Force history dependence of receptor-ligand dissociation

Rate theories for biologists

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.

Design rules for biomolecular adhesion: lessons from force measurements

Cell adhesion to matrix, other cells, or pathogens plays a pivotal role in many processes in biomolecular engineering. Early macroscopic methods of quantifying adhesion led to the development of quantitative models of cell adhesion and migration. The more recent use of sensitive probes to quantify the forces that alter or manipulate adhesion proteins has revealed much greater functional diversity than was apparent from population average measurements of cell adhesion. This review highlights theoretical and experimental methods that identified force-dependent molecular properties that are central to the biological activity of adhesion proteins. Experimental and theoretical methods emphasized in this review include the surface force apparatus, atomic force microscopy, and vesicle-based probes. Specific examples given illustrate how these tools have revealed unique properties of adhesion proteins and their structural origins.

Do membrane undulations help cells probe the world?

Cells sense physical properties of their environment including substratum rigidity, roughness, and topography of recognition sites. The cell surface displays continuous deformations of nanometer-scale amplitude and Hz frequency. Recent results support the hypothesis that these surface undulations constitute a powerful strategy for the rapid acquisition of environmental cues: transient contact with surroundings generates forces of piconewton intensity as a result of rapid formation and dissociation of intermolecular bonds. The combination of binding and steric forces is expected to drive conformational changes and lateral reorganization of membrane biomolecules, thus generating signaling cascades. We propose that spontaneous membrane mobility shapes the initial information generated by cell-to-surface contacts, and thereby biases later consequences of these interactions.

Loss of alpha-catenin decreases the strength of single E-cadherin bonds between human cancer cells

The progression of several human cancers correlates with the loss of cytoplasmic protein alpha-catenin from E-cadherin-rich intercellular junctions and loss of adhesion. However, the potential role of alpha-catenin in directly modulating the adhesive function of individual E-cadherin molecules in human cancer is unknown. Here we use single-molecule force spectroscopy to probe the tensile strength, unstressed bond lifetime, and interaction energy between E-cadherins expressed on the surface of live human parental breast cancer cells lacking alpha-catenin and these cells where alpha-catenin is re-expressed. We find that the tensile strength and the lifetime of single E-cadherin/E-cadherin bonds between parental cells are significantly lower over a wide range of loading rates. Statistical analysis of the force displacement spectra reveals that single cadherin bonds between cancer cells feature an exceedingly low energy barrier against tensile forces and low molecular stiffness. Disassembly of filamentous actin using latrunculin B has no significant effect on the strength of single intercellular E-cadherin bonds. The absence of alpha-catenin causes a dominant negative effect on both global cell-cell adhesion and single E-cadherin bond strength. These results suggest that the loss of alpha-catenin alone drastically reduces the adhesive force between individual cadherin pairs on adjoining cells, explain the global loss of cell adhesion in human breast cancer cells, and show that the forced expression of alpha-catenin in cancer cells can restore both higher intercellular avidity and intercellular E-cadherin bond strength.

Theoretical aspects of the biological catch bond

The biological catch bond is fascinating and counterintuitive. When an external force is applied to a catch bond, either in vivo or in vitro, the bond resists breaking and becomes stronger instead. In contrast, ordinary slip bonds, which represent the vast majority of biological and chemical bonds, dissociate faster when subjected to a force. Catch-bond behavior was first predicted theoretically 20 years ago and has recently been experimentally observed in a number of protein receptor-ligand complexes. In this Account, we review the simplest physical-chemical models that lead to analytic expressions for bond lifetime, the concise universal representations of experimental data, and the explicit requirements for catch binding. The phenomenon has many manifestations: increased lifetime with growing constant force is its defining characteristic. If force increases with time, as in jump-ramp experiments, catch binding creates an additional maximum in the probability density of bond rupture force. The new maximum occurs at smaller forces than the slip-binding maximum, merging with the latter at a certain ramp rate in a process resembling a phase transition. If force is applied periodically, as in blood flows, catch-bond properties strongly depend on force frequency. Catch binding results from a complex landscape of receptor-ligand interactions. Bond lifetime can increase if force (i) prevents dissociation through the native pathway and drives the system over a higher energy barrier or (ii) alters protein conformations in a way that strengthens receptor-ligand binding. The bond deformations can be associated with allostery; force-induced conformational changes at one end of the protein propagate to the binding site at the other end. Surrounding water creates further exciting effects. Protein-water tension provides an additional barrier that can be responsible for significant drops in bond lifetimes observed at low forces relative to zero force. This strong dependence of bond properties on weak protein-water interactions may provide universal activation mechanisms in many biological systems and create new types of catch binding. Molecular dynamics simulations provide atomistic insights: the molecular view of bond dissociation gives a foundation for theoretical models and differentiates between alternative interpretations of experimental data. The number of known catch bonds is growing; analogs are found in enzyme catalysis, peptide translocation through nanopores, DNA unwinding, photoinduced dissociation of chemical bonds, and negative thermal expansion of bulk materials, for example. Finer force resolution will likely provide many more. Understanding the properties of catch bonds offers insight into the behavior of biological systems subjected to external perturbations in general.

