Dissociation of biological catch-bond by periodic perturbation

Oscillating Piconewton Force Manipulation on Single-Molecule Enzymatic Conformational and Reaction Dynamics

Oscillation force has been demonstrated in theoretical studies as a critical role in unraveling the comprehensive enzymatic dynamics and addressing its regulation on enzyme activity. Utilizing the imposed external mechanical oscillation force by our newly developed magnetic tweezers coupled with a single-molecule photon-stamping imaging spectroscopic microscope, we experimentally studied a millisecond-scale oscillation force manipulation on single horseradish peroxidase enzymatic conformational and reaction dynamics. We have studied the enzymatic reaction dynamics and found that the enzyme activity changes under the real-time oscillatory force manipulation. Moreover, the oscillation force shows the capability of manipulating the enzyme active-site conformational state as well as the nascent-formed product's interaction with the active site of the enzyme, which impacts on the product release pathways. Specifically, we have identified that there are two product releasing pathways, the solvation-mediated diffusion releasing pathway and the spilling-out releasing pathway. We have observed that the spilling-out pathway can be significantly perturbed by the oscillatory force manipulation. Our correlated interpretation of enzymatic conformational and reaction dynamics provides a new insight into the comprehensive understanding of the complex conformational dynamics evolved in an enzymatic reaction. Technically, we have also demonstrated a novel approach capable of unfolding an enzyme under an enzymatic reaction condition in real time and, furthermore, by using an oscillatory mechanical weak piconewton force to manipulate enzyme conformations, and the enzyme thermal fluctuation is fully maintained. The real-time in situ fluorescence probe at the enzymatic active site reports the active-site conformational dynamics through each enzymatic reaction turnovers.

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.

Cyclic stretch induces cell reorientation on substrates by destabilizing catch bonds in focal adhesions

A minimal model of cellular mechanosensing system that consists of a single stress fiber adhering on a substrate via two focal adhesions made of catch bonds is adopted to investigate the phenomena of cell reorientation on substrates induced by an applied uniaxial cyclic stretch. The model indicates that the catch bonds in the focal adhesions experience a periodically oscillating internal force with amplitude and frequency controlled by two intrinsic clocks of the stress fiber, one associated with localized activation and the other with homogeneous activation of sarcomere units along the stress fiber. It is shown that this oscillating force due to cyclic stretch tends to destabilize focal adhesions by reducing the lifetime of catch bonds. The resulting slide or relocation of focal adhesions then causes the associated stress fiber to shorten and rotate to configurations nearly perpendicular to the stretching direction. These predicted behaviors from our model are consistent with a wide range of experimental observations.

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.

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.

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.

Periodic forces trigger a complex mechanical response in ubiquitin

Mechanical forces govern physiological processes in all living organisms. Many cellular forces, for example, those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to periodic mechanical information. Ubiquitin is a small protein found in all eukaryotes. We developed molecular dynamics simulations to unfold single and multimeric ubiquitins with periodic forces. By using a coarse-grained representation, we were able to model forces with periods about 2 orders of magnitude longer than the protein's relaxation time. We found that even a moderate periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. A complex dynamic response with secondary structure refolding and an increasing importance of local interactions was revealed. Importantly, repetitive forces with broadly distributed frequencies elicited very similar molecular responses compared to fixed-frequency forces. When testing the influence of pulling geometry on ubiquitin's mechanical stability, it was found that the linkage involved in the mechanical degradation of cellular proteins renders the protein remarkably insensitive to periodic forces. We also devised a complementary kinetic energy landscape model that traces these observations and explains periodic-force, single-molecule measurements. In turn, this analytical model is capable of predicting dynamic protein responses. These results provide new insights into ubiquitin mechanics and a potential mechanical role during protein degradation, as well as first frameworks for dynamic protein stability and the modeling of repetitive mechanical processes.

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.

Allosteric role of the large-scale domain opening in biological catch-binding

The proposed model demonstrates the allosteric role of the two-domain region of the receptor protein in the increased lifetimes of biological receptor/ligand bonds subjected to an external force. The interaction between the domains is represented by a bounded potential, containing two minima corresponding to the attached and separated conformations of the two protein domains. The dissociative potential with a single minimum describing receptor/ligand binding fluctuates between deep and shallow states, depending on whether the domains are attached or separated. A number of valuable analytic expressions are derived and are used to interpret experimental data for two catch bonds. The P-selectin/P-selectin-glycoprotein-ligand-1 (PSGL-1) bond is controlled by the interface between the epidermal growth factor (EGF) and lectin domains of P-selectin, and the type 1 fimbrial adhesive protein (FimH)/mannose bond is governed by the interface between the lectin and pilin domains of FimH. Catch-binding occurs in these systems when the external force stretches the receptor proteins and increases the interdomain distance. The allosteric effect is supported by independent measurements, in which the domains are kept separated by attachment of another ligand. The proposed model accurately describes the experimentally observed anomalous behavior of the lifetimes of the P-selectin/PSGL-1 and FimH/mannose complexes as a function of applied force and provides valuable insights into the mechanism of catch-binding.

