Electrostatic Pressure and Line Tension in a Langmuir Monolayer

Rivière, S.; Hénon, Sylvie; Meunier, Jacques; Albrecht, Geneviève; Boissonnade, Marie-Martine; Baszkin, Adam

doi:10.1103/physrevlett.75.2506

Cited by 47 publications

(46 citation statements)

References 20 publications

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“…In [21] the coefficient f 1 (0) for a dipole domain with no polarization ε I = 1 was quoted, and the result is in agreement with Eq. A7.…”

Section: Discussionsupporting

confidence: 76%

Effect of dipolar moments in domain sizes of lipid bilayers and monolayers

Travesset

2006

The Journal of Chemical Physics

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Lipid domains are found in systems such as multicomponent bilayer membranes and single component monolayers at the air-water interface. It was shown by Keller et al. [J. Phys. Chem. 91, 6417 (1987)] that in monolayers, the size of the domains results from balancing the line tension, which favors the formation of a large single circular domain, against the electrostatic cost of assembling the dipolar moments of the lipids. In this paper, we present an exact analytical expression for the electric potential, ion distribution, and electrostatic free energy for different problems consisting of three different slabs with different dielectric constants and Debye lengths, with a circular homogeneous dipolar density in the middle slab. From these solutions, we extend the calculation of domain sizes for monolayers to include the effects of finite ionic strength, dielectric discontinuities (or image charges), and the polarizability of the dipoles and further generalize the calculations to account for domains in lipid bilayers. In monolayers, the size of the domains is dependent on the different dielectric constants but independent of ionic strength. In asymmetric bilayers, where the inner and outer leaflets have different dipolar densities, domains show a strong size dependence with ionic strength, with molecular-sized domains that grow to macroscopic phase separation with increasing ionic strength. We discuss the implications of the results for experiments and briefly consider their relation to other two dimensional systems such as Wigner crystals or heteroepitaxial growth.

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“…In [21] the coefficient f 1 (0) for a dipole domain with no polarization ε I = 1 was quoted, and the result is in agreement with Eq. A7.…”

Section: Discussionsupporting

confidence: 76%

Effect of dipolar moments in domain sizes of lipid bilayers and monolayers

Travesset

2006

The Journal of Chemical Physics

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“…Since the monolayer is not in a dense phase, the usual 3D viscosity η 3D of the water subphase dominates the 2D one [32,33,34], . We obtain straight lines, which proves that, at these length scales, the line tension is constant despite long-range dipolar interactions [12,13,24,30].…”

mentioning

confidence: 74%

Two-dimensional shear modulus of a Langmuir foam

et al. 2003

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Abstract. -We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 ± 0.4 pJ·m −1 ) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, µ = 38±3 nN·m −1 . The foam effective rigidity is predicted to be 35 ± 3 nN · m −1 , which agrees with the value 37.obtained in an independent mechanical measurement.Introduction. -A liquid foam, made of polyhedral gas bubbles separated by thin liquid walls forming a connected network [1], is a mixture of two fluids. It has nevertheless a solidlike elasticity, characterised by a shear modulus µ, proportional to the surface tension of the walls [2,3]. In fact, shearing a foam modifies the total length of the walls, thus the foam energy. The value of µ can be determined in numerical simulations [4,5,6]; however, it is still an open problem to predict analytically its value for a real foam, which has a finite fluid fraction and an inherent disorder due to its distribution of bubble sizes.Here, we compare two experimental measurements of µ. First, by global mechanical measurements on the scale of the whole foam, described in terms of elasticity of continuous media. Second, and simultaneously, by detailed imaging of the diphasic foam structure, on the local level of a few bubbles: this suggests to use two-dimensional (2D) foams. In the literature, 2D soap froths have been sheared in Couette geometry, either as bubble rafts [7,8,9] or confined in Hele-Shaw cells between two parallel plates of glass [10].We investigate the elasticity of a real 2D system: a "Langmuir foam" [11]. A monomolecular layer of amphiphilic molecules deposited at the surface of water ("Langmuir monolayer") exhibits a first order transition between a 2D gas phase and a denser 2D liquid (also called

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“…Changes in curvature and composition at the bud rim are most likely coupled to each other, because different lipid species involve different spontaneous curvatures. If this were the boundary between ordinary phase-separated (planar) domains of different compositions, then g would be on the order of 1 k B T per molecular diameter (see e.g., Riviere et al, 1995). Most recently, the coupling between curvature and composition has been clearly demonstrated in mixed lipid vesicles, revealing line energies on the order of 1 k B T per nm (Baumgart et al, 2003).…”

Section: Free Energymentioning

confidence: 99%

A Statistical-Thermodynamic Model of Viral Budding

Tzlil

Deserno

Gelbart

et al. 2004

Biophysical Journal

109

111

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We present a simple statistical thermodynamic model for budding of viral nucleocapsids at the cell membrane. The membrane is modeled as a flexible lipid bilayer embedding linker (spike) proteins, which serve to anchor and thus wrap the membrane around the viral capsids. The free energy of a single bud is expressed as a sum of the bending energy of its membrane coat, the spike-mediated capsid-membrane adhesion energy, and the line energy associated with the bud's rim, all depending on the extent of wrapping (i.e., bud size), and density of spikes in the curved membrane. This self-energy is incorporated into a simple free energy functional for the many-bud system, allowing for different spike densities, and hence entropy, in the curved (budding) and planar membrane regions, as well as for the configurational entropy of the polydisperse bud population. The equilibrium spike densities in the coexisting, curved and planar, membrane regions are calculated as a function of the membrane bending energy and the spike-mediated adhesion energy, for different spike and nucleocapsid concentrations in the membrane plane, as well as for several values of the bud's rim energy. We show that complete budding (full wrapping of nucleocapsids) can only take place if the adhesion energy exceeds a certain, critical, bending free energy. Whenever budding takes place, the spike density in the mature virions is saturated, i.e., all spike adhesion sites are occupied. The rim energy plays an important role in determining the size distribution of buds. The fraction of fully wrapped buds increases as this energy increases, resulting eventually in an all-or-nothing mechanism, whereby nucleocapsids at the plasma membrane are either fully enveloped or completely naked (just touching the membrane). We also find that at low concentrations all capsids arriving at the membrane get tightly and fully enveloped. Beyond a certain concentration, corresponding approximately to a stoichiometric spike/capsid ratio, newly arriving capsids cannot be fully wrapped; i.e., the budding yield decreases.

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Electrostatic Pressure and Line Tension in a Langmuir Monolayer

Cited by 47 publications

References 20 publications

Effect of dipolar moments in domain sizes of lipid bilayers and monolayers

Effect of dipolar moments in domain sizes of lipid bilayers and monolayers

Two-dimensional shear modulus of a Langmuir foam

A Statistical-Thermodynamic Model of Viral Budding

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