Role of lamellar membrane structure in tether formation from bilayer vesicles (original) (raw)
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Surface viscosity measurements from large bilayer vesicle tether formation. I. Analysis
Biophysical Journal, 1982
Recent observations indicate that it is possible to form tethers from large phospholipid vesicles. The process of tether formation is analyzed using a continuum mechanical approach to obtain the surface viscosity of the bilayer in terms of experimentally measurable parameters. The membrane is treated as a two-dimensional isotropic material which deforms at constant area. The constitutive equation relates the maximum surface shear resultant to the rate of deformation via the surface viscosity coefficient. The force which acts to increase the tether length is generated by fluid moving past the vesicle. The magnitude of the force is estimated from Stokes's drag equation. The analysis predicts that there is a critical force necessary to produce an increase in the tether length. A dimensionless tether growth parameter is defined, and its value is obtained as a function of the ratio of the applied force on the vesicle to the critical force. This relationship is independent of both the size of the vesicle and the radius of the tether. Knowing the force on the vesicle, the critical force, and the rate of tether growth, the surface viscosity can be calculated. INTRODUCTION Biological membranes behave as two-dimensional materials. Strictly speaking, they can be considered as continuous only in the two dimensions of the surface, with a molecular character in the direction normal to the surface. The erythrocyte membrane has served as a model system for the study of such materials, and the continuum mechanical properties of erythrocyte membrane have been characterized. (See Evans and Skalak, 1980, for a thorough review.) The application of material science to other types of membrane has been slow, largely because of the existence of cytoplasmic structures in most cells which, at best, complicate the mechanical analysis and, at worst, dominate the behavior of the cell in deformation. The mechanical behavior of any membrane reflects the composite properties of the membrane constituents. Therefore, an alternative approach to the study of membrane mechanics is to study the properties of reconstituted membrane components to ascertain the contribution of each constituent. The phospholipid bilayer is a major constituent of virtually all biological membranes, and it is with the bilayer that the study of membrane components logically begins. Recently, it has been observed that large multilamellar phospholipid bilayer vesicles can become attached to glass surfaces and form tethers between the point of attachment and the body of the vesicle (E.
Fluid-membrane tethers: Minimal surfaces and elastic boundary layers
Physical Review E, 2002
Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.
Coalescence of Membrane Tethers: Experiments, Theory, and Applications
Biophysical Journal, 2005
Tethers are nanocylinders of lipid bilayer membrane, arising in situations ranging from micromanipulation experiments on synthetic vesicles to the formation of dynamic tubular networks in the Golgi apparatus. Relying on the extensive theoretical and experimental works aimed to understand the physics of individual tethers formation, we addressed the problem of the interaction between two nanotubes. By using a combination of micropipette manipulation and optical tweezers, we quantitatively studied the process of coalescence that occurred when the separation distance between both vesicle-tether junctions became smaller than a threshold length. Our experiments, which were supported by an original theoretical analysis, demonstrated that the measurements of the tether force and angle between tethers at coalescence directly yield the bending rigidity, k, and the membrane tension, s, of the vesicles. Contrary to other methods used to probe the bending rigidity of vesicles, the proposed approach permits a direct measurement of k without requiring any control of the membrane tension. Finally, after validation of the method and proposal of possible applications, we experimentally investigated the dynamics of the coalescence process.
The Effect of Tethers on Artificial Cell Membranes: A Coarse-Grained Molecular Dynamics Study
PLOS ONE, 2016
Tethered bilayer lipid membranes (tBLMs) provide a stable platform for modeling the dynamics and order of biological membranes where the tethers mimic the cytoskeletal supports present in biological cell membranes. In this paper coarse-grained molecular dynamics (CGMD) is applied to study the effects of tethers on lipid membrane properties. Using results from the CGMD model and the overdamped Fokker-Planck equation, we show that the diffusion tensor and particle density of water in the tBLM is spatially dependent. Further, it is shown that the membrane thickness, lipid diffusion, defect density, free energy of lipid flip-flop, and membrane dielectric permittivity are all dependent on the tether density. The numerically computed results from the CGMD model are in agreement with the experimentally measured results from tBLMs containing different tether densities and lipids derived from Archaebacteria. Additionally, using experimental measurements from Escherichia coli bacteria and Saccharomyces Cerevisiae yeast tethered membranes, we illustrate how previous molecular dynamics results can be combined with the proposed model to estimate the dielectric permittivity and defect density of these membranes as a function of tether density.