Atomistic simulation combined with analytic theory to study the response of the P-selectin/PSGL-1 complex to an external force

Steered molecular dynamics simulations are combined with analytic theory in order to gain insights into the properties of the P-selectin/PSGL-1 catch-slip bond at the atomistic level of detail. The simulations allow us to monitor the conformational changes in the P-selectin/PSGL-1 complex in response to an external force, while the theory provides a unified framework bridging the simulation data with experiment over 9 orders of magnitude. The theory predicts that the probability of bond dissociation by the catch mechanism is extremely low in the simulations; however, a few or even a single trajectory can be sufficient for characterization of the slip mechanism. Theoretical analysis of the simulation data shows that the bond responds to the force in a highly nonlinear way, with the bond stiffness changing considerably as a function of the force ramp rate. The Langevin description of the simulation provides spring constants of the proteins and the binding interaction and gives the friction coefficient associated with the receptor-ligand motion in water. The estimated relaxation time shows that the simple probabilistic description is accurate for the experimental regime and remains approximately valid for the high ramp rates used in simulations. The simulations establish that bond deformation occurs primarily within the P-selectin receptor region. The two interaction sites within the binding pocket dissociate sequentially, raising the possibility of observing these independent rupture events in experiment. The stronger interaction that determines the overall properties of the bond dissociates first, indicating that the experimental data indeed capture the main rupture event and not the secondary weaker site rupture. The main rupture event involves the interaction between the calcium ion of the receptor and the ligand residue FUC-623. It is followed by new interactions, supporting the sliding-rebinding behavior observed in the earlier simulation [ Lou, J. Zhu, C. Biophys. J. 2007 , 92 , 1471 - 1485 ]. The weaker binding site shows fewer interaction features, suggesting that the sliding-rebinding behavior may be determined by the unique properties of the calcium site. The agreement between simulation and experiment provided by the two-pathway and deformation models, each containing only four parameters, indicates that the essential physics of the catch-slip bond should be relatively simple and robust over a wide range of pulling regimes.

Atomic force microscopy studies of the initial interactions between fibrinogen and surfaces

Atomic force microscopy (AFM) was used to analyze the interactions between fibrinogen and model surfaces having different levels of water wettability. In contrast to most AFM studies, proteins were coupled to the substrate while model surface colloids were attached to the end of the AFM probe, thereby ensuring that proteins undergo only a single compression/decompression cycle. Similar values of adhesion force were observed between fibrinogen and all of the highly wettable surfaces; in the same manner, fibrinogen showed similar adhesion forces against all poorly wettable surfaces, with a step-like transition observed between the two groups. Relationships between the adhesion forces and loading rates were used to analyze the energy profiles involved in protein/surface interactions. Multiple energy barriers were found in the interaction of proteins with poorly wettable surfaces; whereas a single energy barrier was found for protein interactions with highly wettable surfaces. Contact time-dependent adhesion data were fit to an exponential model and showed that the rate constants of the protein unfolding process on highly wettable surface were smaller at low loading rates, but increased rapidly to yield values similar to those on poorly wettable surfaces at high loading rates. The activation energies of protein unfolding derived from the data offer insight into the role of surface wettability in affecting adhesion, conformational changes, and ultimately, the activity of proteins at biomaterial surfaces.

Surface-bound selectin-ligand binding is regulated by carrier diffusion

Two-dimensional (2D) kinetics of receptor-ligand interactions governs cell adhesion in many biological processes. While the dissociation kinetics of receptor-ligand bond is extensively investigated, the association kinetics has much less been quantified. Recently receptor-ligand interactions between two surfaces were investigated using a thermal fluctuation assay upon biomembrane force probe technique (Chen et al. in Biophys J 94:694-701, 2008). The regulating factors on association kinetics, however, are not well characterized. Here we developed an alternative thermal fluctuation assay using optical trap technique, which enables to visualize consecutive binding-unbinding transition and to quantify the impact of microbead diffusion on receptor-ligand binding. Three selectin constructs (sLs, sPs, and PLE) and their ligand P-selectin glycoprotein ligand 1 were used to conduct the measurements. It was indicated that bond formation was reduced by enhancing the diffusivity of selectin-coupled carrier, suggesting that carrier diffusion is crucial to determine receptor-ligand binding. It was also found that 2D forward rate predicted upon first-order kinetics was in the order of sPs > sLs > PLE and bond formation was history-dependent. These results further the understandings in regulating association kinetics of surface-bound receptor-ligand interactions.

