Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory

Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed temperature, each vesicle undergoes thermal shape fluctuations. We are able experimentally to characterize the thermal shape ensemble by digitizing the vesicle outline in real time and storing the time-sequence of images. Analysis of this ensemble using the area-difference-elasticity (ADE) model of vesicle shapes allows us to associate (map) each time-sequence to a point in the zero-temperature (shape) phase diagram. Changing the laboratory temperature modifies the control parameters (area, volume, etc.) of each vesicle, so it sweeps out a trajectory across the theoretical phase diagram. It is a nontrivial test of the ADE model to check that these trajectories remain confined to regions of the phase diagram where the corresponding shapes are locally stable. In particular, we study the thermal trajectories of three prolate vesicles which, upon heating, experienced a mechanical instability leading to budding. We verify that the position of the observed instability and the geometry of the budded shape are in reasonable accord with the theoretical predictions. The inability of previous experiments to detect the ``hidden'' control parameters (relaxed area difference and spontaneous curvature) make this the first direct quantitative confrontation between vesicle-shape theory and experiment.Comment: submitted to PRE, LaTeX, 26 pages, 11 ps-fi

Gravity-Induced Shape Transformations of Vesicles

We theoretically study the behavior of vesicles filled with a liquid of higher density than the surrounding medium, a technique frequently used in experiments. In the presence of gravity, these vesicles sink to the bottom of the container, and eventually adhere even on non - attractive substrates. The strong size-dependence of the gravitational energy makes large parts of the phase diagram accessible to experiments even for small density differences. For relatively large volume, non-axisymmetric bound shapes are explicitly calculated and shown to be stable. Osmotic deflation of such a vesicle leads back to axisymmetric shapes, and, finally, to a collapsed state of the vesicle.Comment: 11 pages, RevTeX, 3 Postscript figures uuencode

Giant vesicles at the prolate-oblate transition: A macroscopic bistable system

Giant phospholipid vesicles are shown to exhibit thermally activated transitions between a prolate and an oblate shape on a time scale of several seconds. From the fluctuating contour of such a vesicle we extract ellipticity as an effective reaction coordinate whose temporal probability distribution is bimodal. We then reconstruct the effective potential from which we derive an activation energy of the order of $k_BT$ in agreement with theoretical calculations. The dynamics of this transition is well described within a Kramers model of overdamped diffusion in a bistable potential. Thus, this system can serve as a model for macroscopic bistability.Comment: 10 pages, LaTeX, epsfig, 4 eps figures included, to appear in Europhys. Let

ROSAT HRI observations of Centaurus A

We present results from a sensitive high-resolution X-ray observation of the nearby active galaxy Centaurus A (NGC 5128) with the ROSAT HRI. The 65~ksec X-ray image clearly distinguishes different components of the X-ray emission from Cen A: the nucleus and the jet, the diffuse galaxy halo, and a number of individual sources associated with the galaxy. The luminosity of the nucleus increased by a factor of two compared to an earlier ROSAT observation in 1990. The high spatial resolution of the ROSAT HRI shows that most of the knots in the jet are extended both along and perpendicular to the jet axis. We report the detection of a new X-ray feature, at the opposite side of the X-ray jet which is probably due to compression of hot interstellar gas by the expanding southwestern inner radio lobe.Comment: To be published in Astrophys. Journal Letters. 4 pages, 3 plate

Vesicles in solutions of hard rods

The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shape. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is non-analytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the non-analytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rod-like (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and to a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Vesicle shape, molecular tilt, and the suppression of necks

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.Comment: 10 pages, 7 figures, submitted to Phy. Rew.

Effect of molybdenum on numbers of Azospirillum on Brachiaria Decumbens production

Foram obtidos aumentos de 19% na produção de materia seca e 29% na produção de N total em Brachiaria decumbens cv. Basilisk (australiana) mantida sob pastejo com 2,5 ua/ha, em resposta à adubação com 160 g de Mo/ha, na forma de molibdato de sódio. O experimento foi conduzido em um Latossolo Vermelho-Escuro fase Cerradão, fertilizado com P, K, Cu, Zn e B. O período de avaliação foi entre setembro/82 e abril/83. Levantamentos quinzenais da ocorrência de Azospirillum spp. mostraram consistentemente maior número de bactérias em raízes de plantas crescidas nas áreas com Mo do que em áreas sem este elemento.Production of dry matter and total N of Brachiaria decumbens cv. Basilisk under a grazing pressure of 2.5 au/ha were increased by 19% and 29% respectively, in response to fertilization with 160 g of Mo/ha, applied as sodium molybdate. The experiment was conducted on a Dark-Red Latosol phase Cerradão fertilized with P, K, Cu, Zn and B, and evaluated between September/82 and April/83. The Azospirillum countings made every 15 days consistently indicated higher numbers of bacters in roots of plants growing in the Mo treatments than in treatments without Mo