh
, Z.
, 2023
, “Magnetic and Ionic Liquid Inclusions in Soft Materials and Engineering Enhanced Electro-magneto-mechanical Response
,” Int. J. Solids Struct.
, 262
, p. 112081
. 9.
Winterhalter
, M.
, and Helfrich
, W.
, 1988
, “Deformation of Spherical Vesicles by Electric Fields
,” J. Colloid Interface Sci.
, 122
(2
), pp. 583
–586
. 10.
Schwalbe
, J. T.
, Vlahovska
, P. M.
, and Miksis
, M. J.
, 2011
, “Vesicle Electrohydrodynamics
,” Phys. Rev. E
, 83
(4
), p. 046309
. 11.
Peterlin
, P.
, Svetina
, S.
, and Žekš
, B.
, 2007
, “The Prolate-to-Oblate Shape Transition of Phospholipid Vesicles in Response to Frequency Variation of an AC Electric Field Can be Explained by the Dielectric Anisotropy of a Phospholipid Bilayer
,” J. Phys.: Condens. Matter
, 19
(13
), p. 136220
. 12.
Mitov
, M.
, Méléard
, P.
, Winterhalter
, M.
, Angelova
, M.
, and Bothorel
, P.
, 1993
, “Electric-Field-Dependent Thermal Fluctuations of Giant Vesicles
,” Phys. Rev. E
, 48
(1
), p. 628
. 13.
Hyuga
, H.
, Kinosita Jr
, K.
, and Wakabayashi
, N.
, 1991
, “Deformation of Vesicles Under the Influence of Strong Electric Fields
,” Jpn. J. Appl. Phys.
, 30
(5R
), p. 1141
. 14.
Krichen
, S.
, Liu
, L.
, and Sharma
, P.
, 2019
, “Liquid Inclusions in Soft Materials: Capillary Effect, Mechanical Stiffening and Enhanced Electromechanical Response
,” J. Mech. Phys. Solids
, 127
, pp. 332
–357
. 15.
Rivlin
, R. S.
, 1974
, “Stability of Pure Homogeneous Deformations of an Elastic Cube Under Dead Loading
,” Quart. Appl. Math.
, 32
(3
), pp. 265
–271
. 16.
Linke
, G. T.
, Lipowsky
, R.
, and Gruhn
, T.
, 2005
, “Free Fluid Vesicles Are Not Exactly Spherical
,” Phys. Rev. E
, 71
(5
), p. 051602
. 17.
Liu
, L.
, 2014
, “An Energy Formulation of Continuum Magneto-electro-elasticity With Applications
,” J. Mech. Phys. Solids
, 63
, pp. 451
–480
. 18.
Liu
, L.
, 2013
, “On Energy Formulations of Electrostatics for Continuum Media
,” J. Mech. Phys. Solids
, 61
(4
), pp. 968
–990
. 19.
Picas
, L.
, Rico
, F.
, and Scheuring
, S.
, 2012
, “Direct Measurement of the Mechanical Properties of Lipid Phases in Supported Bilayers
,” Biophys. J.
, 102
(1
), pp. L01
–L03
. 20.
Nielsen
, C.
, Goulian
, M.
, and Andersen
, O. S.
, 1998
, “Energetics of Inclusion-Induced Bilayer Deformations
,” Biophys. J.
, 74
(4
), pp. 1966
–1983
. 21.
Gramse
, G.
, Dols-Perez
, A.
, Edwards
, M.
, Fumagalli
, L.
, and Gomila
, G.
, 2013
, “Nanoscale Measurement of the Dielectric Constant of Supported Lipid Bilayers in Aqueous Solutions With Electrostatic Force Microscopy
,” Biophys. J.
, 104
(6
), pp. 1257
–1262
. 22.
Alberts
, B.
, Johnson
, A.
, Lewis
, J.
, Raff
, M.
, Roberts
, K.
, and Walter
, P.
, 2014
, “Membrane Structure,” Molecular Biology of the Cell
, 5th ed., Garland Science, Taylor & Francis Group LLC
, New York
, pp. 617
–650
.23.
Alberts
, B.
, Johnson
, A.
, Lewis
, J.
, Raff
, M.
, Roberts
, K.
, and Walter
, P.
, 2014
, “Visualizing Cells,” Molecular Biology of the Cell
, 5th ed., Garland Science, Taylor & Francis Group LLC
, New York
, pp. 617
–650
.24.
Yang
, S.
, and Sharma
, P.
, 2023
, “A Tutorial on the Stability and Bifurcation Analysis of the Electromechanical Behaviour of Soft Materials
,” ASME Appl. Mech. Rev.
, 75
(4
), p. 044801
. 25.
Krichen
, S.
, Liu
, L.
, and Sharma
, P.
, 2017
, “Biological Cell as a Soft Magnetoelectric Material: Elucidating the Physical Mechanisms Underpinning the Detection of Magnetic Fields by Animals
,” Phys. Rev. E
, 96
(4
), p. 042404
. 26.
Wang
, B.
, Yang
, S.
, and Sharma
, P.
, 2019
, “Flexoelectricity as a Universal Mechanism for Energy Harvesting From Crumpling of Thin Sheets
,” Phys. Rev. B
, 100
(3
), p. 035438
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