Studying Molecular Interactions at the Single Bond Level with a Laminar Flow Chamber

During the last decade, many investigators developed new methodologies allowing to study ligand-receptor interactions with unprecedented accuracy, up to the single bond level. Reported results include information on bond mechanical properties, association behaviour of surface-attached molecules, and dissection of energy landscapes and reaction pathways. The purpose of the present review is to discuss the potential and limitations of laminar flow chambers operated at low shear rates. This includes a brief review of basic principles, practical tips and problems associated with data interpretation. It is concluded that flow chambers are ideally suited to analyze weak interactions between a number of biomolecules, including the main families of adhesion receptors such as selectins, integrins, cadherins and members of the immunoglobulin superfamily. The sensitivity of the method is limited by the quality of surfaces and efficiency of the studied ligand-receptor couple rather than the hardware. Analyzing interactions with a resolution of a piconewton and a few milliseconds shows that ligand-receptor complexes may experience a number of intermediate binding states, making it necessary to examine the definition of association and dissociation rates. Finally, it is emphasized that association rates measured on surface-bound molecules are highly dependent on parameters unrelated to binding surfaces.

Event-tracking model of adhesion identifies load-bearing bonds in rolling leukocytes

OBJECTIVES

P-selectin binding to P-selectin glycoprotein ligand-1 (PSGL)-1 mediates leukocyte rolling under conditions of inflammation and injury. The aims of this study were to develop an efficient, high temporal resolution model for direct simulation of leukocyte rolling and conduct a study of load-bearing bonds using the model.

MATERIALS AND METHODS

A stochastic pi-calculus-driven event-tracking model of adhesion (ETMA) was developed and compared with experimental data. Multiple simulations for each case were conducted to obtain high-confidence numerical characteristics of leukocyte rolling.

RESULTS

Leukocyte rolling and the underlying P-selectin-PSGL-1 bonds were studied under low wall shear rate (25-50 s(-1)) conditions from measured parameters of leukocyte rolling and bond properties. For the first time, the location, number, lifetime, history, and kinetics of load-bearing bonds and their influence on cell rolling were identified and instantaneous cell displacements, translational and rotational velocities, and cell-substrate distances derived. The model explains the commonly observed "stop-start" type rolling behavior and reveals that a few load-bearing bonds are sufficient to support rolling, while a large number of bonds dissociate before becoming load bearing.

CONCLUSIONS

ETMA provides a method for more precise, direct simulation of leukocyte rolling at low wall shear rates and sets a foundation upon which further refinements can be introduced.

Human neutrophil surface protrusion under a point load: location independence and viscoelasticity

Mechanical properties of neutrophils have been recognized as key contributors to stabilizing neutrophil rolling on the endothelium during the inflammatory response. In particular, accumulating evidence suggests that surface protrusion and tether extraction from neutrophils facilitate stable rolling by relieving the disruptive forces on adhesive bonds. Using a customized optical trap setup, we applied piconewton-level pulling forces on targeted receptors that were located either on the microvillus tip (CD162) or intermicrovillus surface of neutrophils (CD18 and CD44). Under a constant force-loading rate, there always occurred an initial tent-like surface protrusion that was terminated either by rupture of the adhesion or by a "yield" or "crossover" to tether extraction. The corresponding protrusional stiffness of neutrophils was found to be between 0.06 and 0.11 pN/nm, depending on the force-loading rate and the cytoskeletal integrity, but not on the force location, the medium osmolality, nor the temperature increase from 22 degrees C to 37 degrees C. More importantly, we found that neutrophil surface protrusion was accompanied by force relaxation and hysteresis. In addition, the crossover force did not change much in the range of force-loading rates studied, and the protrusional stiffness of lymphocytes was similar to that of neutrophils. These results show that neutrophil surface protrusion is essentially viscoelastic, with a protrusional stiffness that stems primarily from the actin cortex, and the crossover force is independent of the receptor-cytoskeleton interaction.

Beyond structure: mechanism and dynamics of intercellular adhesion

This review summarizes findings from multiple complementary quantitative investigations of adhesion by classical cadherins. The systems investigated range from single molecules to cells, and the approaches used quantify the kinetics, energetics and mechanical strengths of cadherin bonds. The cumulative results demonstrate that cadherins adhere via a multistage binding mechanism that involves multiple extracellular domains. In kinetic measurements of cell adhesion, cell pairs first form a low-probability-binding state with fast kinetics. This is followed by a lag and a slow transition to a second, high-probability, binding state. This two-stage process is independent of the cytoplasmic domain. Studies with domain-deletion mutants demonstrate that the N-terminal domains are required for the first, fast, weak binding. However, the full-ectodomain and EC3 (extracellular repeat 3), in particular, are required to form the second, high-probability, binding state, which is characterized by slow dissociation kinetics and much stronger adhesive bonds. Together, these different studies reveal a more complex multistage binding mechanism than was predicted by structural models.

