Understanding the catch-bond kinetics of biomolecules on a one-dimensional energy landscape

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.

Bidirectional Allostery Mechanism in Catch-Bond Formation of CD44 Mediated Cell Adhesion

Catch-bonds, whereby noncovalent ligand-receptor interactions are counterintuitively reinforced by tensile forces, play a major role in cell adhesion under mechanical stress. A basic prerequisite for catch-bond formation, as implicated in classic catch-bond models, is that force-induced remodeling of the ligand binding interface occurs prior to bond rupture. However, what strategy receptor proteins utilize to meet such specific kinetic control remains elusive. Here we report a bidirectional allostery mechanism of catch-bond formation based on theoretical and molecular dynamics simulation studies. Binding of ligand allosterically reduces the threshold force for unlocking of otherwise stably folded force-sensing element (i.e., forward allostery), so that a much smaller tensile force can trigger the conformational switching of receptor protein to high binding-strength state via backward allosteric coupling before bond rupture. Such bidirectional allostery fulfills the specific kinetic control required by catch-bond formation and is likely to be commonly utilized in cell adhesion. The essential thermodynamic and kinetic features of receptor proteins essential for catch-bond formation were identified.

Mechanochemistry: Fundamental Principles and Applications

Mechanochemistry is an emerging research field at the interface of physics, mechanics, materials science, and chemistry. Complementary to traditional activation methods in chemistry, such as heat, electricity, and light, mechanochemistry focuses on the activation of chemical reactions by directly or indirectly applying mechanical forces. It has evolved as a powerful tool for controlling chemical reactions in solid state systems, sensing and responding to stresses in polymer materials, regulating interfacial adhesions, and stimulating biological processes. By combining theoretical approaches, simulations and experimental techniques, researchers have gained intricate insights into the mechanisms underlying mechanochemistry. In this review, the physical chemistry principles underpinning mechanochemistry are elucidated and a comprehensive overview of recent significant achievements in the discovery of mechanically responsive chemical processes is provided, with a particular emphasis on their applications in materials science. Additionally, The perspectives and insights into potential future directions for this exciting research field are offered.

Theory and Examples of Catch Bonds

We discuss slip bonds, catch bonds, and the tug-of-war mechanism using mathematical arguments. The aim is to explain the theoretical tool of molecular potential energy surfaces (PESs). For this, we propose simple 2-dimensional surface models to demonstrate how a molecule under an external force behaves. Examples are selectins. Catch bonds, in particular, are explained in more detail, and they are contrasted to slip bonds. We can support special two-dimensional molecular PESs for E- and L-selectin which allow the catch bond property. We demonstrate that Newton trajectories (NT) are powerful tools to describe these phenomena. NTs form the theoretical background of mechanochemistry.

Unraveling the Dual-Stretch-Mode Impact on Tension Gauge Tethers' Mechanical Stability

Tension gauge tethers (TGTs), short DNA segments serving as extracellular tension sensors, are instrumental in assessing the tension dynamics in mechanotransduction. These TGTs feature an initial shear-stretch region and an unzip-stretch region. Despite their utility, no theoretical model has been available to estimate their tension-dependent lifetimes [τ(f)], restricting insights from cellular mechanotransduction experiments. We have now formulated a concise expression for τ(f) of TGTs, accommodating contributions from both stretch regions. Our model uncovers a tension-dependent energy barrier shift occurring when tension surpasses a switching force of approximately 13 pN for the recently developed TGTs, greatly influencing τ(f) profiles. Experimental data from several TGTs validated our model. The calibrated expression can predict τ(f) of TGTs at 37 °C based on their sequences with minor fold changes, supporting future applications of TGTs.

Catch bond models may explain how force amplifies TCR signaling and antigen discrimination

The TCR integrates forces in its triggering process upon interaction with pMHC. Force elicits TCR catch-slip bonds with strong pMHCs but slip-only bonds with weak pMHCs. We develop two models and apply them to analyze 55 datasets, demonstrating the models' ability to quantitatively integrate and classify a broad range of bond behaviors and biological activities. Comparing to a generic two-state model, our models can distinguish class I from class II MHCs and correlate their structural parameters with the TCR/pMHC's potency to trigger T cell activation. The models are tested by mutagenesis using an MHC and a TCR mutated to alter conformation changes. The extensive comparisons between theory and experiment provide model validation and testable hypothesis regarding specific conformational changes that control bond profiles, thereby suggesting structural mechanisms for the inner workings of the TCR mechanosensing machinery and plausible explanations of why and how force may amplify TCR signaling and antigen discrimination.

