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

Catch Bonds in Immunology

Catch bonds are molecular bonds that last longer under force than slip bonds, which become shorter-lived under force. Although catch bonds were initially discovered in studies of leukocyte and bacterial adhesions two decades ago, they have since been found in many other contexts, including platelet binding to blood vessel walls during clotting, structural support within the cell and between cells, force transmission in the cell's machineries for motility and mechanotransduction, viral infection of host cells, and immunoreceptor mechanosensing. Catch bonds are strengthened by increasing force, which induces structural changes in one or both interacting molecules either locally or allosterically to enable additional contacts at their binding interface, thus lengthening bond lifetimes. They can be modeled by the kinetics of a system escaping from the energy well(s) of the bound state(s) over the energy barrier(s) to the free state by traversing along the dissociation path(s) across a hilly energy landscape modulated by force. Catch bond studies are important for understanding the mechanics of biological systems and developing treatment strategies for infectious diseases, immune disorders, cancer, and other ailments.

Cardiac desmosomal adhesion relies on ideal-, slip- and catch bonds

The cardiac muscle consists of individual cardiomyocytes that are mechanically linked by desmosomes. Desmosomal adhesion is mediated by densely packed and organized cadherins which, in presence of Ca2+, stretch out their extracellular domains (EC) and dimerize with opposing binding partners by exchanging an N-terminal tryptophan. The strand-swap binding motif of cardiac cadherins like desmocollin 2 (Dsc2) (and desmoglein2 alike) is highly specific but of low affinity with average bond lifetimes in the range of approximately 0.3 s. Notably, despite this comparatively weak interaction, desmosomes mediate a stable, tensile-resistant bond. In addition, force mediated dissociation of strand-swap dimers exhibit a reduced bond lifetime as external forces increase (slip bond). Using atomic force microscopy based single molecule force spectroscopy (AFM-SMFS), we demonstrate that Dsc2 has two further binding modes that, in addition to strand-swap dimers, most likely play a significant role in the integrity of the cardiac muscle. At short interaction times, the Dsc2 monomers associate only loosely, as can be seen from short-lived force-independent bonds. These ideal bonds are a precursor state and probably stabilize the formation of the self-inhibiting strand-swap dimer. The addition of tryptophan in the measurement buffer acts as a competitive inhibitor, preventing the N-terminal strand exchange. Here, Dsc2 dimerizes as X-dimer which clearly shows a tri-phasic slip-catch-slip type of dissociation. Within the force-mediated transition (catch) regime, Dsc2 dimers switch between a rather brittle low force and a strengthened high force adhesion state. As a result, we can assume that desmosomal adhesion is mediated not only by strand-swap dimers (slip) but also by their precursor states (ideal bond) and force-activated X-dimers (catch bond).

Exploring the Sulfatase 1 Catch Bond Free Energy Landscape using Jarzynski's Equality

In non-covalent biological adhesion, molecular bonds commonly exhibit a monotonously decreasing life time when subjected to tensile forces (slip bonds). In contrast, catch bonds behave counter intuitively, as they show an increased life time within a certain force interval. To date only a hand full of catch bond displaying systems have been identified. In order to unveil their nature, a number of structural and phenomenological models have been introduced. Regardless of the individual causes for catch bond behavior, it appears evident that the free energy landscapes of these interactions bear more than one binding state. Here, we investigated the catch bond interaction between the hydrophilic domain of the human cell surface sulfatase 1 (Sulf1HD) and its physiological substrate heparan sulfate (HS) by atomic force microscopy based single molecule force spectroscopy (AFM-SMFS). Using Jarzynski’s equality, we estimated the associated Gibbs free energy and provide a comprehensive thermodynamic and kinetic characterization of Sulf1HD/HS interaction. Interestingly, the binding potential landscape exhibits two distinct potential wells which confirms the recently suggested two state binding. Even though structural data of Sulf1HD is lacking, our results allow to draft a detailed picture of the directed and processive desulfation of HS.

Measuring Force-Induced Dissociation Kinetics of Protein Complexes Using Single-Molecule Atomic Force Microscopy

Proteins respond to mechanical force by undergoing conformational changes and altering the kinetics of their interactions. However, the biophysical relationship between mechanical force and the lifetime of protein complexes is not completely understood. In this chapter, we provide a step-by-step tutorial on characterizing the force-dependent regulation of protein interactions using in vitro and in vivo single-molecule force clamp measurements with an atomic force microscope (AFM). While we focus on the force-induced dissociation of E-cadherins, a critical cell-cell adhesion protein, the approaches described here can be readily adapted to study other protein complexes. We begin this chapter by providing a brief overview of theoretical models that describe force-dependent kinetics of biomolecular interactions. Next, we present step-by-step methods for measuring the response of single receptor-ligand bonds to tensile force in vitro. Finally, we describe methods for quantifying the mechanical response of single protein complexes on the surface of living cells. We describe general protocols for conducting such measurements, including sample preparation, AFM force clamp measurements, and data analysis. We also highlight critical limitations in current technologies and discuss solutions to these challenges.

