Lipid membranes are versatile biological structures that undergo significant structural remodelling, often triggered by instabilities. Since they invariably possess heterogeneous properties, owing to the presence of multiple lipid species and their interactions with proteins, heterogeneity can have a significant impact on their equilibrium state and stability. In this work, we use curvature elasticity to derive the generalized stability criterion for heterogeneous lipid membranes. Our formulation entertains strain energies that go beyond the Helfrich energy and exhibit higher-order dependence on curvature invariants or spatially varying properties.
BoalD.Mechanics of the cell. Cambridge: Cambridge University Press, 2012.
2.
PhillipsRKondevJTheriotJ. Physical biology of the cell. New York: Garland Science, 2012.
3.
KasJSackmannE.Shape transitions and shape stability of giant phospholipid vesicles in pure water induced by area-to-volume changes. Biophys J1991; 60(4): 825–844.
4.
EvansEASkalakRWeinbaumS.Mechanics and thermodynamics of biomembranes. Boca Raton: CRC Press, 1980.
5.
KummrowMHelfrichW.Deformation of giant lipid vesicles by electric fields. Phys Rev A1991; 44(12): 8356.
6.
CanhamPB.The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J Theor Biol1970; 26(1): 61–81.
7.
HelfrichW.Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch C1973; 28: 693–703.
8.
JenkinsJT.The equations of mechanical equilibrium of a model membrane. SIAM J Appl Math1977; 32(4): 755–764.
9.
LipowskyR.The conformation of membranes. Nature1991; 349(6309): 475–481.
10.
SeifertU.Configurations of fluid membranes and vesicles. Adv Phys1997; 46(1): 13–137.
11.
SteigmannDJ.Fluid films with curvature elasticity. Arch Rational Mech Anal1999; 150: 127–152.
12.
DesernoM.Fluid lipid membranes: from differential geometry to curvature stresses. Chem Phys Lipids2015; 185: 11–45.
13.
Zhong-CanOYHelfrichW.Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys Rev A1989; 39(10): 5280.
14.
CapovillaRGuvenJSantiagoJA.Deformations of the geometry of lipid vesicles. J Phys A – Math Gen2003; 36(23): 6281.
15.
CapovillaRGuvenJ.Second variation of the Helfrich–Canham Hamiltonian and reparametrization invariance. J Phys A – Math Gen2004; 37(23): 5983.
16.
YinY.Integral theorems based on a new gradient operator derived from biomembranes (Part I): fundamentals. Tsinghua Science and Technology2005; 10(3): 372–375.
17.
YinY.Integral theorems based on a new gradient operator derived from biomembranes (Part II): applications. Tsinghua Science and Technology2005; 10(3): 376–380.
18.
NelsonPPowersTSeifertU.Dynamical theory of the pearling instability in cylindrical vesicles. Phys Rev Lett1995; 74(17): 3384.
19.
PowersTRGoldsteinRE.Pearling and pinching: propagation of Rayleigh instabilities. Phys Rev Lett1997; 78(13): 2555.
20.
MalekiMFriedE.Stability of discoidal high-density lipoprotein particles. Soft Matter2013; 9(42): 9991–9998.
21.
LiJZhangHQiuF. Emergence and stability of intermediate open vesicles in disk-to-vesicle transitions. Phys Rev E2013; 88(1): 012719.
22.
AgrawalASteigmannDJ.Modeling protein-mediated morphology in biomembranes. Biomech Model Mechanobiol2009; 8(5): 371–379.
WalaniNTorresJAgrawalA.Endocytic proteins drive vesicle growth via instability in high membrane tension environment. Proc Natl Acad Sci USA2015; 112(12): E1423–E1432.
25.
TianACapraroBREspositoC. Bending stiffness depends on curvature of ternary lipid mixture tubular membranes. Biophys J2009; 97(6): 1636–1646.
26.
BaumgartTCapraroBRZhuC. Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids. Ann Rev Phys Chem2011; 62: 483.
27.
AgrawalASteigmannDJ.Coexistent fluid-phase equilibria in biomembranes with bending elasticity. J Elasticity2008; 93(1): 63–80.
28.
SteigmannDJOgdenRW.Elastic surface–substrate interactions. P Roy Soc Lond A Mat1999; 455: 437–474.
