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.

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.

Recent advancements in single-molecule tracking methods with nanometer-level precision now allow researchers to observe the movement, recruitment, and activation of single molecules in the plasma membrane in living cells. In particular, on the basis of the observations by high-speed single-particle tracking at a frame rate of 40,000 frames s(1), the partitioning of the fluid plasma membrane into submicron compartments throughout the cell membrane and the hop diffusion of virtually all the molecules have been proposed. This could explain why the diffusion coefficients in the plasma membrane are considerably smaller than those in artificial membranes, and why the diffusion coefficient is reduced upon molecular complex formation (oligomerization-induced trapping). In this review, we first describe the high-speed single-molecule tracking methods, and then we critically review a new model of a partitioned fluid plasma membrane and the involvement of the actin-based membrane-skeleton "fences" and anchored-transmembrane protein "pickets" in the formation of compartment boundaries.

The diffusion rate of lipids in the cell membrane is reduced by a factor of 5–100 from that in artificial bilayers. This slowing mechanism has puzzled cell biologists for the last 25 yr. Here we address this issue by studying the movement of unsaturated phospholipids in rat kidney fibroblasts at the single molecule level at the temporal resolution of 25 μs. The cell membrane was found to be compartmentalized: phospholipids are confined within 230-nm-diameter (φ) compartments for 11 ms on average before hopping to adjacent compartments. These 230-nm compartments exist within greater 750-nm-φ compartments where these phospholipids are confined for 0.33 s on average. The diffusion rate within 230-nm compartments is 5.4 μm2/s, which is nearly as fast as that in large unilamellar vesicles, indicating that the diffusion in the cell membrane is reduced not because diffusion per se is slow, but because the cell membrane is compartmentalized with regard to lateral diffusion of phospholipids. Such compartmentalization depends on the actin-based membrane skeleton, but not on the extracellular matrix, extracellular domains of membrane proteins, or cholesterol-enriched rafts. We propose that various transmembrane proteins anchored to the actin-based membrane skeleton meshwork act as rows of pickets that temporarily confine phospholipids.

Plasma membrane compartments, delimited by transmembrane proteins anchored to the membrane skeleton (anchored-protein picket model), would provide the membrane with fundamental mosaicism because they would affect the movement of practically all molecules incorporated in the cell membrane. Understanding such basic compartmentalized structures of the cell membrane is critical for further studies of a variety of membrane functions. Here, using both high temporal-resolution single particle tracking and single fluorescent molecule video imaging of an unsaturated phospholipid, DOPE, we found that plasma membrane compartments generally exist in various cell types, including CHO, HEPA-OVA, PtK2, FRSK, HEK293, HeLa, T24 (ECV304), and NRK cells. The compartment size varies from 30 to 230 nm, whereas the average hop rate of DOPE crossing the boundaries between two adjacent compartments ranges between 1 and 17 ms. The probability of passing a compartment barrier when DOPE is already at the boundary is also cell-type dependent, with an overall variation by a factor of approximately 7. These results strongly indicate the necessity for the paradigm shift of the concept on the plasma membrane: from the two-dimensional fluid continuum model to the compartmentalized membrane model in which its constituent molecules undergo hop diffusion over the compartments.

Adhesion and cytoskeletal structure are intimately related in biological cell function. Even with the vast amount of biological and biochemical data that exist, little is known at the molecular level about physical mechanisms involved in attachments between cells or about consequences of adhesion on the material structure. To expose physical actions at soft biological interfaces, we have combined an ultrasensitive transducer and reflection interference microscopy to image submicroscopic displacements of probe contact with a test surface under minuscule forces. The transducer is a cell-size membrane capsule pressurized by micropipette suction where displacement normal to the membrane under tension is proportional to the applied force. Pressure control of the tension tunes the sensitivity in operation over four orders of magnitude through a range of force from 0.01 pN up to the strength of covalent bonds (approximately 1000 pN)! As the surface probe, a microscopic bead is biochemically glued to the transducer with a densely-bound ligand that is indifferent to the test surface. Movements of the probe under applied force are resolved down to an accuracy of approximately 5 nm from the interference fringe pattern created by light reflected from the bead. With this arrangement, we show that local mechanical compliance of a cell surface can be measured at a displacement resolution set by structural fluctuations. When desired, a second ligand is bound sparsely to the probe for focal adhesion to specific receptors in the test surface. We demonstrate that monitoring fluctuations in probe position at low transducer stiffness enhances detection of molecular adhesion and activation of cytoskeletal structure. Subsequent loading of an attachment tests mechanical response of the receptor-substrate linkage throughout the force-driven process of detachment.

Bond dissociation under steadily rising force occurs most frequently at a time governed by the rate of loading (Evans and Ritchie, 1997 Biophys. J. 72:1541-1555). Multiplied by the loading rate, the breakage time specifies the force for most frequent failure (called bond strength) that obeys the same dependence on loading rate. The spectrum of bond strength versus log(loading rate) provides an image of the energy landscape traversed in the course of unbonding. However, when a weak bond is connected to very compliant elements like long polymers, the load applied to the bond does not rise steadily under constant pulling speed. Because of nonsteady loading, the most frequent breakage force can differ significantly from that of a bond loaded at constant rate through stiff linkages. Using generic models for wormlike and freely jointed chains, we have analyzed the kinetic process of failure for a bond loaded by pulling the polymer linkages at constant speed. We find that when linked by either type of polymer chain, a bond is likely to fail at lower force under steady separation than through stiff linkages. Quite unexpectedly, a discontinuous jump can occur in bond strength at slow separation speed in the case of long polymer linkages. We demonstrate that the predictions of strength versus log(loading rate) can rationalize conflicting results obtained recently for unfolding Ig domains along muscle titin with different force techniques.

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