Mechanics of Tether Formation in Liposomes

[+] Author and Article Information
C. R. Calladine, J. A. Greenwood

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK

J Biomech Eng 124(5), 576-585 (Sep 30, 2002) (10 pages) doi:10.1115/1.1500341 History: Received October 01, 2001; Revised May 01, 2002; Online September 30, 2002
Copyright © 2002 by ASME
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Schematic view of an experimental setup for drawing a tether. A liposome has been partially drawn into a vertical micro-pipette by pressure −ΔP, measured relative to the pressure of the surrounding fluid, and the buoyant weight of a small glass bead is drawing out a tether.
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A portion of a lipid bilayer vesicle and tether, with key parameters shown
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A small element of lipid bilayer, showing principal bending and stretching stress-resultants in the s(=meridional) and θ(=circumferential) directions.
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Plot of experimental data from Waugh et al. 3, Table 1. Values of F and R0 as tabulated. Values of tension T=PRv/2, where Rv is the radius of the main vesicle and P is evaluated from P=ΔP/((Rv/Rp)−1) (for equal T in the main vesicle and in the hemisphere within the pipette), where Rp is the radius of the pipette, here taken as 3.5μm. The best-fitting lines of slope ±0.5 (cf equations (5,6)) give an experimental value of B=1.5×10−19 Nm.
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“Thick-walled” effects. (a) An idealized lipid bilayer tube of mean radius R0 and thickness h, showing isotropic tensile and compressive membrane force per unit length of equal magnitude in the outer and inner layers, respectively. (b) Another model of a doubly-curved element with a continuum distribution of isotropic stress in the through-thickness y-direction. The shaded edges are “cut” perpendicular to the central surface, which has curvature Ks,Kθ in the s,θ directions respectively
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Portion of a general meridian in dimensionless geometrical coordinates, with dimensionless stress resultants, for the purpose of performing a more accurate “sliding-skin” energy calculation
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Cut-off end of tether, for purposes of axial force-balance between dimensionless versions of tether force f, membrane stress-resultant ns and interior pressure p
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Numerical results for the case p=0.1: (a) Profile r(z), as far as the “equator.” (b) Plots of m(s),q(s). (c) Plots of ns(s),nθ(s),κs(s),κ0(s).
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Schematic description of the bending of a liposome element, here regarded as being of thickness 2h and made of uniform material. (a) Monolithic element. (b) Two layers, each of thickness h and free to slide over one another. (c) “Two-flange” bending that must be added to (b) in order to recover (a).




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