Bending rigidities of some biological model membranes as obtained from the Fourier analysis of contour sections

Mutz, Michael; Helfrich, W.

doi:10.1051/jphys:019900051010099100

Cited by 102 publications

(63 citation statements)

References 24 publications

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“…where κ c is the bending modulus and σ is the effective lateral tension (16). Good agreement between theoretical prediction and experiment demonstrates that curvature elasticity governs the long-wavelength fluctuations of the monolayer membranes ( Fig.…”

Section: Resultsmentioning

confidence: 61%

Entropy driven self-assembly of nonamphiphilic colloidal membranes

Barry

Dogic

2010

Proc. Natl. Acad. Sci. U.S.A.

130

186

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We demonstrate that homogeneous monodisperse rods in the presence of attractive interactions assemble into equilibrium 2D fluid-like membranes composed of a one-rod length thick monolayer of aligned rods. Unique features of our system allow us to simultaneously investigate properties of these membranes at both continuum and molecular lengthscales. Analysis of thermal fluctuations at continuum lengthscales yields the membranes' lateral compressibility and bending rigidity and demonstrates that the properties of colloidal membranes are comparable to those of traditional lipid bilayers. Fluctuations at molecular lengthscales, in which single rods protrude from the membrane surface, are directly measured by comparing the positions of individual fluorescently labeled rods within a membrane to that of the membrane's continuum conformation. As two membranes approach each other in suspension, protrusion fluctuations are suppressed leading to effective repulsive interactions. Motivated by these observations, we propose an entropic mechanism that explains the stability of colloidal membranes and offers a general design principle for the self-assembly of 2D nanostructured materials from rod-like molecules.colloids | liquid crystals | nanorods | depletion interaction I n hard-body fluids, interactions between individual particles are described by a steep repulsive potential that imposes an infinite energetic penalty for any overlapping particles. It follows that any accessible state of a hard particle fluid has no internal energy and that minimizing the free energy of such a system is equivalent to maximizing its entropy. Hard particles have served as essential model systems for our understanding of the liquid and solid state, demonstrating the existence of nematic and smectic phases in hard rods (1, 2) and a 3D crystalline phase in hard spheres (3). These results exemplify the counterintuitive yet well established notion that entropy alone can drive the self-assembly of ordered structures. In this paper, we extend these ideas of entropic self-assembly to a equilibrium structure, a colloidal membrane. We demonstrate that in the presence of attractive (depletion) interactions mediated by nonadsorbing polymer, monodisperse rod-like colloids (filamentous viruses) spontaneously assemble into 2D membranes. In contrast to the previous examples of entropic self-assembly, in which the constituent molecules assemble into 3D structures, the self-assembly of homogeneous rods into colloidal membranes is self-limited to two dimensions, similar to what is observed for the assembly of amphiphilic lipids into ubiquitous biological membranes (4). However, unlike amphiphilic molecules that have a heterogeneous molecular structure, all the molecules involved in assembly of colloidal membranes are homogeneous, suggesting that geometry as well as chemical heterogeneity can be used to design pathways for self-assembly of various molecular species (5).In what follows, we utilize two unique features of our model experimental virus/polymer system t...

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Section: Resultsmentioning

confidence: 61%

Entropy driven self-assembly of nonamphiphilic colloidal membranes

Barry

Dogic

2010

Proc. Natl. Acad. Sci. U.S.A.

130

186

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“…The experimental fluctuation spectrum was obtained by Fourier transform as u k 1 a R a=2 ÿa=2 dsr s e ÿiks , where a is the arclength of the contour patch, and k n 2 a with n a nonzero integer. Taking into account the finite patch size [21] and following the spectral analysis of a closed vesicle shell developed by Pécréaux et al [22] leads to a power spectrum for the vesicle fluctuation…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 29 Februmentioning

confidence: 99%

Accurate Determination of Elastic Parameters for Multicomponent Membranes

et al. 2008

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Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line tension and the bending moduli, are crucially involved in the kinetics and the asymptotic behavior of phase separation. In this Letter we present a combined analytical and experimental approach to determine the properties of phase-separated vesicle systems. First we develop an analytical model for the vesicle shape of weakly budded biphasic vesicles. Subsequently experimental data on vesicle shape and membrane fluctuations are taken and compared to the model. The combined approach allows for a reproducible and reliable determination of the physical parameters of complex vesicle systems. The parameters obtained set limits for the size and stability of nanodomains in the plasma membrane of living cells.

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“…We can safely ignore the thermodynamic fluctuation of the curved bilayer at the room temperature because of k c ≈ 10 −19 J ≫ k B T [4,5], where k B is the Boltzmann factor and T the room temperature. Based on Helfrich's curvature energy, the free energy of the closed bilayer under the osmotic pressure p (the outer pressure minus the inner one) is written as…”

Section: Introductionmentioning

confidence: 99%

A geometric theory on the elasticity of bio-membranes

Tu¹,

Ouyang²

2004

J. Phys. A: Math. Gen.

113

196

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Abstract. The purpose of this paper is to study the shapes and stabilities of biomembranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of biomembranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on the surfaces embedded in three-dimensional Euclidean space by using exterior differential forms.

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Bending rigidities of some biological model membranes as obtained from the Fourier analysis of contour sections

Cited by 102 publications

References 24 publications

Entropy driven self-assembly of nonamphiphilic colloidal membranes

Entropy driven self-assembly of nonamphiphilic colloidal membranes

Accurate Determination of Elastic Parameters for Multicomponent Membranes

A geometric theory on the elasticity of bio-membranes

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