Low spring constant regulates P-selectin-PSGL-1 bond rupture

Forced dissociation of selectin-ligand bonds is crucial to such biological processes as leukocyte recruitment, thrombosis formation, and tumor metastasis. Although the bond rupture has been well known at high loading rate r(f) (>or=10(2) pN/s), defined as the product of spring constant k and retract velocity v, how the low r(f) (<10(2) pN/s) or the low k regulates the bond dissociation remains unclear. Here an optical trap assay was used to quantify the bond rupture at r(f) <or= 20 pN/s with low k ( approximately 10(-3)-10(-2) pN/nm) when P-selectin and P-selectin glycoprotein ligand 1 (PSGL-1) were respectively coupled onto two glass microbeads. Our data indicated that the bond rupture force f retained the similar values when r(f) increased up to 20 pN/s. It was also found that f varied with different combinations of k and v even at the same r(f). The most probable force, f*, was enhanced with the spring constant when k < 47.0 x 10(-3) pN/nm, indicating that the bond dissociation at low r(f) was spring constant dependent and that bond rupture force depended on both the loading rate and the mechanical compliance of force transducer. These results provide new insights into understanding the P-selectin glycoprotein ligand 1 bond dissociation at low r(f) or k.

What is the biological relevance of the specific bond properties revealed by single-molecule studies?

During the last decade, many authors took advantage of new methodologies based on atomic force microscopy (AFM), biomembrane force probes (BFPs), laminar flow chambers or optical traps to study at the single-molecule level the formation and dissociation of bonds between receptors and ligands attached to surfaces. Experiments provided a wealth of data revealing the complexity of bond response to mechanical forces and the dependence of bond rupture on bond history. These results supported the existence of multiple binding states and/or reaction pathways. Also, single bond studies allowed us to monitor attachments mediated by a few bonds. The aim of this review is to discuss the impact of this new information on our understanding of biological molecules and phenomena. The following points are discussed: (i) which parameters do we need to know in order to predict the behaviour of an encounter between receptors and ligands, (ii) which information is actually yielded by single-molecule studies and (iii) is it possible to relate this information to molecular structure?

How Cells feel their environment: a focus on early dynamic events

It is now well demonstrated that cell adhesion to a foreign surface strongly influences prominent functions such as survival, proliferation, differentiation, migration or mediator release. Thus, a current challenge of major practical and theoretical interest is to understand how cells process and integrate environmental cues to determine future behaviour. The purpose of this review is to summarize some pieces of information that might serve this task. Three sequential points are discussed. First, selected examples are presented to illustrate the influence of substratum chemistry, topography and mechanical properties on nearly all aspects of cell behaviour observed during the days following adhesion. Second, we review reported evidence that long term cell behaviour is highly dependent on the alterations of cell shape and cytoskeletal organization that are often initiated during the minutes to hours following adhesion. Third, we review recently obtained information on cell membrane roughness and dynamics, as well as kinetics and mechanics of molecular interactions. This knowledge is required to understand the influence of substratum structure on cell signaling during the first minute following contact, before the appearance of detectable structural changes. It is suggested that unraveling the earliest phenomena following cell-to-substratum encounter might provide a tractable way of better understanding subsequent events.

Adhesion from tethered ligand-receptor bonds with microsecond lifetimes

According to classical thermodynamics, biological ligand-receptor bonds should have a median lifetime of about 2 ms, and nearly half should have lifetimes of nanoseconds to microseconds. As a result, it is clear that many "weak" bonds are indispensable for cellular adhesion, signaling, and other critical events. However, the forces required to rupture such weak bonds and the adhesion they provide between surfaces are largely unknown because of their propensity to dissociate rapidly from a measuring probe. To measure such weak bond forces quantitatively, we followed nature's example of adhering surfaces with many weak ligand-receptor bonds. Analogously to how multiplicity promotes stronger adhesion between cellular membranes, multiple bonds created significant adhesion between model cellular surfaces. Specifically, we used an automated surface forces apparatus to measure the adhesion between complementary surfaces bearing dense populations of streptavidin receptors and flexible PEG tethers that each anchored a weakly binding ligand (HABA, or 2-(4-hydroxyphenylazo) benzoic acid). We show that this short-lived bond (<100 mus) leads to low forces of dissociation and only a small fraction being simultaneously bound. These results are significant because the HABA-streptavidin bond energy ( approximately 10.5kBT) is similar to the average found in nature (14.7kBT). The measurements exemplify how a single ligand-receptor bond may fall apart and rejoin many times before completing a cellular function yet can still exhibit strength in numbers.