Beyond molecular recognition: using a repulsive field to tune interfacial valency and binding specificity between adhesive surfaces

Surface-bound biomolecular fragments enable "smart" materials to recognize cells and other particles in applications ranging from tissue engineering and medical diagnostics to colloidal and nanoparticle assembly. Such smart surfaces are, however, limited in their design to biomolecular selectivity. This feature article demonstrates, using a completely nonbiological model system, how specificity can be achieved for particle (and cell) binding, employing surface designs where immobilized nanoscale adhesion elements are entirely nonselective. Fundamental principles are illustrated by a model experimental system where 11 nm cationic nanoparticles on a planar negative silica surface interact with flowing negative silica microspheres having 1.0 and 0.5 microm diameters. In these systems, the interfacial valency, defined as the number of cross-bonds needed to capture flowing particles, is tunable through ionic strength, which alters the range of the background repulsion and therefore the effective binding strength of the adhesive elements themselves. At high ionic strengths where long-range electrostatic repulsions are screened, single surface-bound nanoparticles capture microspheres, defining the univalent regime. At low ionic strengths, competing repulsions weaken the effective nanoparticle adhesion so that multiple nanoparticles are needed for microparticle capture. This article discusses important features of the univalent regime and then illustrates how multivalency produces interfacial-scale selectivity. The arguments are then generalized, providing a possible explanation for highly specific cell binding in nature, despite the degeneracy of adhesion molecules and cell types. The mechanism for the valency-related selectivity is further developed in the context of selective flocculation in the colloidal literature. Finally, results for multivalent binding are contrasted with the current thinking for interfacial design and the presentation of adhesion moieties on engineered surfaces.

Sticky chain model for shear response of red blood cells

A sticky chain model has been proposed to describe the unfolding of spectrin network under applied mechanical loads. With the model, the response of a red blood cell (RBC) under static and cyclic shear loading has been predicted, which agrees qualitatively with relevant experimental results.

Dynamics of the photoexcited electron at the chromophore-semiconductor interface

Electron dynamics at molecular-bulk interfaces play a central role in a number of different fields, including molecular electronics and sensitized semiconductor solar cells. Describing electron behavior in these systems is difficult because it requires a union between disparate interface components, molecules and solid-state materials, that are studied by two different communities, chemists and physicists, respectively. This Account describes recent theoretical efforts to bridge that gap by analyzing systems that serve as good general models of the interfacial electron dynamics. The particular systems that we examine, dyes attached to TiO2, are especially important since they represent the key component of dye-sensitized semiconductor solar cells, or Gratzel cells. Gratzel cells offer a cheap, efficient alternative to traditional Si-based solar cells. The chromophore-TiO2 interface is a remarkably good target for theorists because it has already been the subject of many excellent experimental investigations. The electron dynamics in the chromophore-semiconductor systems are surprisingly rich and involve a great variety of processes as illustrated in the scheme above. The exact rates and branching ratios depend on the system details, including the semiconductor type, its bulk phase, and its exposed surface, the chromophore type, the presence or absence of a chromophore-semiconductor bridge, the alignment of the chromophore and semiconductor energy levels, the surface termination, the active vibrational modes, the solvent, the type of electrolyte, the presence of surface defects, etc. Still, the general principles governing the electron dynamics at the bulk-semiconductor interface can be understood and formulated by considering a few specific examples. The ultrafast time scale of the electronic and vibrational processes at the molecule-bulk interface make it difficult to invoke traditional theories. Instead, we perform explicit time-domain simulations with an atomistic representation of the interface. This approach most directly mimics the time-resolved experimental data and provides a detailed description of the processes as they occur in real time. The simulations described in this Account take into consideration the chemical structure of the system, determine the role of the vibrational motion and non-adiabatic coupling, uncover a vast variety of electron dynamics scenarios, and ultimately, allow us to establish the basic criteria that provide an understanding of this complicated physical process. The insights attained in the theoretical studies let us formulate a number of practical suggestions for improving the properties of the dye-sensitized semiconductor solar cell and for controlling the electron transfer across molecular-bulk interfaces.

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.

Dynamic Competition between Catch and Slip Bonds in Selectins Bound to Ligands

Atomic force measurements of unbinding rates (or off-rates) of ligands bound to a class of cell adhesion molecules from the selectin family show a transition from catch to slip bonds as the value of external force (f) is increased. At low forces (<10 pN), the unbinding rates decrease (catch regime), while, at high forces, the rates increase in accord with the Bell model (slip regime). The energy landscape underlying the catch-slip transition can be captured by a two-state model that considers the possibility of redistribution of population from the force-free bound state to the force-stabilized bound state. The excellent agreement between theory and experiments is used to extract the parameters characterizing the energy landscape of the complex by fitting the calculated curves to lifetime data (obtained at constant f) for the monomeric form of PSGL-1 (sPSGL-1). We used the constant force parameters to predict the distributions of unbinding times and unbinding forces as a function of the loading rate. The general two-state model, which also correctly predicts the absence of catch bonds in the binding of antibodies to selectins, is used to resolve the energy landscape parameters characterizing adhesive interactions of P- and L-selectins with physiological ligands such as sPSGL-1 and endoglycan and antibodies such as G1 and DREG56. Despite high sequence similarity, the underlying shapes of the energy landscape of P-selectin and L-selectin interacting with sPSGL-1 are markedly different. The underlying energy landscape of the selectin cell adhesion complex is sensitive to the nature of the ligand. The unified description of selectins bound to physiological ligands and antibodies in conjunction with experimental data can be used to extract the key parameters that describe the dynamics of cell adhesion complexes.