S. A. Safran

Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates

Mechanical forces play a major role in the regulation of cell adhesion and cytoskeletal organization. In order to explore the molecular mechanism underlying this regulation, we have investigated the relationship between local force applied by the cell to the substrate and the assembly of focal adhesions. A novel approach was developed for real-time, high-resolution measurements of forces applied by cells at single adhesion sites. This method combines micropatterning of elastomer substrates and fluorescence imaging of focal adhesions in live cells expressing GFP-tagged vinculin. Local forces are correlated with the orientation, total fluorescence intensity and area of the focal adhesions, indicating a constant stress of 5.5 ± 2 nNμm-2. The dynamics of the force-dependent modulation of focal adhesions were characterized by blocking actomyosin contractility and were found to be on a time scale of seconds. The results put clear constraints on the possible molecular mechanisms for the mechanosensory response of focal adhesions to applied force.

Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization.

Forces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time.

Metabolic remodeling of the human red blood cell membrane

The remarkable deformability of the human red blood cell (RBC) results from the coupled dynamic response of the phospholipid bilayer and the spectrin molecular network. Here we present quantitative connections between spectrin morphology and membrane fluctuations of human RBCs by using dynamic full-field laser interferometry techniques. We present conclusive evidence that the presence of adenosine 5′-triphosphate (ATP) facilitates non-equilibrium dynamic fluctuations in the RBC membrane that are highly correlated with the biconcave shape of RBCs. Spatial analysis of the fluctuations reveals that these non-equilibrium membrane vibrations are enhanced at the scale of spectrin mesh size. Our results indicate that the dynamic remodeling of the coupled membranes powered by ATP results in non-equilibrium membrane fluctuations manifesting from both metabolic and thermal energies and also maintains the biconcave shape of RBCs.

Capillary instabilities in thin films. I: Energetics

A stability theory is presented which describes the conditions under which thin films rupture. It is found that holes in the film will either grow or shrink, depending on whether their initial radius is larger or smaller than a critical value. If the holes grow large enough, they impinge to form islands; the size of which are determined by the surface energies. The formation of grooves where the grain boundary meets the free surface is a potential source of holes which can lead to film rupture. Equilibrium grain boundary groove depths are calculated for finite grain sizes. Comparison of groove depth and film thickness yields microstructural conditions for film rupture. In addition, pits which form at grain boundary vertices, where three grains meet, are another source of film instability.

Fingering Instabilities of Driven Spreading Films

We show that a thin film with small dynamic contact angle and driven by an external body force is unstable to the formation of fingers in the direction perpendicular to the main flow. The instability is largest in the capillary region near the contact line, where the force due to surface tension is comparable to the viscous and gravitational forces. The fastest growing wavelength is calculated in the limit of small-amplitude disturbances. These instabilities may be related to finger patterns observed in gravitational flows and spinning drops.

Molecular theory of curvature elasticity in surfactant films

We develop a microscopic‐level formulation for the curvature elasticity of monolayer and bilayer systems of typical surfactant molecules. It is argued that both the bending and saddle‐splay force constants k and k are determined primarily by the conformational entropy of the flexible hydrocarbon chain rather than by the electrostatic interactions associated with hydrophilic head groups. A priori estimates of the chain contributions are made for the first time, without the use of any adjustable parameters. Both k and k are shown to be calculable wholly from the conformational statistics describing the planar film. In particular, these constants are expressed in terms of the derivatives and moments of the lateral pressure profile characterizing chain packing in the unbent layers. By considering the dependence of the curvature elasticity on chain length, area per molecule, and composition in mixed films, we are able to account for the order‐of‐magnitude variations in k observed in a variety of different su...

Theory of Spontaneous Vesicle Formation in Surfactant Mixtures

The curvature elastic energy of bilayer vesicles formed by a mixture of two surfactants, which individually form either micelles or lamellar bilayer phases is described theoretically. In the limit of large bending elastic modulus K being much greater than the temperature T, the free energy is minimized by vesicles with different concentrations of the two surfactants in each monolayer of the bilayer. Vesicles are more stable than lameliar structures only when interactions or complexing of the two surfactants is taken into account.

Capillary instabilities in thin films. II. Kinetics

We consider the kinetic evolution of perturbations to thin films. Since all small (nonsubstrate intersecting) perturbations to the film surface decay, we consider the evolution of large perturbations, in the form of a single hole which exposes the substrate. For large holes, the hole radius increases at a constant rate under the assumption of evaporation/condensation kinetics. When the dominant transport mode is surface diffusion, large holes grow with a rate proportional to t−3/4[log3(t/ ρ4c) ]. Small holes with a radii less than  ρc shrink, where  ρc is the film thickness divided by the tangent of the equilibrium wetting angle. The growth of these holes eventually leads to hole impingement which ruptures the film, creating a set of disconnected islands. The relaxation time for these islands to go to their equilibrium shape and size ( ρeq) scales as  ρ2eq or  ρ4eq for evaporation/condensation or surface diffusion kinetics, respectively.

Interaction between inclusions embedded in membranes.

We calculate the membrane-induced interaction between inclusions, in terms of the membrane stretching and bending moduli and the spontaneous curvature. We find that the membrane-induced interaction between inclusions varies nonmonotonically as a function of the inclusion spacing. The location of the energy minimum depends on the spontaneous curvature and the membrane perturbation decay length, where the latter is set by the membrane moduli. The membrane perturbation energy increases with the inclusion radius. The Ornstein-Zernike theory, with the Percus-Yevick closure, is used to calculate the radial distribution function of inclusions. We find that when the spontaneous curvature is zero, the interaction between inclusions due to the membrane deformation is qualitatively similar to the hard-core interaction. However, in the case of finite spontaneous curvature, the effective interaction is dramatically modified.

Effect of Lipid Characteristics on the Structure of Transmembrane Proteins

The activity of embedded proteins is known to vary with lipid characteristics. Indeed, it has been shown that some cell-membrane proteins cannot function unless certain non-bilayer-forming lipids (i.e., nonzero spontaneous curvature) are present. In this paper we show that membranes exert a line tension on transmembrane proteins. The line tension, on the order of 1-100 kT/protein, varies with the lipid properties and the protein configuration. Thus, membranes composed of different lipids favor different protein conformations. Model predictions are in excellent agreement with the data of Keller et al. (Biophys. J. 1993, 65:23-27) regarding the conductance of alamethicin channels.