Extending Bell's model: how force transducer stiffness alters measured unbinding forces and kinetics of molecular complexes

Forced unbinding of complementary macromolecules such as ligand-receptor complexes can reveal energetic and kinetic details governing physiological processes ranging from cellular adhesion to drug metabolism. Although molecular-level experiments have enabled sampling of individual ligand-receptor complex dissociation events, disparities in measured unbinding force F(R) among these methods lead to marked variation in inferred binding energetics and kinetics at equilibrium. These discrepancies are documented for even the ubiquitous ligand-receptor pair, biotin-streptavidin. We investigated these disparities and examined atomic-level unbinding trajectories via steered molecular dynamics simulations, as well as via molecular force spectroscopy experiments on biotin-streptavidin. In addition to the well-known loading rate dependence of F(R) predicted by Bell's model, we find that experimentally accessible parameters such as the effective stiffness of the force transducer k can significantly perturb the energy landscape and the apparent unbinding force of the complex for sufficiently stiff force transducers. Additionally, at least 20% variation in unbinding force can be attributed to minute differences in initial atomic positions among energetically and structurally comparable complexes. For force transducers typical of molecular force spectroscopy experiments and atomistic simulations, this energy barrier perturbation results in extrapolated energetic and kinetic parameters of the complex that depend strongly on k. We present a model that explicitly includes the effect of k on apparent unbinding force of the ligand-receptor complex, and demonstrate that this correction enables prediction of unbinding distances and dissociation rates that are decoupled from the stiffness of actual or simulated molecular linkers.

Determination of the shear force at the balance between bacterial attachment and detachment in weak-adherence systems, using a flow displacement chamber

We introduce a procedure for determining shear forces at the balance between attachment and detachment of bacteria under flow. This procedure can be applied to derive adhesion forces in weak-adherence systems, such as polymer brush coatings, which are currently at the center of attention for their control of bacterial adhesion and biofilm formation.

Nonlinear mechanical modeling of cell adhesion

Cell adhesion, which is mediated by the receptor-ligand bonds, plays an essential role in various biological processes. Previous studies often described the force-extension relationship of receptor-ligand bond with linear assumption. However, the force-extension relationship of the bond is intrinsically nonlinear, which should have significant influence on the mechanical behavior of cell adhesion. In this work, a nonlinear mechanical model for cell adhesion is developed, and the adhesive strength was studied at various bond distributions. We find that the nonlinear mechanical behavior of the receptor-ligand bonds is crucial to the adhesive strength and stability. This nonlinear behavior allows more bonds to achieve large bond force simultaneously, and therefore the adhesive strength becomes less sensitive to the change of bond density at the outmost periphery of the adhesive area. In this way, the strength and stability of cell adhesion are soundly enhanced. The nonlinear model describes the cell detachment behavior better than the linear model.

Energy landscape of chelated uranyl: antibody interactions by dynamic force spectroscopy

We used dynamic force spectroscopy (DFS) to explore the energy landscape of interactions between a chelated uranyl compound and a monoclonal antibody raised against the uranyl-dicarboxy-phenanthroline complex. We estimated the potential energy barrier widths and the relevant thermodynamic rate constants along the dissociation coordinate. Using atomic force microscopy, four different experimental setups with or without the uranyl ion in the chelate ligand, we have distinguished specific and nonspecific binding in the binding affinity of the uranyl compound to the antibody. The force loading rates for our system were measured from 15 to 26,400 pN/s. The results showed two regimes in the plot of the most probable unbinding force versus the logarithm of the loading rate, revealing the presence of two (at least) activation barriers. Analyses of DFS suggest parallel multivalent binding present in either regime. We have also built a molecular model for the variable fragment of the antibody and used computational graphics to dock the chelated uranyl ion into the binding pocket. The structural analysis led us to hypothesize that the two regimes originate from two interaction modes: the first one corresponds to an energy barrier with a very narrow width of 0.5 +/- 0.2 A, inferring dissociation of the uranyl ion from its first coordination shell (Asp residue); the second one with a broader energy barrier width (3.9 +/- 0.3 A) infers the entire chelate compound dissociated from the antibody. Our study highlights the sensitivity of DFS experiments to dissect protein-metal compound interactions.