Mechanical Stabilization of a Bacterial Adhesion Complex

The adhesions between Gram-positive bacteria and their hosts are exposed to varying magnitudes of tensile forces. Here, using an ultrastable magnetic tweezer-based single-molecule approach, we show the catch-bond kinetics of the prototypical adhesion complex of SD-repeat protein G (SdrG) to a peptide from fibrinogen β (Fgβ) over a physiologically important force range from piconewton (pN) to tens of pN, which was not technologically accessible to previous studies. At 37 °C, the lifetime of the complex exponentially increases from seconds at several pN to ∼1000 s as the force reaches 30 pN, leading to mechanical stabilization of the adhesion. The dissociation transition pathway is determined as the unbinding of a critical β-strand peptide (“latch” strand of SdrG that secures the entire adhesion complex) away from its binding cleft, leading to the dissociation of the Fgβ ligand. Similar mechanical stabilization behavior is also observed in several homologous adhesions, suggesting the generality of catch-bond kinetics in such bacterial adhesions. We reason that such mechanical stabilization confers multiple advantages in the pathogenesis and adaptation of bacteria.

Unexpected Low Mechanical Stability of Titin I27 Domain at Physiologically Relevant Temperature

The extensively studied immunoglobulin (Ig) domain I27 of the giant force-bearing protein titin has provided a basis for our current understanding of the structural stability, dynamics, and function of the numerous mechanically stretched Ig domains in the force-bearing I-band of titin. The current consensus is that titin I27 has a high mechanical stability characterized by very low unfolding rate (<10^-3 s^-1) in physiological force range and high unfolding forces (>100 pN) at typical physiological force loading rates from experiments at typical laboratory temperatures. Here, we report that when the temperature is increased from 23 to 37 °C, the unfolding rate of I27 drastically increases by ∼100-fold at the physiological level of forces, indicating a low mechanical stability of I27 at physiological conditions. The result provides new insights into the structural states and the associated functions of I27 and other similar titin I-band Ig domains.

Hidden Intermediate State and Second Pathway Determining Folding and Unfolding Dynamics of GB1 Protein at Low Forces

Atomic force microscopy experiments found that GB1, a typical two-state model protein used for study of folding and unfolding dynamics, can sustain forces of more than 100 pN, but its response to low forces still remains unclear. Using ultrastable magnetic tweezers, we discovered that GB1 has an unexpected nonmonotonic force-dependent unfolding rate at 5-160 pN, from which a free energy landscape with two main barriers and a hidden intermediate state was constructed. A model combining two separate models by Dudko et al. with two pathways between the native state and this intermediate state is proposed to rebuild the unfolding dynamics over the full experimental force range. One candidate of this transient intermediate state is the theoretically proposed molten globule state with a loosely collapsed conformation, which might exist universally in the folding and unfolding processes of two-state proteins.

Structural basis of αE-catenin-F-actin catch bond behavior

Cell-cell and cell-matrix junctions transmit mechanical forces during tissue morphogenesis and homeostasis. α-Catenin links cell-cell adhesion complexes to the actin cytoskeleton, and mechanical load strengthens its binding to F-actin in a direction-sensitive manner. Specifically, optical trap experiments revealed that force promotes a transition between weak and strong actin-bound states. Here, we describe the cryo-electron microscopy structure of the F-actin-bound αE-catenin actin-binding domain, which in solution forms a five-helix bundle. In the actin-bound structure, the first helix of the bundle dissociates and the remaining four helices and connecting loops rearrange to form the interface with actin. Deletion of the first helix produces strong actin binding in the absence of force, suggesting that the actin-bound structure corresponds to the strong state. Our analysis explains how mechanical force applied to αE-catenin or its homolog vinculin favors the strongly bound state, and the dependence of catch bond strength on the direction of applied force.

Modulating mechanical stability of heterodimerization between engineered orthogonal helical domains

Mechanically stable specific heterodimerization between small protein domains have a wide scope of applications, from using as a molecular anchorage in single-molecule force spectroscopy studies of protein mechanics, to serving as force-bearing protein linker for modulation of mechanotransduction of cells, and potentially acting as a molecular crosslinker for functional materials. Here, we explore the possibility to develop heterodimerization system with a range of mechanical stability from a set of recently engineered helix-heterotetramers whose mechanical properties have yet to be characterized. We demonstrate this possibility using two randomly chosen helix-heterotetramers, showing that their mechanical properties can be modulated by changing the stretching geometry and the number of interacting helices. These helix-heterotetramers and their derivatives are sufficiently stable over physiological temperature range. Using it as mechanically stable anchorage, we demonstrate the applications in single-molecule manipulation studies of the temperature dependent unfolding and refolding of a titin immunoglobulin domain and α-actinin spectrin repeats.

