In biology, molecular linkages at, within, and beneath cell interfaces arise mainly from weak noncovalent interactions. These bonds will fail under any level of pulling force if held for sufficient time. Thus, when tested with ultrasensitive force probes, we expect cohesive material strength and strength of adhesion at interfaces to be time- and loading rate-dependent properties. To examine what can be learned from measurements of bond strength, we have extended Kramers' theory for reaction kinetics in liquids to bond dissociation under force and tested the predictions by smart Monte Carlo (Brownian dynamics) simulations of bond rupture. By definition, bond strength is the force that produces the most frequent failure in repeated tests of breakage, i.e., the peak in the distribution of rupture forces. As verified by the simulations, theory shows that bond strength progresses through three dynamic regimes of loading rate. First, bond strength emerges at a critical rate of loading (> or = 0) at which spontaneous dissociation is just frequent enough to keep the distribution peak at zero force. In the slow-loading regime immediately above the critical rate, strength grows as a weak power of loading rate and reflects initial coupling of force to the bonding potential. At higher rates, there is crossover to a fast regime in which strength continues to increase as the logarithm of the loading rate over many decades independent of the type of attraction. Finally, at ultrafast loading rates approaching the domain of molecular dynamics simulations, the bonding potential is quickly overwhelmed by the rapidly increasing force, so that only naked frictional drag on the structure remains to retard separation. Hence, to expose the energy landscape that governs bond strength, molecular adhesion forces must be examined over an enormous span of time scales. However, a significant gap exists between the time domain of force measurements in the laboratory and the extremely fast scale of molecular motions. Using results from a simulation of biotin-avidin bonds (Izrailev, S., S. Stepaniants, M. Balsera, Y. Oono, and K. Schulten. 1997. Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J., this issue), we describe how Brownian dynamics can help bridge the gap between molecular dynamics and probe tests.

Micropipette pressurization of giant bilayer vesicles was used to measure both elastic bending k(c) and area stretch K(A) moduli of fluid-phase phosphatidylcholine (PC) membranes. Twelve diacyl PCs were chosen: eight with two 18 carbon chains and degrees of unsaturation from one double bond (C18:1/0, C18:0/1) to six double bonds per lipid (diC18:3), two with short saturated carbon chains (diC13:0, diC14:0), and two with long unsaturated carbon chains (diC20:4, diC22:1). Bending moduli were derived from measurements of apparent expansion in vesicle surface area under very low tensions (0.001-0.5 mN/m), which is dominated by smoothing of thermal bending undulations. Area stretch moduli were obtained from measurements of vesicle surface expansion under high tensions (>0.5 mN/m), which involve an increase in area per molecule and a small-but important-contribution from smoothing of residual thermal undulations. The direct stretch moduli varied little (< +/-10%) with either chain unsaturation or length about a mean of 243 mN/m. On the other hand, the bending moduli of saturated/monounsaturated chain PCs increased progressively with chain length from 0.56 x 10(-19) J for diC13:0 to 1.2 x 10(-19) J for diC22:1. However, quite unexpectedly for longer chains, the bending moduli dropped precipitously to approximately 0.4 x 10(-19) J when two or more cis double bonds were present in a chain (C18:0/2, diC18:2, diC18:3, diC20:4). Given nearly constant area stretch moduli, the variations in bending rigidity with chain length and polyunsaturation implied significant variations in thickness. To test this hypothesis, peak-to-peak headgroup thicknesses h(pp) of bilayers were obtained from x-ray diffraction of multibilayer arrays at controlled relative humidities. For saturated/monounsaturated chain bilayers, the distances h(pp) increased smoothly from diC13:0 to diC22:1 as expected. Moreover, the distances and elastic properties correlated well with a polymer brush model of the bilayer that specifies that the elastic ratio (k(c)/K(A))(1/2) = (h(pp) - h(o))/24, where h(o) approximately 1 nm accounts for separation of the headgroup peaks from the deformable hydrocarbon region. However, the elastic ratios and thicknesses for diC18:2, diC18:3, and diC20:4 fell into a distinct group below the correlation, which showed that poly-cis unsaturated chain bilayers are thinner and more flexible than saturated/monounsaturated chain bilayers.

Atomic force microscopy (AFM) has been used to measure the strength of bonds between biological receptor molecules and their ligands. But for weak noncovalent bonds, a dynamic spectrum of bond strengths is predicted as the loading rate is altered, with the measured strength being governed by the prominent barriers traversed in the energy landscape along the force-driven bond-dissociation pathway. In other words, the pioneering early AFM measurements represent only a single point in a continuous spectrum of bond strengths, because theory predicts that these will depend on the rate at which the load is applied. Here we report the strength spectra for the bonds between streptavidin (or avidin) and biotins-the prototype of receptor-ligand interactions used in earlier AFM studies, and which have been modelled by molecular dynamics. We have probed bond formation over six orders of magnitude in loading rate, and find that the bond survival time diminished from about 1 min to 0.001 s with increasing loading rate over this range. The bond strength, meanwhile, increased from about 5 pN to 170 pN. Thus, although they are among the strongest noncovalent linkages in biology (affinity of 10(13) to 10(15) M(-1)), these bonds in fact appear strong or weak depending on how fast they are loaded. We are also able to relate the activation barriers derived from our strength spectra to the shape of the energy landscape derived from simulations of the biotin-avidin complex.