Quantitative measurements of the strength of adhesion of human neutrophils to a substratum in a microfluidic device

We describe a quantitative assay of the strength of adhesion of activated and nonactivated human neutrophils to a substratum, which is carried out in a custom-made microfluidic device. The strength of adhesion is quantified by the fraction of cells remaining adherent (ACF) after a given time of exposure to shear stress in a test microchannel. The microfluidic device is made of two layers of poly(dimethylsiloxane) with integrated membrane valves. This construction allows concurrent testing of two different populations of cells, as well as setting well-defined times of exposure of cells to stress and of their incubation prior to the exposure. The test microchannels have a tapered profile, exposing cells to nearly an order of magnitude range of shear stress. ACF is measured periodically by computer-controlled videomicroscopy scans of the device, with up to 60,000 individual cells identified within a 90 seconds scan. The high throughput of the scans allows reliable quantitative assessment of the ACF. Adhesion of untreated neutrophils and neutrophils activated with formyl-Met-Leu-Phe was tested concurrently in a series of experiments with a fibrinogen-coated glass substratum. At optimized testing conditions, the ACF of activated cells was consistently found to be three times higher than that of nonactivated cells. An adhesion assay could be completed within 11 min from the loading of cells into the device without any intervention by the operator. The proposed device and assay could be used to assess the state of activation of neutrophils in human blood with a potential application to diagnostics of inflammation.

Cellular chemomechanics at interfaces: sensing, integration and response

Living cells are complex entities whose remarkable, emergent capacity to sense, integrate, and respond to environmental cues relies on an intricate series of interactions among the cell's macromolecular components. Defects in mechanosensing, transduction,or responses underlie many diseases such as cancers, immune disorders, cardiac hypertrophy, genetic malformations, and neuropathies. Here, we highlight micro- and nanotechnology-based tools that have been used to study how chemical and mechanical cues modulate the responses of single cells in contact with the extracellular environment. Understanding the physical aspects of these complex processes at the micro- and nanometer scale could produce profound and fundamental new insights into how the processes of cell migration, metastasis, immune function and other areas which are regulated by mechanical forces.

Energy landscape roughness of the streptavidin–biotin interaction

Molecular interactions between receptors and ligands can be characterized by their free energy landscape. In its simplest representation, the energy landscape is described by a barrier of certain height and width that determines the dissociation rate of the complex, as well as its dynamic strength. Some interactions, however, require a more complex landscape with additional barriers and roughness along the reaction coordinate. This roughness slows down the dissociation kinetics of the interaction and contributes to its dynamic strength. The streptavidin-biotin complex has been extensively studied due to its remarkably low dissociation kinetics. However, single molecule measurements from independent experiments showed scattered and disparate results. In this work, the energy landscape roughness of the streptavidin-biotin interaction was estimated to be in the range of 5-8kBT using dynamic force spectroscopy (DFS) measurements at three different temperatures. These results can be used to explain both its slow dissociation kinetics and the discrepancies in the reported force measurements.

Universal laws in the force-induced unraveling of biological bonds

Universal laws in the force-induced unbinding of receptor-ligand complexes are established for a general functional dependence of the dissociation rate constant on the applied force and are detailed with the two-pathway model that describes the recently discovered biological catch bond. The relationships link the data obtained with constant and time-dependent forces in different regimes, provide common representation for the previously unrelated data sets, and, thereby, greatly facilitate analysis and interpretation of experiments. The universal laws are demonstrated with the monomeric and dimeric catch-slip bonds between P-selectins and P-selectin glycoprotein ligands-1, and the slip bond between E-selectin and sialyl Lewis;{x} antigen.

Adhesive dynamics simulations of the shear threshold effect for leukocytes

Many experiments have measured the effect of force on the dissociation of single selectin bonds, but it is not yet clear how the force dependence of molecular dissociation can influence the rolling of cells expressing selectin molecules. Recent experiments using constant-force atomic force microscopy or high-resolution microscopic observations of pause-time distributions of cells in a flow chamber show that for some bonds, the dissociation rate is high at low force and initially decreases with force, indicating a catch bond. As the force continues to increase, the dissociation rate increases again, like a slip bond. It has been proposed that this catch-slip bond leads to the shear threshold effect, in which a certain level of shear rate is required to achieve rolling. We have incorporated a catch-slip dissociation rate into adhesive dynamics simulations of cell rolling. Using a relatively simple model for the shear-controlled association rate for selectin bonds, we were able to recreate characteristics of the shear threshold effect seen most prominently for rolling through L-selectin. The rolling velocity as a function of shear rate showed a minimum near 100 s-1. Furthermore, cells were observed to roll at a shear rate near the threshold, but detach and move more quickly when the shear rate was dropped below the threshold. Finally, using adhesive dynamics, we were able to determine ranges of parameters necessary to see the shear threshold effect in the rolling velocity. In summary, we found through simulation that the catch-slip behavior of selectin bonds can be responsible for the shear threshold effect.

