Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles

Engelhardt, H.; Duwe, H. P.; Sackmann, E.

doi:10.1051/jphyslet:01985004608039500

Cited by 155 publications

(97 citation statements)

References 10 publications

(21 reference statements)

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“…The bending modulus calculated ((0.21±0.08) × 10 −19 J) from force plots is in the same magnitude range (10 −20 to 10 −19 J) of literature reported value for the same EggPC lipid [9][10][11][12][47][48][49][50] (see Table 2) regardless of different geometry and size of the samples. Variations in bending modulus measured have been reported and the reason for the discrepancy still needs further analysis [49][50][51].…”

Section: Data Analysis According To Hertz Modelsupporting

confidence: 78%

“…Several possibilities are proposed to explain the variations of bending modulus observed: (1) different experimental method: Niggemann et al [51] found that the values of the rigidity for the same lipid differed significantly between methods. Our data was derived from Young's modulus based on AFM force curves and others use phase contrast microscopy [9][10][11]47,48], magnetic-field [12], and electric field method [49,50]; (2) bending modulus (Eq. (2)) is based on three-dimensional, isotropic planar surface assumptions, while the vesicles on substrate is not prefect isotropic planar surface; (3) our data is based on the result on the adsorbed small size vesicles while other methods deal with giant liposomes (>10 m) vesicles.…”

Section: Data Analysis According To Hertz Modelmentioning

confidence: 99%

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Probing small unilamellar EggPC vesicles on mica surface by atomic force microscopy

Liang

Mao

2004

Colloids and Surfaces B: Biointerfaces

123

168

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Section: Data Analysis According To Hertz Modelsupporting

confidence: 78%

Section: Data Analysis According To Hertz Modelmentioning

confidence: 99%

Probing small unilamellar EggPC vesicles on mica surface by atomic force microscopy

Liang

Mao

2004

Colloids and Surfaces B: Biointerfaces

123

168

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“…The bending rigidity of amphiphilic bilayers has been measured in many experiments: while phospholipid membranes [4,8,[20][21][22] are characterized by a bending rigidity of the order of tens of k B T , lamellar and fluid microemulsion phases composed of single chain surfactants, short chain alcohols, oil and water [23][24][25][26] exhibit a bending rigidity of the order of k B T . The bilayer studied in our Molecular Dynamics simulations are composed of single-chain amphiphiles and have bending rigidities which are of the same order of magnitude as those studied in the second group of experiments.…”

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confidence: 99%

Shape fluctuations and elastic properties of two-component bilayer membranes

2005

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Abstract. -The elastic properties of two-component bilayer membranes are studied using a coarse grain model for amphiphilic molecules. The two species of amphiphiles considered here differ only in their length. Molecular Dynamics simulations are performed in order to analyze the shape fluctuations of the two-component bilayer membranes and to determine their bending rigidity. Both the bending rigidity and its inverse are found to be nonmonotonic functions of the mole fraction xB of the shorter B-amphiphiles and, thus, do not satisfy a simple lever rule. The intrinsic area of the bilayer also exhibits a nonmonotonic dependence on xB and a maximum close to xB ≃ 1/2.Biological membranes are multicomponent systems consisting of mixtures of many different lipids and proteins. Because the composition of lipid bilayers affects their physical properties and biological functions, this composition varies from one organism to the other and between organelles in the same cell [1]. Biological membranes contain a fluid bilayer which is highly flexible and, thus, can easily change its shape. Typical examples are provided by the plasma membranes of red and white blood cells which are so flexible that they can move through rather small capillaries. This flexibility is also responsible for the thermally excited shape fluctuations of biomembranes in physiological conditions, the amplitude of which depends on temperature, membrane composition and mechanical constraints. One important example is provided by mixed membranes containing phospholipids and cholesterol which exhibit a strong increase in rigidity with increasing amount of cholesterol [2][3][4]. In erythrocytes, on the other hand, the amplitude of the shape fluctuations is influenced by the spectrin-ankyrin network which is coupled to the interior of the plasma membrane [5,6]. The study of these fluctuations can thus provide information on the elastic properties of the bilayer membrane and on how these properties depend on membrane composition. One important elastic parameter is the bending rigidity [7], which describes the resistance of the membrane to bending, and which can be obtained from the spectrum of the shape fluctuations [8].

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“…We also predict an observable tension jump for membranes decorated with polymer "brushes". [6,7,8]. Here, σ is an effective surface tension, i.e., an adjustable thermodynamic parameter arising from the constraint of constant surface area, which is usually several orders of magnitude smaller than the surface tensions of ordinary liquid interfaces [9,10].…”

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confidence: 99%

Fluctuation Spectrum of Fluid Membranes Coupled to an Elastic Meshwork: Jump of the Effective Surface Tension at the Mesh Size

2004

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We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function F el [A ξ ] not of the real microscopic membrane area A, but of a smoothed membrane's area A ξ , which corresponds to the area of the membrane coarse-grained at the mesh size ξ. We show that the meshwork modifies the membrane tension σ both below and above the scale ξ, inducing a tension-jump ∆σ = dF el /dA ξ . The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes". [6,7,8]. Here, σ is an effective surface tension, i.e., an adjustable thermodynamic parameter arising from the constraint of constant surface area, which is usually several orders of magnitude smaller than the surface tensions of ordinary liquid interfaces [9,10]. Additional complexity arises if the membrane interacts with other systems (e.g., a rigid substrate, another membrane, a network of polymers or filaments) [11,12,13], or contains inclusions (passive or active) [14,15].In this paper, we identify a class of composite membranes, i.e., of membranes coupled to an external system (like the cytoskeleton of red blood cells [16]), for which the coupling energy can be described, in a first approximation, by a function of the membrane area coarsegrained at a characteristic length scale ξ (the mesh size in the cytoskeleton case). For such systems, we show that the effective membrane tension should exhibit a jump of amplitude ∆σ at the scale ξ. In other words, the fluctuation spectrum is proportional to (κq 4 + σ < q 2 ] −1 for q < ∼ ξ −1 , and to (κq 4 + σ > q 2 ) −1 for q > ∼ ξ −1 . As we shall see, ∆σ = σ < − σ > is directly related to the coupling between the membrane and the external system. Understanding the scale dependence of the effective surface tension, and in particular its value at short length-scales, is important in a number of phenomena, e.g., membrane adhesion [17,18], cell fusion [19,20] and other microscopic biological mechanisms, such as endocytosis [21]. It should also help interpret experiments on composite membranes [22,23,24], which attempt to determine the value of κ by fitting the fluctuation spectrum.We shall consider two different systems for which our model predicts a jump in surface tension: (i) membranes decorated with polymer "brushes" [25], and (ii) red blood cell membranes interacting with their attached cytoskeleton [16]. Polymer decorated membranes are useful in providing a sterical stabilization for liposome drug carriers [26,27]; we expect that better understanding their membrane tension should yield new insight in their stability and mechanical properties. Here, we shall mainly focus, however, on the composite membrane of the red blood cell (or erythrocyte). The cytoskelet...

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Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles

Cited by 155 publications

References 10 publications

Probing small unilamellar EggPC vesicles on mica surface by atomic force microscopy

Probing small unilamellar EggPC vesicles on mica surface by atomic force microscopy

Shape fluctuations and elastic properties of two-component bilayer membranes

Fluctuation Spectrum of Fluid Membranes Coupled to an Elastic Meshwork: Jump of the Effective Surface Tension at the Mesh Size

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