Rate turnover in mechano-catalytic coupling: A model and its microscopic origin

A novel aspect in the area of mechano-chemistry concerns the effect of external forces on enzyme activity, i.e., the existence of mechano-catalytic coupling. Recent experiments on enzyme-catalyzed disulphide bond reduction in proteins under the effect of a force applied on the termini of the protein substrate reveal an unexpected biphasic force dependence for the bond cleavage rate. Here, using atomistic molecular dynamics simulations combined with Smoluchowski theory, we propose a model for this behavior. For a broad range of forces and systems, the model reproduces the experimentally observed rates by solving a reaction-diffusion equation for a "protein coordinate" diffusing in a force-dependent effective potential. The atomistic simulations are used to compute, from first principles, the parameters of the model via a quasiharmonic analysis. Additionally, the simulations are also used to provide details about the microscopic degrees of freedom that are important for the underlying mechano-catalysis.

Catch bond interaction between cell-surface sulfatase Sulf1 and glycosaminoglycans

In biological adhesion, the biophysical mechanism of specific biomolecular interaction can be divided in slip and catch bonds, respectively. Conceptually, slip bonds exhibit a reduced bond lifetime under increased external force and catch bonds, in contrast, exhibit an increased lifetime (for a certain force interval). Since 2003, a handful of biological systems have been identified to display catch bond properties. Upon investigating the specific interaction between the unique hydrophilic domain (HD) of the human cell-surface sulfatase Sulf1 against its physiological glycosaminoglycan (GAG) target heparan sulfate (HS) by single molecule force spectroscopy (SMFS), we found clear evidence of catch bond behavior in this system. The HD, ∼320 amino acids long with dominant positive charge, and its interaction with sulfated GAG-polymers were quantitatively investigated using atomic force microscopy (AFM) based force clamp spectroscopy (FCS) and dynamic force spectroscopy (DFS). In FCS experiments, we found that the catch bond character of HD against GAGs could be attributed to the GAG 6-O-sulfation site whereas only slip bond interaction can be observed in a GAG system where this site is explicitly lacking. We interpreted the binding data within the theoretical framework of a two state two path model, where two slip bonds are coupled forming a double-well interaction potential with an energy difference of ΔE ≈ 9 kBT and a compliance length of Δx ≈ 3.2 nm. Additional DFS experiments support this assumption and allow identification of these two coupled slip-bond states that behave consistently within the Kramers-Bell-Evans model of force-mediated dissociation.

Biomechanics of cell adhesion: how force regulates the lifetime of adhesive bonds at the single molecule level

Cell adhesion proteins play critical roles in positioning cells during development, segregating cells into distinct tissue compartments and in maintaining tissue integrity. The principle function of these proteins is to bind cells together and resist mechanical force. Adhesive proteins also enable migrating cells to adhere and roll on surfaces even in the presence of shear forces exerted by fluid flow. Recently, several experimental and theoretical studies have provided quantitative insights into the physical mechanisms by which adhesion proteins modulate their unbinding kinetics in response to tensile force. This perspective reviews these biophysical investigations. We focus on single molecule studies of cadherins, selectins, integrins, the von Willebrand factor and FimH adhesion proteins; the effect of mechanical force on the lifetime of these interactions has been extensively characterized. We review both theoretical models and experimental investigations and discuss future directions in this exciting area of research.

Resolving the molecular mechanism of cadherin catch bond formation

Classical cadherin Ca(2+)-dependent cell-cell adhesion proteins play key roles in embryogenesis and in maintaining tissue integrity. Cadherins mediate robust adhesion by binding in multiple conformations. One of these adhesive states, called an X-dimer, forms catch bonds that strengthen and become longer lived in the presence of mechanical force. Here we use single-molecule force-clamp spectroscopy with an atomic force microscope along with molecular dynamics and steered molecular dynamics simulations to resolve the molecular mechanisms underlying catch bond formation and the role of Ca(2+) ions in this process. Our data suggest that tensile force bends the cadherin extracellular region such that they form long-lived, force-induced hydrogen bonds that lock X-dimers into tighter contact. When Ca(2+) concentration is decreased, fewer de novo hydrogen bonds are formed and catch bond formation is eliminated.

Mechanochemitry: a molecular biomechanics view of mechanosensing

Molecular biomechanics includes two themes: the study of mechanical aspects of biomolecules and the study of molecular biology of the cell using mechanical tools. The two themes are interconnected for obvious reasons. The present review focuses on one of the interconnected areas-the mechanical regulation of molecular interaction and conformational change. Recent conceptual developments are summarized, including catch bonds, regulation of molecular interaction by the history of force application, and cyclic mechanical reinforcement. These studies elucidate the mechanochemistry of some of the candidate mechanosensing molecules, thereby providing a natural connection to mechanobiology.

