Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.
Single-molecule mechanical manipulation has enabled the quantitative understanding of the kinetics of bond ruptures as well as protein unfolding mechanism. Single-molecule experiments with theoretical models have allowed one to gain insight into free energy landscape for chemical bond and/or protein folding. For mechanically induced bond rupture, the bond-rupture kinetics may be governed by loading device. However, the role of loading device on the kinetics of mechanical rupture has been rarely received much attention until recently. In this work, we have theoretically and/or computationally s…
In dynamic force spectroscopy, a (bio-)molecular complex is subjected to a steadily increasing force until the chemical bond breaks. Repeating the same experiment many times results in a broad distribution of rupture forces, whose quantitative interpretation represents a formidable theoretical challenge. In this study we address the situation that more than a single molecular bond is involved in one experimental run, giving rise to multiple rupture events which are even more difficult to analyze and thus are usually eliminated as far as possible from the further evaluation of the experimental …
Adhesion interactions mediated by multiple bond types are relevant for many biological and soft matter systems, including the adhesion of biological cells and functionalized colloidal particles to various substrates. To elucidate advantages and disadvantages of multiple bond populations for the stability of heterogeneous adhesion clusters of receptor-ligand pairs, a theoretical model for a homogeneous parallel adhesion bond cluster under constant loading is extended to several bond types. The stability of the entire cluster can be tuned by changing densities of different bond populations as we…
We probe the dynamic strength of multiple biotin-streptavidin adhesion bonds under linear loading using the biomembrane force probe setup for dynamic force spectroscopy. Measured rupture force histograms are compared to results from a master equation model for the stochastic dynamics of bond rupture under load. This allows us to extract the distribution of the number of initially closed bonds. We also extract the molecular parameters of the adhesion bonds, in good agreement with earlier results from single bond experiments. Our analysis shows that the peaks in the measured histograms are not s…
Cell adhesion complexes (CACs), which are activated by ligand binding, play key roles in many cellular functions ranging from cell cycle regulation to mediation of cell extracellular matrix adhesion. Inspired by single molecule pulling experiments on leukocyte function-associated antigen-1 (LFA-1), expressed in T-cells, bound to intercellular adhesion molecules (ICAM), we performed constant loading rate ($r_f$) and constant force ($F$) simulations using the Self-Organized Polymer (SOP) model to describe the mechanism of ligand rupture from CACs. The simulations reproduce the major experimental…
Cell migration in morphogenesis and cancer metastasis typically involves interplay between different cell types. We construct and study a minimal, one-dimensional model comprised of two different motile cells with each cell represented as an active elastic dimer. The interaction between the two cells via cadherins is modeled as a spring that can rupture beyond a threshold force as it undergoes dynamic loading via the attached motile cells. We obtain a phase diagram consisting of chase-and-run dynamics and clumping dynamics as a function of the stiffness of the interaction spring and the thresh…
Curvatures in the most probable rupture force ($f^*$) versus log-loading rate ($\log{r_f}$) observed in dynamic force spectroscopy (DFS) on biomolecular complexes are interpreted using a one-dimensional free energy profile with multiple barriers or a single barrier with force-dependent transition state. Here, we provide a criterion to select one scenario over another. If the rupture dynamics occurs by crossing a single barrier in a physical free energy profile describing unbinding, the exponent $ν$, from $(1- f^*/f_c)^{1/ν}\sim(\log r_f)$ with $f_c$ being a critical force in the absence of for…
We study the effects of the shear force on the rupture mechanism on a double stranded DNA. Motivated by recent experiments, we perform the atomistic simulations with explicit solvent to obtain the distributions of extension in hydrogen and covalent bonds below the rupture force. We obtain a significant difference between the atomistic simulations and the existing results in the iterature based on the coarse-grained models (theory and simulations). We discuss the possible reasons and improve the coarse-grained model by incorporating the consequences of semi-microscopic details of the nucleotide…
Measurement of the life time of attachments formed by a single microtubule (MT) with a single kinetochore (kt) {\it in-vitro} under force-clamp conditions had earlier revealed a catch-bond-like behavior. In the past the physical origin of this apparently counter-intuitive phenomenon was traced to the nature of the force-dependence of the (de-)polymerization kinetics of the MTs. Here first the same model MT-kt attachment is subjected to external tension that increases linearly with time until rupture occurs. In our {\it force-ramp} experiments {\it in-silico}, the model displays the well known …
Using the Langevin Dynamics simulation, we have studied the effects of the shear force on the rupture of short double stranded DNA at different temperatures. We show that the rupture force increases linearly with the chain length and approaches to the asymptotic value in accordance with the experiment. The qualitative nature of these curves almost remains same for different temperatures but with a shift in the force. We observe three different regimes in the extension of covalent bonds (back bone) under the shear force.
