From Macroscopic Adhesion Energy to Molecular Bonds: A Test of the Theory (original) (raw)
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Mechanics of membrane–membrane adhesion
Mathematics and Mechanics of Solids, 2011
Curvature elasticity is used to derive the equilibrium conditions that govern the mechanics of membrane–membrane adhesion. These include the Euler–Lagrange equations and the interface conditions which are derived here for the most general class of strain energies permissible for fluid surfaces. The theory is specialized for homogeneous membranes with quadratic ‘Helfrich’-type energies with non-uniform spontaneous curvatures. The results are employed to solve four-point boundary value problems that simulate the equilibrium shapes of lipid vesicles that adhere to each other. Numerical studies are conducted to investigate the effect of relative sizes, osmotic pressures, and adhesion-induced spontaneous curvature on the morphology of adhered vesicles.
Adhesion of membranes with competing specific and generic interactions
The European Physical Journal E, 2002
Biomimetic membranes in contact with a planar substrate or a second membrane are studied theoretically. The membranes contain specific adhesion molecules (stickers) which are attracted by the second surface. In the absence of stickers, the trans-interaction between the membrane and the second surface is assumed to be repulsive at short separations. It is shown that the interplay of specific attractive and generic repulsive interactions can lead to the formation of a potential barrier. This barrier induces a line tension between bound and unbound membrane segments which results in lateral phase separation during adhesion. The mechanism for adhesion-induced phase separation is rather general, as is demonstrated by considering two distinct cases involving: i) stickers with a linear attractive potential, and ii) stickers with a short-ranged square-well potential. In both cases, membrane fluctuations reduce the potential barrier and, therefore, decrease the tendency of phase separation.
Dynamic strength of molecularly bonded surfaces
This study reports a theoretical analysis of the forced separation of two adhesive surfaces linked via a large number of parallel noncovalent bonds. To describe the bond kinetics, we implement a three-state reaction model with kinetic rates obtained from a simple integral expression of the mean first passage time for diffusive barrier crossing in a pulled-distance-dependent potential. We then compute the rupture force for the separation of adhesive surfaces at a constant rate. The results correspond well with a Brownian dynamics simulation of the same system. The separation rate relative to the intrinsic relaxation time of the bonds defines three loading regimes and the general dependence of the adhesion on kinetic or thermodynamic parameters of the bonds. In the equilibrium regime, the rupture force asymptotically approaches the equilibrium rupture force, which increases linearly with the equilibrium bond energy. In the near-equilibrium regime, the rupture force increases with the separation rate and increasingly correlates with the bond rupture barrier. In the far-from-equilibrium regime where rebinding is irrelevant, the rupture force varies linearly with the rupture barrier.
Adhesion dynamics of confined membranes
Soft Matter, 2018
Models of lipid membranes confined between adhesive planes exhibit frozen states or coarsening with coexistence of wrinkles with flat domains.
The European Physical Journal E, 2009
The fundamental study of the adhesion of cells to each other or to a substrate is a key research topic in cellular biophysics because cell adhesion is important to many biological processes. We report on the adhesion of a model cell, a liposome, and a living HeLa cell to a substrate measured with a novel experimental technique. The cells are held at the end of a micropipette mounted on a micromanipulator and brought into contact with a surface. The adhesion energy and membrane tension are measured directly using the deflection of the micropipette when binding or unbinding the cell from the substrate. Since the force applied on the cells is known throughout the experiment, the technique presented enables the measurement of dynamics such as changes in the adhesion, elasticity, and membrane tension with time.
Adhesion induced by mobile binders: Dynamics
Proceedings of the National Academy of Sciences, 2002
We consider a vesicle bilayer loaded with molecules that can bind (upon contact) with a solid surface, following the classical model of Bell, Dembo, and Bongrand. We are interested in situations where the contact area varies with time: we assume that binders can then migrate via diffusion. The resulting dissipation and lag create a retarded force on the contact line, which could be significant in squeezing or rolling experiments. However, there are two cases where we expect the lag force to be ineffective: (i) separation by shrinking of an adhesive patch (where the Evans ''tear out'' process turns out to be less costly) and (ii) spontaneous growth of a patch from a point contact. In this last case, the lag force is weak, and we give detailed predictions for the growth laws.
Geometry of Lipid Vesicle Adhesion
Physical Review E, 2002
The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich hamiltonian quadratic in the mean curvature; it interacts by contact with the substrate, with an interaction energy proportional to the area of contact. We identify the constraints on the geometry at the boundary of the shared surface. The result is interpreted in terms of the balance of the force normal to this boundary. No assumptions are made either on the symmetry of the vesicle or on that of the substrate. The strong bonding limit as well as the effect of curvature asymmetry on the boundary are discussed.
The equilibria of vesicles adhered to substrates by short-ranged potentials
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013
In equilibrium, a vesicle that is adhered to a horizontal substrate by a long-range attractive, short-range repulsive force traps a thin layer of fluid beneath it. In the asymptotic limit that this layer is very thin, there are quasi-two-dimensional boundary-layer structures near the edges of the vesicle, where the membrane's shape is governed by a balance between bending and adhesive stresses. These boundary layers are analysed to obtain corrections to simpler models that instead represent the adhesive interaction by a contact potential, thereby resolving apparent discontinuities that arise when such models are used. Composite expansions of the shapes of two-dimensional vesicles are derived. When, in addition, the adhesive interaction is very strong, there is a nested boundary-layer structure for which the adhesive boundary layers match towards sharp corners where bending stresses remain important but adhesive stresses are negligible. Outside these corners, bending stresses are...
Effective line tension and contact angles between membrane domains in biphasic vesicles
The European Physical Journal E, 2011
Inhomogeneities in membranes give rise to localized interactions at the interface between domains in two-component vesicles. The corresponding energy is expressed as a line tension between the two phases. In this paper we study the implications of the thickness mismatch between domains which has been experimentally reported to be of order 20-30% and the conditions under which the induced line tension can destabilize the domains in inhomogeneous vesicles. For asymmetric lipidic membranes we prove an increase of the line tension and the existence of a contact angle. Adsorption of impurities is also examined, our scope being the extension of the Canham-Helfrich model to describe elastic deformations and chemical interactions arising at microscopic scales. This mismatch effect may have important consequences for the stability of very small domains.