The two-pathway model of the biological catch-bond as a limit of the allosteric model

Catch-binding is a counterintuitive phenomenon in which the lifetime of a receptor/ligand bond increases when a force is applied to break the bond. Several mechanisms have been proposed to rationalize catch-binding. In the two-pathway model, the force drives the system away from its native dissociation pathway into an alternative pathway involving a higher energy barrier. Here, we analyze an allosteric model suggesting that a force applied to the complex alters the distribution of receptor conformations, and as a result, induces changes in the ligand-binding site. The model assumes explicitly that the allosteric transitions govern the properties of the ligand site. We demonstrate that the dynamics of the ligand is described by two relaxation times, one of which arises from the allosteric site. Therefore, we argue that one can characterize the allosteric transitions by studying the receptor/ligand binding. We show that the allosteric description reduces to the two-pathway model in the limit when the allosteric transitions are faster than the bond dissociation. The formal results are illustrated with two systems, P-selectin/PSGL-1 and FimH/mannose, subjected to both constant and time-dependent forces. The report advances our understanding of catch-binding by combining alternative physical models into a unified description and makes the problem more tractable for the bond mechanics community.

Polymer-based catch-bonds

Catch-bonds refer to the counterintuitive notion that the average lifetime of a bond has a maximum at a nonzero applied force. They have been found in several ligand-receptor pairs and their origin is still a topic of debate. Here, we use coarse-grained simulations and kinetic theory to demonstrate that a multimeric protein, with self-interacting domain pairs, can display catch-bond behavior. Our model is motivated by one of the largest proteins in the human body, the von Willebrand Factor, which has been found to display this behavior. In particular, our model polymer consists of a series of repeating units that self-interact with their nearest neighbors along the chain. Each of the units mimics a domain of the protein. Apart from the short-range specific interaction, we also include a linker chain that will hold the domains together if unbinding occurs. This linker molecule represents the sequence of unfolded amino acids that connect contiguous domains, as is typically found in multidomain proteins. The units also interact with an immobilized ligand, but the interaction is masked by the presence of the self-interacting neighbor along the chain. Our results show that this model displays all the features of catch-bonds because the average lifetime of a binding event between the polymer and the immobilized receptor has a maximum at a nonzero pulling force of the polymer. The effects of the energy barriers for detaching the masking domain and the ligand from the binding domain, as well as the effects of the properties of the polypeptide chain connecting the contiguous domains, are also studied. Our study suggests that multimeric proteins can engage in catch-bonds if their self-interactions are carefully tuned, and this mechanism presumably plays a major role in the mechanics of extracellular proteins that share a multidomain character. Furthermore, our biomimetic design clearly shows how one could build and tune macromolecules that exhibit catch-bond characteristics.

Regulation of catch binding by allosteric transitions

An allosteric model is used to describe changes in lifetimes of biological receptor-ligand bonds subjected to an external force. Force-induced transitions between the two states of the allosteric site lead to changes in the receptor conformation. The ligand bound to the receptor fluctuates between two different potentials formed by the two receptor conformations. The effect of the force on the receptor-ligand interaction potential is described by the Bell mechanism. The probability of detecting the ligand in the bound state is found to depend on the relaxation times of both ligand and allosteric sites. An analytic expression for the bond lifetime is derived as a function of force. The formal theoretical results are used to explain the anomalous force and time dependences of the integrin-fibronectin bond lifetimes measured by atomic force microscopy (Kong, F.; et al J. Cell Biol. 2009, 185, 1275-1284). The analytic expression and model parameters describe very well all anomalous dependences identified in the experiments.

Analyzing single-bond experiments: influence of the shape of the energy landscape and universal law between the width, depth, and force spectrum of the bond

Experimentalists who measure the rupture force of a single molecular bond usually pull on that bond at a constant speed, keeping the loading rate r=df/dt constant. The challenge is to extract the energy landscape of the interaction between the two molecules involved from the experimental rupture force distribution under several loading rates. This analysis requires the use of a model for the shape of this energy landscape. Several barriers can compose the landscape, though molecular bonds with a single barrier are often observed. The Bell model is commonly used for the analysis of rupture force measurements with bonds displaying a single barrier. It provides an analytical expression of the most likely rupture force which makes it very simple to use. However, in principle, it can only be applied to landscapes with extrema whose positions do not vary under force. Here, we evaluate the general relevance of the Bell model by comparing it with another analytical model for which the landscape is harmonic in the vicinity of its extrema. Similar shapes of force distributions are obtained with both models, making it difficult to confirm the validity of the Bell model for a given set of experimental data. Nevertheless, we show that the analysis of rupture force experiments on such harmonic landscapes with the Bell model provides excellent results in most cases. However, numerical computation of the distributions of the rupture forces on piecewise-linear energy landscapes indicates that the blind use of any model such as the Bell model may be risky, since there often exist several landscapes compatible with a given set of experimental data. Finally, we derive a universal relation between the range and energy of the bond and the force spectrum. This relation does not depend on the shape of the energy landscape and can thus be used to characterize unambiguously any one-barrier landscape from experiments. All the results are illustrated with the streptavidin-biotin bond.