Mechanically stable specific heterodimerization formed with reversible bonds are used as a molecular anchorage in single-molecule force spectroscopy studies with unique mechanical properties. Here authors develop a variety of heterodimerization molecular systems with a range of mechanical stability from a set of recently engineered helix-heterotetramers.

Correcting molecular transition rates measured by single-molecule force spectroscopy for limited temporal resolution

Equilibrium free-energy-landscape parameters governing biomolecular folding can be determined from nonequilibrium force-induced unfolding by measuring the rates k for transitioning back and forth between states as a function of force F. However, bias in the observed forward and reverse rates is introduced by limited effective temporal resolution, which includes the mechanical response time of the force probe and any smoothing used to improve the signal-to-noise ratio. Here we use simulations to characterize this bias, which is most prevalent when the ratio of forward and reverse rates is far from unity. We find deviations in k(F) at high rates, due to unobserved transitions from short- to long-lived states, and at low rates, due to the corresponding unobserved transitions from long- to short-lived states. These missing events introduce erroneous curvature in log(k) vs F that leads to incorrect landscape parameter determination. To correct the measured k(F), we derive a pair of model-independent analytical formulas. The first correction accounts for unobserved transitions from short- to long-lived states, but does surprisingly little to correct the erroneous energy-landscape parameters. Only by subsequently applying the second formula, which corrects the corresponding reverse process, do we recover the expected k(F) and energy-landscape quantities. Going forward, these corrections should be applied to transition-rate data whenever the highest measured rate is not at least an order of magnitude slower than the effective temporal resolution.

A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach

Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding-unbonding rate of RANK/RANKL/OPG receptor-ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.

Direct single-molecule quantification reveals unexpectedly high mechanical stability of vinculin-talin/α-catenin linkages

The vinculin-mediated mechanosensing requires establishment of stable mechanical linkages between vinculin to integrin at focal adhesions and to cadherins at adherens junctions through associations with the respective adaptor proteins talin and α-catenin. However, the mechanical stability of these critical vinculin linkages has yet to be determined. Here, we developed a single-molecule detector assay to provide direct quantification of the mechanical lifetime of vinculin association with the vinculin binding sites in both talin and α-catenin, which reveals a surprisingly high mechanical stability of the vinculin-talin and vinculin-α-catenin interfaces that have a lifetime of >1000 s at forces up to 10 pN and can last for seconds to tens of seconds at 15 to 25 pN. Our results suggest that these force-bearing intermolecular interfaces provide sufficient mechanical stability to support the vinculin-mediated mechanotransduction at cell-matrix and cell-cell adhesions.

Dynamic bonds and their roles in mechanosensing

Mechanical forces are ubiquitous in a cell's internal structure and external environment. Mechanosensing is the process that the cell employs to sense its mechanical environment. In receptor-mediated mechanosensing, cell surface receptors interact with immobilized ligands to provide a specific way to receive extracellular force signals to targeted force-transmitting, force-transducing and force-supporting structures inside the cell. Conversely, forces generated endogenously by the cell can be transmitted via cytoplasmic protein-protein interactions and regulate cell surface receptor activities in an 'inside-out' manner. Dynamic force spectroscopy analyzes these interactions on and inside cells to reveal various dynamic bonds. What is more, by integrating analysis of molecular interactions with that of cell signaling events involved in force-sensing and force-responding processes, one can investigate how dynamic bonds regulate the reception, transmission and transduction of mechanical signals.