Force modulating dynamic disorder: a physical model of catch-slip bond transitions in receptor-ligand forced dissociation experiments

Recent experiments found that some adhesive receptor-ligand complexes have counterintuitive catch-slip transition behaviors: the mean lifetimes of these complexes first increase (catch) with initial application of a small external force, and then decrease (slip) when the force is beyond some threshold. In this work we suggest that the forced dissociation of these complexes might be a typical rate process with dynamic disorder. The one-dimensional force modulating Agmon-Hopfield model is used to describe the transitions in the single-bond P-selectin glycoprotein ligand 1-P-selectin forced dissociation experiments, which were respectively performed in the constant force [Marshall, Nature (Landon) 423, 190 (2003)] and the ramping force [Evans, Proc. Natl. Acad. Sci. U.S.A 98, 11281 (2004)] modes. We find that, an external force can not only accelerate the bond dissociation, but also modulate the complex from the lower-energy barrier to the higher one; the catch-slip bond transition can arise from a particular energy barrier shape. The agreement between our calculation and the experimental data is satisfactory.

Dynamic force spectroscopy of E. coli P pili

Surface organelles (so-called pili) expressed on the bacterial membrane mediate the adhesion of Escherichia coli causing urinary tract infection. These pili possess some extraordinary elongation properties that are assumed to allow a close bacterium-to-host contact even in the presence of shear forces caused by urine flow. The elongation properties of P pili have therefore been assessed for low elongation speeds (steady-state conditions). This work reports on the behavior of P pili probed by dynamic force spectroscopy. A kinetic model for the unfolding of a helixlike chain structure is derived and verified. It is shown that the unfolding of the quaternary structure of the PapA rod takes place at a constant force that is almost independent of elongation speed for slow elongations (up to approximately 0.4 mum/s), whereas it shows a dynamic response with a logarithmic dependence for fast elongations. The results provide information about the energy landscape and reaction rates. The bond length and thermal bond opening and closure rates for the layer-to-layer bond have been assessed to approximately 0.76 nm, approximately 0.8 Hz, and approximately 8 GHz, respectively. The results also support a previously constructed sticky-chain model for elongation of the PapA rod that until now had been experimentally verified only under steady-state conditions.

Development of glutathione-coupled cantilever for the single-molecule force measurement by scanning force microscopy

The accuracy and the fidelity of a single-molecule force measurement largely rely on how the molecule of interest is attached to the solid substrate surface (bead, cantilever, cover glass and etc.). A site-specific attachment of a protein without affecting its structure and enzymatic function has been a major concern. Here, we established a glutathione-coupled cantilever to which any glutathione S-transferase (GST)-fused proteins can be attached in a desired direction. The rupture force between glutathione and GST was approximately 100 pN on average. By using this cantilever, we succeeded in measuring the interaction force between importin alpha and importin beta.

Mechanics of actomyosin bonds in different nucleotide states are tuned to muscle contraction

Muscle contraction and many other cell movements are driven by cyclic interactions between actin filaments and the motor enzyme myosin. Conformational changes in the actin-myosin binding interface occur in concert with the binding of ATP, binding to actin, and loss of hydrolytic by-products, but the effects of these conformational changes on the strength of the actomyosin bond are unknown. The force-dependent kinetics of the actomyosin bond may be particularly important at high loads, where myosin may detach from actin before achieving its full power stroke. Here we show that over a physiological range of rapidly applied loads, actomyosin behaves as a "catch" bond, characterized by increasing lifetimes with increasing loads up to a maximum at approximately 6 pN. Surprisingly, we found that the myosin-ADP bond is possessed of longer lifetimes under load than rigor bonds, although the load at which bond lifetime is maximal remains unchanged. We also found that actomyosin bond lifetime is ultimately dependent not only on load, but loading history as well. These data suggest a complex relationship between the rate of actomyosin dissociation and muscle force and shortening velocity. The 6-pN load for maximum bond lifetime is near the force generated by a single myosin molecule during isometric contraction. This raises the possibility that all catch bonds between load-bearing molecules are "mechanokinetically" tuned to their physiological environment.

Dissociation of biological catch-bond by periodic perturbation

The analysis of the P-selectin/PSGL-1 catch-slip bond that is periodically driven by a detaching force predicts that in the frequency range on the order of 1 s(-1) the bond lifetime undergoes significant changes with respect to both frequency and amplitude of the force. The result indicates how variations in the heart rate could have a substantial effect on leukocyte and lymphoid cell transport and adhesion to endothelial cells and platelets during inflammatory processes.

