title: Membrane stress tensor in the presence of lipid density and composition inhomogeneities.
abstract: We derive the expression of the stress tensor for one- and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.
authors: Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, Paris Cedex, France.
authors: A-F
authors: AF
authors: Bitbol
authors: L
authors: L
authors: Peliti
authors: J-B
authors: JB
authors: Fournier
references: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1995 Oct;52(4):4251-4266
references: 9963896
references: Biophys J. 2008 Nov 15;95(10):4924-33
references: 18689447
references: Nature. 2003 Oct 23;425(6960):821-4
references: 14574408
references: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Jun;49(6):5389-5407
references: 9961866
references: Biophys J. 1980 May;30(2):265-84
references: 7260275
references: J Chem Phys. 2006 Dec 21;125(23):234905
references: 17190575
references: Phys Rev Lett. 2002 Jun 10;88(23):238101
references: 12059401
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011921
references: 17677508
references: Eur Phys J E Soft Matter. 2010 Mar;31(3):333-42
references: 20306278
references: Eur Phys J E Soft Matter. 2002 Oct;9(2):143-60
references: 15015113
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 1):061407
references: 16485947
references: Proc Natl Acad Sci U S A. 2002 Dec 24;99(26):16766-9
references: 12471152
references: Eur Phys J E Soft Matter. 2009 Jun;29(2):183-9
references: 19521726
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Aug;66(2 Pt 1):021607
references: 12241189
references: Phys Rev Lett. 2008 Feb 22;100(7):078103
references: 18352601
references: Proc Natl Acad Sci U S A. 2009 May 5;106(18):7294-8
references: 19383800
references: Phys Rev Lett. 2009 Jan 9;102(1):018102
references: 19257244
references: J Math Biol. 1977 May 23;4(2):149-69
references: 886227
references: Z Naturforsch C. 1973 Nov-Dec;28(11):693-703
references: 4273690
references: Eur Phys J E Soft Matter. 2005 Apr;16(4):439-61
references: 19177658
references: Eur Biophys J. 1989;17(2):101-11
references: 2766997
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011605
references: 17677462
references: Biophys J. 1974 Dec;14(12):923-31
references: 4429770
references: Phys Rev Lett. 1990 Apr 23;64(17):2094-2097
references: 10041575
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 1):041604
references: 12443213
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5 Pt 1):050903
references: 20866178
references: Phys Rev Lett. 2001 May 21;86(21):4970-3
references: 11384394
references: Biophys J. 2010 Aug 4;99(3):808-16
references: 20682258