On laboratory time scales, the energy landscape of a weak bond along a dissociation pathway is fully explored through Brownian-thermal excitations, and energy barriers become encoded in a dissociation time that varies with applied force. Probed with ramps of force over an enormous range of rates (force/time), this kinetic profile is transformed into a dynamic spectrum of bond rupture force as a function of loading rate. On a logarithmic scale in loading rate, the force spectrum provides an easy-to-read map of the prominent energy barriers traversed along the force-driven pathway and exposes the differences in energy between barriers. In this way, the method of dynamic force spectroscopy (DFS) is being used to probe the complex relation between force-lifetime-and chemistry in single molecular bonds. Most important, DFS probes the inner world of molecular interactions to reveal barriers that are difficult or impossible to detect in assays of near equilibrium dissociation but that determine bond lifetime and strength under rapid detachment. To use an ultrasensitive force probe as a spectroscopic tool, we need to understand the physics of bond dissociation under force, the impact of experimental technique on the measurement of detachment force (bond strength), the consequences of complex interactions in macromolecular bonds, and effects of multiply-bonded attachments.

Simple micromechanical methods provide direct measurements of surface cohesion, elasticity, rigidity, and mutual attraction properties of surfactant double-layer membranes in aqueous media. Temperature-dependent tests yield explicit data for thermal phase transitions. Properties of mixtures of phospholipids (neutral and charged), cholesterol, and polypeptides have been studied. The results are essential for evaluation of theories of surfactant mixing, lamellar phase transitions, colloidal stabilization, and flocculation. IntroductionThe lamellar configuration of biological membrane structures is peculiar to the preferential assembly of amphiphilic molecules into molecular double layers. The strong preference for the lamellar configuration is evidenced by the negligible solubility of these molecules-and extremely slow rate of exchange from a membrane capsule-in aqueous media. In this condensed state, bilayer membranes exhibit solid-or liquidlike material behavior with the common feature of limited surface compressibility (Le. great resistance to change in surface density). Because of the thin structure (~( 3 -4 ) X lo-' cm), bilayer fragility and limited detectability by optical methods create significant obstacles to measurement of the physical-mechanical properties. Recently, micromechanical techniques have been developed to investigate thermal transitions, cohesion, elasticity, and surface rigidity of bilayer membranes in situ. '-3 Bilayers interact nonspecifically via long-range electrostatic, electrodynamic, and solvation These colloidal forces are commonly recognized as van der Waals attraction, electric double-layer repulsion, and hydration repulsion. Other steric and structural interactions exist that are not yet clearly understood. Even though the magnitude of each interaction can be very large, the free energy minimum at stable contact is extremely low. Again because of micromechanical technology, it is possible to directly measure the cumulated free energy potential for assembly (adhesion) of membrane surfaces to stable ~o n t a c t .~,~-' * In this article, we discuss how mixtures of lipids, cholesterol, and polypeptides affect the thermal-mechanical and colloidal interaction properties of bilayer membranes. We outline prominent

The motivation for this review arises from the conviction that, as a result of the mass of experimental data and observations collected in recent years, the study of the physical properties of membranes is now entering a new stage of development. More and more, experiments are being designed to answer specific, detailed questions about membranes which will lead to a quantitative understanding of the way in which the physical properties of membranes are related to and influence their biological function.

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Continuous deformation and entry flow of single blood granulocytes into small caliber micropipets at various suction pressures have been studied to determine an apparent viscosity for the cell contents and to estimate the extent that dissipation in a cortical layer adjacent to the cell surface contributes to the total viscous flow resistance. Experiments were carried out with a wide range of pipet sizes (2.0-7.5 microns) and suction pressures (10(2)-10(4) dyn/cm2) to examine the details of the entry flow. The results show that the outer cortex of the cell maintains a small persistent tension of approximately 0.035 dyn/cm. The tension creates a threshold pressure below which the cell will not enter the pipet. The superficial plasma membrane of these cells appears to establish an upper limit to surface dilation which is reached after microscopic "ruffles" and "folds" have been pulled smooth. With aspiration of cells by small pipets (less than 2.7 microns), the limit to surface expansion was derived from the maximal extension of the cell into the pipet; final areas were measured to be 2.1 to 2.2 times the area of the initial spherical shape. For suctions in excess of a threshold, the response to constant pressure was continuous flow in proportion to excess pressure above the threshold with only a small nonlinearity over time until the cell completely entered the pipet (for pipet calibers greater than 2.7 microns). With a theoretical model introduced in a companion paper, (Yeung, A., and E. Evans., 1989, Biophys. J. 56:139-149) the entry flow response versus pipet size and suction pressure was analyzed to estimate the apparent viscosity of the cell interior and the ratio of cortical flow resistance to flow resistance from the cell interior. The apparent viscosity was found to depend strongly on temperature with values on the order of 2 x 10(3) poise at 23 degrees C, lower values of 1 x 10(3) poise at 37 degrees C, but extremely large values in excess of 10(4) poise below 10 degrees C. Because of scatter in cell response, it was not possible to accurately establish the characteristic ratio for flow resistance in the cortex to that inside the cell; however, the data showed that the cortex does not contribute significantly to the total flow resistance.