Force-induced deformations and stability of biological bonds

A deformation model of the forced-induced dissociation of biological bonds is developed. A simple illustration shows that protein deformations can change the receptor-ligand interaction linearly with applied force at small forces, either increasing or decreasing the bond stability, and that a minor external work can lead to notable changes in the interaction energy. The deformation-induced increase of bond stability is illustrated with the remarkable catch-bond phenomenon in P and L selections. Additionally, the model rationalizes the frequently seen disparity between the bond dissociation rates of many free complexes and the zero-force asymptotic rates measured by force spectroscopy.

Catch-bond model derived from allostery explains force-activated bacterial adhesion

High shear enhances the adhesion of Escherichia coli bacteria binding to mannose coated surfaces via the adhesin FimH, raising the question as to whether FimH forms catch bonds that are stronger under tensile mechanical force. Here, we study the length of time that E. coli pause on mannosylated surfaces and report a double exponential decay in the duration of the pauses. This double exponential decay is unlike previous single molecule or whole cell data for other catch bonds, and indicates the existence of two distinct conformational states. We present a mathematical model, derived from the common notion of chemical allostery, which describes the lifetime of a catch bond in which mechanical force regulates the transitions between two conformational states that have different unbinding rates. The model explains these characteristics of the data: a double exponential decay, an increase in both the likelihood and lifetime of the high-binding state with shear stress, and a biphasic effect of force on detachment rates. The model parameters estimated from the data are consistent with the force-induced structural changes shown earlier in FimH. This strongly suggests that FimH forms allosteric catch bonds. The model advances our understanding of both catch bonds and the role of allostery in regulating protein activity.

The solution to the streptavidin-biotin paradox: the influence of history on the strength of single molecular bonds

In the past few years, many studies have attempted to measure the strength of a single molecular bond. In general, these experiments consisted in pulling on the bond and measuring the force necessary to dissociate the molecules. However, seemingly contradictory experimental results led to draw the intriguing conclusion that the strength of the bond could depend on the experiment even if the pulling conditions are similar: this paradox was first observed on the widely used streptavidin-biotin bond. Here, by doing supplementary measurements and by reanalyzing the controversial experimental results using Kramers' theory, we show that they can be conciliated. This allows us to show that the strength of a bond is very sensitive to the history of its formation, which is the key to the paradox.

Neutrophil-bead collision assay: pharmacologically induced changes in membrane mechanics regulate the PSGL-1/P-selectin adhesion lifetime

Visualization of flowing neutrophils colliding with adherent 1-mum-diameter beads presenting P-selectin allowed the simultaneous measurement of collision efficiency (epsilon), membrane tethering fraction (f), membrane tether growth dynamics, and PSGL-1/P-selectin binding lifetime. For 1391 collisions analyzed over venous wall shear rates from 25 to 200 s(-1), epsilon decreased from 0.17 to 0.004, whereas f increased from 0.15 to 0.70, and the average projected membrane tether length, L(tether)(m), increased from 0.35 mum to approximately 2.0 mum over this shear range. At all shear rates tested, adhesive collisions lacking membrane tethers had average bond lifetimes less than those observed for collisions with tethers. For adhesive collisions that failed to form membrane tethers, the regressed Bell parameters (consistent with single bond Monte Carlo simulation) were zero-stress off-rate, k(off)(0) = 0.56 s(-1) and reactive compliance, r = 0.10 nm, similar to published atomic force microscopy (AFM) measurements. For all adhesion events (+/- tethers), the bond lifetime distributions were more similar to those obtained by rolling assay and best simulated by Monte Carlo with the above Bell parameters and an average of 1.48 bonds (n = 1 bond (67%), n = 2 (22%), and n = 3-5 (11%)). For collisions at 100 s(-1), pretreatment of neutrophils with actin depolymerizing agents, latrunculin or cytochalasin D, had no effect on epsilon, but increased L(tether)(m) by 1.74- or 2.65-fold and prolonged the average tether lifetime by 1.41- or 1.65-fold, respectively. Jasplakinolide, an actin polymerizing agent known to cause blebbing, yielded results similar to the depolymerizing agents. Conversely, cholesterol-depletion with methyl-beta-cyclodextrin or formaldehyde fixation had no effect on epsilon, but reduced L(tether)(m) by 66% or 97% and reduced the average tether lifetime by 30% or 42%, respectively. The neutrophil-bead collision assay combines advantages of atomic force microscopy (small contact zone), aggregometry (discrete interactions), micropipette manipulation (tether visualization), and rolling assays (physiologic flow loading). Membrane tether growth can be enhanced or reduced pharmacologically with consequent effects on PSGL-1/P-selectin lifetimes.