Force-Dependent Facilitated Dissociation Can Generate Protein-DNA Catch Bonds

Cellular structures are continually subjected to forces, which may serve as mechanical signals for cells through their effects on biomolecule interaction kinetics. Typically, molecular complexes interact via "slip bonds," so applied forces accelerate off rates by reducing transition energy barriers. However, biomolecules with multiple dissociation pathways may have considerably more complicated force dependencies. This is the case for DNA-binding proteins that undergo "facilitated dissociation," in which competitor biomolecules from solution enhance molecular dissociation in a concentration-dependent manner. Using simulations and theory, we develop a generic model that shows that proteins undergoing facilitated dissociation can form an alternative type of molecular bond, known as a "catch bond," for which applied forces suppress protein dissociation. This occurs because the binding by protein competitors responsible for the facilitated dissociation pathway can be inhibited by applied forces. Within the model, we explore how the force dependence of dissociation is regulated by intrinsic factors, including molecular sensitivity to force and binding geometry and the extrinsic factor of competitor protein concentration. We find that catch bonds generically emerge when the force dependence of the facilitated unbinding pathway is stronger than that of the spontaneous unbinding pathway. The sharpness of the transition between slip- and catch-bond kinetics depends on the degree to which the protein bends its DNA substrate. This force-dependent kinetics is broadly regulated by the concentration of competitor biomolecules in solution. Thus, the observed catch bond is mechanistically distinct from other known physiological catch bonds because it requires an extrinsic factor-competitor proteins-rather than a specific intrinsic molecular structure. We hypothesize that this mechanism for regulating force-dependent protein dissociation may be used by cells to modulate protein exchange, regulate transcription, and facilitate diffusive search processes.

Force-Dependent Regulation of Talin-KANK1 Complex at Focal Adhesions

KANK proteins mediate cross-talk between dynamic microtubules and integrin-based adhesions to the extracellular matrix. KANKs interact with the integrin/actin-binding protein talin and with several components of microtubule-stabilizing cortical complexes. Because of actomyosin contractility, the talin-KANK complex is likely under mechanical force, and its mechanical stability is expected to be a critical determinant of KANK recruitment to focal adhesions. Here, we quantified the lifetime of the complex of the talin rod domain R7 and the KN domain of KANK1 under shear-force geometry and found that it can withstand forces for seconds to minutes over a physiological force range up to 10 pN. Complex stability measurements combined with cell biological experiments suggest that shear-force stretching promotes KANK1 localization to the periphery of focal adhesions. These results indicate that the talin-KANK1 complex is mechanically strong, enabling it to support the cross-talk between microtubule and actin cytoskeleton at focal adhesions.

Multiplexed protein force spectroscopy reveals equilibrium protein folding dynamics and the low-force response of von Willebrand factor

Single-molecule force spectroscopy has provided unprecedented insights into protein folding, force regulation, and function. So far, the field has relied primarily on atomic force microscope and optical tweezers assays that, while powerful, are limited in force resolution, throughput, and require feedback for constant force measurements. Here, we present a modular approach based on magnetic tweezers (MT) for highly multiplexed protein force spectroscopy. Our approach uses elastin-like polypeptide linkers for the specific attachment of proteins, requiring only short peptide tags on the protein of interest. The assay extends protein force spectroscopy into the low force (<1 pN) regime and enables parallel and ultra-stable measurements at constant forces. We present unfolding and refolding data for the small, single-domain protein ddFLN4, commonly used as a molecular fingerprint in force spectroscopy, and for the large, multidomain dimeric protein von Willebrand factor (VWF) that is critically involved in primary hemostasis. For both proteins, our measurements reveal exponential force dependencies of unfolding and refolding rates. We directly resolve the stabilization of the VWF A2 domain by Ca²⁺ and discover transitions in the VWF C domain stem at low forces that likely constitute the first steps of VWF's mechano-activation. Probing the force-dependent lifetime of biotin-streptavidin bonds, we find that monovalent streptavidin constructs with specific attachment geometry are significantly more force stable than commercial, multivalent streptavidin. We expect our modular approach to enable multiplexed force-spectroscopy measurements for a wide range of proteins, in particular in the physiologically relevant low-force regime.

Force-Dependent Binding Constants

Life is an emergent property of transient interactions between biomolecules and other organic and inorganic molecules that somehow leads to harmony and order. Measurement and quantitation of these biological interactions are of value to scientists and are major goals of biochemistry, as affinities provide insight into biological processes. In an organism, these interactions occur in the context of forces and the need for a consideration of binding affinities in the context of a changing mechanical landscape necessitates a new way to consider the biochemistry of protein–protein interactions. In the past few decades, the field of mechanobiology has exploded, as both the appreciation of, and the technical advances required to facilitate the study of, how forces impact biological processes have become evident. The aim of this review is to introduce the concept of force dependence of biomolecular interactions and the requirement to be able to measure force-dependent binding constants. The focus of this discussion will be on the mechanotransduction that occurs at the integrin-mediated adhesions with the extracellular matrix and the major mechanosensors talin and vinculin. However, the approaches that the cell uses to sense and respond to forces can be applied to other systems, and this therefore provides a general discussion of the force dependence of biomolecule interactions.