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 is that force-induced remodeling of ligand binding interface occurs prior to bond rupture. However, what strategy receptor proteins utilize to meet such specific kinetic control is still unclear, rendering the mechanistic understanding of catch-bond an open question. Here we report a bidirectional allostery mechanism of catch-bond for the hyaluronan (HA) receptor CD44 which is…
We introduce a model for microtubule mechanics containing lateral bonds between dimers in neighboring protofilaments, bending rigidity of dimers, and repulsive interactions between protofilaments modeling steric constraints to investigate the influence of mechanical forces on hydrolysis and catastrophes. We use the allosteric dimer model, where tubulin dimers are characterized by an equilibrium bending angle, which changes from $0^\circ$ to $22^\circ$ by hydrolysis of a dimer. This also affects the lateral interaction and bending energies and, thus, the mechanical equilibrium state of the micr…
The forced rupture of single chemical bonds under external load is addressed. A general framework is put forward to optimally utilize the experimentally observed rupture force data for estimating the parameters of a theoretical model. As an application we explore to what extent a distinction between several recently proposed models is feasible on the basis of realistic experimental data sets.
Sacrificial bonds and hidden length in structural molecules account for the greatly increased fracture toughness of biological materials compared to synthetic materials without such structural features, by providing a molecular-scale mechanism for energy dissipation. One example is in the polymeric glue connection between collagen fibrils in animal bone. In this paper, we propose a simple kinetic model that describes the breakage of sacrificial bonds and the release of hidden length, based on Bell's theory. We postulate a master equation governing the rates of bond breakage and formation. This…
Heterogeneity in biological molecules, resulting in molecule-to-molecule variations in their dynamics and function, is an emerging theme. To elucidate the consequences of heterogeneous behavior at the single molecule level, we propose an exactly solvable model in which the unfolding rate due to mechanical force depends parametrically on an auxiliary variable representing an entropy barrier arising from fluctuations in internal dynamics. When the rate of fluctuations, a measure of dynamical disorder, is comparable to or smaller than the rate of force-induced unbinding, we show that there are tw…
Mechanical forces acting on cell adhesion receptor proteins regulate a range of cellular functions by formation and rupture of non-covalent interactions with ligands. Typically, force decreases the lifetimes of intact complexes (slip-bonds), making the discovery that these lifetimes can also be prolonged ("catch-bonds"), a surprise. We created a microscopic analytic theory by incorporating the structures of selectin and integrin receptors into a conceptual framework based on the theory of stochastic equations, which quantitatively explains a wide range of experimental data (including catch-bon…
Collagen fibrils, when subjected to cyclic loading, are known to exhibit hysteretic behaviour with energy dissipation that is partially recovered on relaxation. In this paper, we develop a kinetic model for a collagen fibril incorporating presence of hidden loops and stochastic fragmentation as well as reformation of sacrificial bonds. We show that the model reproduces well the characteristic features of reported experimental data on cyclic response of collagen fibrils, such as moving hysteresis loops, time evolution of residual strains and energy dissipation, recovery on relaxation, etc. We s…
Focal adhesions are the loci of cellular adhesion to the extracellular matrix. At these sites, various integrins forge connections between the intracellular cytoskeleton and the outside world: large patches of multiple types of integrins together grip hold of collagen, fibronectin and other extracellular matrix components. The mixture of integrins composing the FA will, in general, contain both slip bond integrins and catch bond integrins---bonds whose lifetime increases with applied load and bonds for whom it decreases when forced. Prior work suggests that catch bonds are essential for proper…
Analysis of bond rupture data from single-molecule force spectroscopy experiments commonly relies on the strong assumption that the bond dissociation process is irreversible. However, with increased spatiotemporal resolution of instruments it is now possible to observe multiple unbinding-rebinding events in a single pulling experiment. Here, we augment the theory of force-induced unbinding by explicitly taking into account rebinding kinetics, and provide approximate analytic solutions of the resulting rate equations. Furthermore, we use a short-time expansion of the exact kinetics to construct…
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situ…
The concept of molecular mechanics force field has been widely accepted nowadays for studying various processes in biomolecular systems. In this paper, we suggest a modification for the standard CHARMM force field that permits simulations of systems with dynamically changing molecular topologies. The implementation of the modified force field was carried out in the popular program MBN Explorer, and, to support the development, we provide several illustrative case studies where dynamical topology is necessary. In particular, it is shown that the modified molecular mechanics force field can be a…
