Elasticity and shape equation of a liquid membrane

The density of the elastic energy of a deformed membrane in a liquid state is calculated. The thermodynamic equilibrium of its different parts is taken into account. The shape equation of a closed membrane is deduced. The quantity which keeps its value, when the variations of the energy of the system are calculated, is not the area of the deformed membrane, but its area in the flat tension free state. Because of this, additional terms appear in the second variation around the stable state. The case of a lipid bilayer and its fluctuations is examined for both free and blocked exchange of molecules between the monolayers, comprising the bilayer

Pores and their number in bilayer lipid membranes

A proper definition of pores in lipid bilayers is given in this work. The pore number is determined by the area S of the membrane and by the energy E necessary for generation of one pore. A comparison is made with other existing approaches for the explanation of the pore formation.Dans cet article on donne la définition d'un pore dans une bicouche lipidique. Le nombre des pores est déterminé par la surface S de la membrane et par l'énergie E nécessaire pour la formation d'un pore. Une comparaison est faite avec les méthodes existant jusqu'à présent pour l'explication de la formation des pores

Elasticity of bilayers containing PEG lipids

The addition of lipids with a poly(ethylene glycol) head group (Stealth or grafted or PEG lipids) to a phosphatidylcholine bilayer changes the mechanical properties of the membrane. We calculate the dependences of the bending and stretching elasticities of the bilayer on the PEG lipid concentration and on the monomer number in its polymer chain. The role of the bending elasticity at blocked flip-flop of the pure bilayer is revealed

Correlations between the form fluctuation modes of flaccid quasispherical lipid vesicles and their role in the calculation of the curvature elastic modulus of the vesicle membrane. Numerical results

It is shown in this paper that the existing theories of the form fluctuations of quasispherical lipid vesicle give a too mean stretching energy of its membrane. A more precise theory taking into account the area conservation of the membrane is proposed. The relation between the amplitudes of the form fluctuations and the curvature elastic modulus of the membrane is obtained numerically by means of a suitable Monte Carlo simulation.Dans cet article nous montrons que les théories existantes des fluctuations de la forme d'une vésicule lipidique quasisphérique donnent des valeurs trop élevées pour l'énergie moyenne de dilatation de sa membrane. Une théorie propre, qui tient compte de la conservation de la surface de la membrane, est proposée. La relation entre les amplitudes des fluctuations de la forme et le module d'élasticité de courbure de la membrane est obtenue numériquement au moyen d'une simulation Monte Carlo convenable

In vitro Plant Regeneration from Seedling‐derived Explants of two Cultivars of White Jute (Corchorus capsularies L.)

An in vitro regeneration system for two varieties of white jute (Corchorus capsularis L.) namely, BJC‐7370 and BJC‐83 was developed. The regeneration protocol was based upon direct organogenesis from seedling‐derived explants such as cotyledon with petioles, cotyledonary node. Shoot regeneration was achieved from cotyledon with petiole and cotyledonary node through use of MS supplemented with 0.5 mg/l BAP and 1.0 mg/l IAA for BJC‐7370 while for BJC‐83 shoot initiation was obtained on 1.25 mg/l BAP and 0.25 mg/l NAA using the same explants. Elongation of shoots was achieved on MS containing 0.2 mg/l BAP for the two said jute varieties. Regenerated excised shoots developed effective in vitro root system on half strength of MS supplemented with 0.3 mg/l IBA for both the varieties. The in vitro grown plantlets were transferred to soil for acclimation. These plants grew up to maturity, flowered and produced seeds identical to the control plants

Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements

Thermal fluctuations of giant lipid vesicles have been investigated both theoretically and experimentally. At the theoretical level, the model developed here takes explicitly into account the conservation of vesicle volume and membrane area. Under these conditions, the amplitude of thermal fluctuations depends critically not only on the bending elasticity of the bilayer, but also on the membrane tension and/or hydrostatic pressure difference between the interior and exterior of the vesicle. At the experimental level, the determination of the bending modulus kc first requires the analysis of a large number (several hundred) of vesicle contours to obtain a significant statistics. Secondly, the contribution of the experimental error on the contour coordinates, which results in a white noise on the Fourier amplitudes, must be eliminated, and this can be done by using the angular autocorrelation function of the fluctuations. Finally, the amplitudes of harmonics having short correlation times must be corrected from the effect of the integration time (40 ms) of the video camera, which otherwise leads to an overestimation of kc. All these theoretical and experimental requirements have been considered in the analysis of the thermal fluctuations of 42 giant vesicles composed of egg phosphatidylcholine. The behaviour of this population of vesicles can be accounted for with a bending modulus kc equal to 0.4 - 0.5 x 10-19 J, and extremely low membrane tensions, ranging below 15 × 10-5 mN/m.Les fluctuations thermiques de vésicules lipidiques géantes ont été étudiées d'un point de vue théorique et expérimental. Au niveau théorique, le modèle développé prend explicitement en compte la conservation du volume de la vésicule et de la surface de la membrane. I1 en résulte que l' amplitude des fluctuations thermiques dépend non seulement de l'élasticité de courbure de la bicouche, mais aussi de la tension de membrane et/ou de la différence de pression hydrostatique entre l'intérieur et l'extérieur de la vésicule. Au niveau expérimental, la détermination du module de courbure kc nécessite d'abord l'analyse d'un grand nombre (plusieurs centaines) de contours afin d'obtenir une bonne statistique. En second lieu, la contribution de l'erreur expérimentale sur les coordonnées du contour, qui se traduit par un bruit blanc sur les amplitudes de Fourier, doit être éliminée, et ceci peut être réalisé grâce à l'utilisation de la fonction d'autocorrélation angulaire des fluctuations. Enfin, les amplitudes des harmoniques ayant des temps de corrélation courts doivent être corrigées de l'effet du temps d'intégration (40 ms) de la caméra vidéo, qui, dans le cas contraire, conduit à une surestimation de k c. Toutes ces exigences théoriques et expérimentales ont été prises en compte dans l'analyse des fluctuations thermiques de 42 vésicules géantes de phosphatidylcholine du jaune d'œuf. Il peut être rendu compte du comportement de cette population de vésicules avec un module de courbure kc égal à 0.4 - 0.5 x 10-19 J, et des tensions de membrane extrêmement faibles, de moins de 15 x 10-5 mN/m