Biophysical Journal, 1992
Bilayer membranes exhibit an elastic resistance to changes in curvature. This resistance depends both on the intrinsic stiffness of the constituent monolayers and on the curvature-induced expansion or compression of the monolayers relative to each other. The monolayers are constrained by hydrophobic forces to remain in contact, but they are capable of independent lateral redistribution to minimize the relative expansion or compression of each leaflet. Therefore, the magnitude of the expansion and compression of the monolayers relative to each other depends on the integral of the curvature over the entire membrane capsule. The coefficient characterizing the membrane stiffness resulting from relative expansion is the nonlocal bending modulus kr. Both the intrinsic (local) bending modulus (kc) and the nonlocal bending modulus (kr) can be measured by the formation of thin cylindrical membrane strands (tethers) from giant phospholipid vesicles. Previously, we reported measurements of kc based on measurements of tether radius as a function of force (Song and Waugh, 1991, J. Biomech. Engr. 112:233). Further analysis has revealed that the contribution from the nonlocal bending stiffness can be detected by measuring the change in the aspiration pressure required to establish equilibrium with increasing tether length. Using this approach, we obtain a mean value for the nonlocal bending modulus k, of-4.1 x 10-'9 J. The range of values is broad (1.1-10.1 x 10-19 J) and could reflect contributions other than simple mechanical equilibrium. Inclusion of the nonlocal bending stiffness in the calculation of kc results in a value for that modulus of 1.20 ± 0.17 x 10-19 J, in close agreement with values obtained by other methods.
Excess area dependent scaling behavior of nano-sized membrane tethers
Physical biology, 2017
Thermal fluctuations in cell membranes manifest as an excess area (Aex) which governs a multitude of physical process at the sub-micron scale. We present a theoretical framework, based on an in silico tether pulling method, which may be used to reliably estimate Aex in live cells. We perform our simulations in two different thermodynamic ensembles: (i) the constant projected area and (ii) the constant frame tension ensembles and show the equivalence of our results in the two. The tether forces estimated from our simulations compare well with our experimental measurements for tethers extracted from ruptured GUVs and HeLa cells. We demonstrate the significance and validity of our method by showing that all our calculations performed in the initial tether formation regime (i.e., when the length of the tether is comparable to its radius) along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether rad...
A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers
The tensile force along a cylindrical lipid bilayer tube is proportional to the membrane's bending modulus and inversely proportional to the tube radius. We show that this relation, which is experimentally exploited to measure bending rigidities, can be applied with even greater ease in computer simulations. Using a coarse-grained bilayer model we efficiently obtain bending rigidities that compare very well with complementary measurements based on an analysis of thermal undulation modes. We furthermore illustrate that no deviations from simple quadratic continuum theory occur up to a radius of curvature comparable to the bilayer thickness.
The effect of tethered polymers on the conformation of a lipid membrane
Macromolecular Theory and Simulations, 1997
We consider the effect of tethered macromolecules on the stability of the flat conformation of a lipid bilayer in a dense brush regime when anchored chains are significantly overlapped. On the basis of a scaling approach we have shown that redistribution of polymer chains from inner to outer layers reduces the free energy of the system and stabilizes spherically bent configurations of the membrane.
Biophysical Journal, 2002
Fundamental to all mammalian cells is the adherence of the lipid bilayer membrane to the underlying membrane associated cytoskeleton. To investigate this adhesion, we physically detach the lipid membrane from the cell by mechanically forming membrane tethers. For the most part these have been tethers formed from either neutrophils or red cells. Here we do a simple thermodynamic analysis of the tether formation process using the entire cell, including tether, as the control volume. For a neutrophil, we show that the total adhesion energy per unit area between lipid membrane and cytoskeleton depends on the square of the tether force. For a flaccid red cell, we show that the total adhesion energy minus the tension in the spectrin cytoskeleton depends also on the square of the tether force. Finally, we discuss briefly the viscous flow of membrane. Using published data we calculate and compare values for the various adhesion energies and viscosities.