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

Döbereiner, Jürgen; Evans, Evan; Kraus, Martin; Seifert, Udo; Wortis, Michael

doi:10.1103/physreve.55.4458

Cited by 223 publications

(228 citation statements)

References 44 publications

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“…(5), the obtained shapes [10,16] included all the eight shapes above. And also, all these eight shapes except the self-intersecting cases have been observed in laboratory [16][17][18].…”

Section: A Comparison Of Our Results With the Previous Experimentmentioning

confidence: 99%

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Spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous-curvature fluid-membrane model

et al. 1999

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An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E 48, 2304 54, 2816(1996), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy. 87.16.Dg, 47.10.Hg, 68.15.+e, 02.40.Hw

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“…(5), the obtained shapes [10,16] included all the eight shapes above. And also, all these eight shapes except the self-intersecting cases have been observed in laboratory [16][17][18].…”

Section: A Comparison Of Our Results With the Previous Experimentmentioning

confidence: 99%

“…(5) with C = 0 [9]. Except the self-intersecting cases, they all have real correspondence in vitro and in vivo on vesicle shapes [16][17][18]. The closed shapes ii)-vii) form two separate prolate and oblate ellipsoid branches which are bifurcated from a sphere.…”

Section: Discussionmentioning

confidence: 99%

Spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous-curvature fluid-membrane model

et al. 1999

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“…Lipid membranes in water can form fairly complex equilibrium structures in which stable tubular necks connect membrane compartments (6,8,9,37). Usually, neck formation is directed purely by minimization of membrane-bending energy (27,37,38). The scenario in which tension and bending moments compete for control over neck stability and geometrical parameters has attracted less attention.…”

Section: Discussionmentioning

confidence: 99%

Shape bistability of a membrane neck: A toggle switch to control vesicle content release

Frolov

Lizunov

Dunina-Barkovskaya

et al. 2003

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

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Shape dynamics and permeability of a membrane neck connecting a vesicle and plasma membrane are considered. The neck is modeled by a lipid membrane tubule extended between two parallel axisymmetric rings. Within a range of lengths, defined by system geometry and mechanical properties of the membrane, the tubule has two stable shapes: catenoidal microtubule and cylindrical nanotubule. The permeabilities of these two shapes, measured as ionic conductivity of the tubule interior, differ by up to four orders of magnitude. Near the critical length the transitions between the shapes occur within less than a millisecond. Theoretical estimates show that the shape switching is controlled by a single parameter, the tubule length. Thus the tubule connection can operate as a conductivity microswitch, toggling the release of vesicle content in such cellular processes as ''kiss-and-run'' exocytosis. In support of this notion, bistable behavior of membrane connections between vesicles and the cell plasma membrane in macrophages is demonstrated.

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“…Movies were digitized at 1/∆t = 3Hz. Individual frames are counted using an index n. The cell edge is determined with a custom C program by a local contour algorithm [19] allowing nanometer accuracy. We obtain a sub-pixel resolution of 15 nm for relative displacements, which translates into a minimal detectable velocity of 45 nm/s between frames.…”

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confidence: 99%

Dynamic Phase Transitions in Cell Spreading

et al. 2004

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We monitored isotropic spreading of mouse embryonic fibroblasts on fibronectin-coated substrates. Cell adhesion area versus time was measured via total internal reflection fluorescence microscopy. Spreading proceeds in well-defined phases. We found a power-law area growth with distinct exponents ai in three sequential phases, which we denote basal (a1 = 0.4±0.2), continous (a2 = 1.6±0.9) and contractile (a3 = 0.3 ± 0.2) spreading. High resolution differential interference contrast microscopy was used to characterize local membrane dynamics at the spreading front. Fourier power spectra of membrane velocity reveal the sudden development of periodic membrane retractions at the transition from continous to contractile spreading. We propose that the classification of cell spreading into phases with distinct functional characteristics and protein activity patterns serves as a paradigm for a general program of a phase classification of cellular phenotype. Biological variability is drastically reduced when only the corresponding phases are used for comparison across species/different cell lines. [5,6] for which detailed elastic models have been developed [7]. In vivo, cell spreading on matrix-coated surfaces provides a simplified system of analyzing motile behavior. A substantial amount of experimental and theoretical work has been done along these lines [8,9,10,11]. However, only quite recently, quantitative experiments of whole cell spreading and subsequent migration could be performed with high spatial and temporal resolution [12,13]. We found that there are well defined and distinct states of spreading. It is the goal of this work to show that these states can indeed be considered phases of motility by demonstrating the existence of dynamic phase transitions between them.Spreading cells extend a 200 nm thick sheet called the lamellipodium from the cell body onto the substrate, see Fig. 1. This process is driven by actin polymerization at the leading membrane edge, the precise mechanism of which is still under debate [14,15]. The meshwork of actin fibers is crosslinked by various proteins. The molecular motor myosin II enables the meshwork to contract by moving along actin fibers and relative to other cytoskeletal elements. Thus, the lammelipodium is an active gel enclosed in a flat membrane bag adhering to the substrate. The physics of active gels has recently attracted a lot of attention. Rheological experiments of simple mixtures of purified actin and myosin solutions [16] and quite general theoretical modeling [17,18] have been carried out. There are dynamic phase transitions involving extended and contracted actin density states as a function of myosin-actin coupling strength [17]. We will show that our cellular system exhibits similar transitions which express themselves prominently in the dynamics of the leading membrane edge. Mouse embryonic fibroblasts (MEF) were allowed to settle onto fibronectin coated glass slides and observed with either total internal reflection fluorescence (TIRF) or differential inte...

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

Cited by 223 publications

References 44 publications

Spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous-curvature fluid-membrane model

Spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous-curvature fluid-membrane model

Shape bistability of a membrane neck: A toggle switch to control vesicle content release

Dynamic Phase Transitions in Cell Spreading

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