Theoretical determination of the strength of soft noncovalent molecular bonds

Direction-dependent force-induced dissociation dynamics of an entropic-driven lock-and-key assembly

The unbinding dynamics of a nanosized sphere-and-cavity assembly under the pulling of constant force and constant loading rate is explored by dissipative particle dynamics simulations. The formation of this matched lock-and-key pair in a polymer solution is driven by the depletion attraction. The two-dimensional free energy landscape U(x,z) associated with this assembly is constructed. Our results indicate that the unbinding pathway along the orientation of the assembly is unfavorable due to the relatively high energy barrier compared to that along the tortuous minimum path whose energy barrier is not high. It is also found that the dissociation rate depends on the direction of the external force (θ) with respect to the assembly orientation. The presence of the force component perpendicular to the assembly orientation can reduce the bond lifetime significantly by driving the key particle to approach the minimum path. Moreover, the dissociation dynamics can be facilitated even by a pushing force compared to the spontaneous dissociation (without forces). To elucidate the effective pathway under pulling, the escaping position is analyzed and its mean direction with respect to the assembly orientation rises generally with increasing θ, revealing that the presence of the force component along the minimum pathway is helpful. The importance of the direction of the external pulling has been demonstrated in our simple system. Therefore, this effect should be considered in more complicated unbinding experiments.

BROWNIAN DYNAMICS SIMULATION OF CATCH TO SLIP TRANSITION OVER A MODEL ENERGY LANDSCAPE

We perform Brownian dynamics simulation (BDS) of catch to slip transition over a model energy landscape. Through our BDS we demonstrate that for forces below the critical force the bond rupture occurs mostly through the catch pathway while for forces above the critical force the bond rupture occurs mostly through the slip pathway. We also demonstrate that the shoulder in the bond rupture force distribution switches to peak as the loading rate increases progressively and the bond lifetime is maximized at the model dependent critical force. The force dependent bond lifetime obtained via transforming the bond rupture force distribution at a given loading rate is in excellent agreement with that obtained from our BDS at constant forces. An alternative to the current mechanism of catch to slip transition is presented and validated through BDS.

Graphical methods for the analysis of shear-induced detachment of cells and microorganisms

Treating shear stress induced detachment of micro-organisms as a bond breaking mechanism, the authors present three intuitive graphical approaches to determine the relevant parameters in the Arrhenius rate equation, i.e., attachment energy, prefactor, and maximum shear stress. They demonstrate the methods with the detachment of polystyrene spheres and show that having three different methods presents the opportunity to check the consistency of the results.

Colloidal transport and diffusion over a tilted periodic potential: dynamics of individual particles

A tilted two-layer colloidal system is constructed for the study of force-assisted barrier-crossing dynamics over a periodic potential. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the diffusing particles. The measured mean drift velocity v(F, Eb) and diffusion coefficient D(F, Eb) of the particles as a function of F and energy barrier height Eb agree well with the exact results of the one-dimensional drift velocity (R. L. Stratonovich, Radiotekh. Elektron, 1958, 3, 497) and diffusion coefficient (P. Reimann, et al., Phys. Rev. Lett., 2001, 87, 010602 and P. Reimann, et al., Phys. Rev. E, 2002, 65, 031104). Based on these exact results, we show analytically and verify experimentally that there exists a scaling region, in which v(F, Eb) and D(F, Eb) both scale as ν'(F)exp[-E(F)/kBT], where the Arrhenius pre-factor ν'(F) and effective barrier height E(F) are both modified by F. The experiment demonstrates the applications of this model system in evaluating different scaling forms of ν'(F) and E(F) and their accuracy, in order to extract useful information about the external potential, such as the intrinsic barrier height Eb.

Stochastic simulation of single-molecule pulling experiments

Single-molecule pulling experiments are widely used for studying the structure, dynamics, and function of single biological molecules via applying mechanical forces on them in a controlled way. Pulling at a constant speed or at a constant force builds up a mechanical force on a molecule or molecular complex leading to a molecular transition such as the dissociation of a molecular complex, unfolding of a protein, or unwrapping of a higher-order structure. We perform Brownian dynamics and Monte Carlo simulations of single-molecule pulling experiments. Through our simulations we demonstrate that the molecular transition rate based on the Kramers theory in the high-barrier limit becomes unsuitable as the applied force approaches the critical force at which the barrier disappears. We also demonstrate that use of molecular transition rate based on mean first passage time (MFPT) approach would be more relevant in describing molecular transition especially as the applied force approaches the critical force.

Free energy and critical force for adhesion clusters

Cooperative clusters of N parallel bonds confined to an anchoring surface by springs of stiffness ks are considered. The free energy of a cluster can be obtained from its force-displacement relation. The dissociation kinetics of the cluster can be modeled as the dissociation of an effective single bond. There is a critical force Fc beyond which the barrier for the cluster dissociation vanishes. Fc scales such as ks1/2 and Fc/N is small compared to the critical force of a single bond. The theoretical predictions of free energy landscape and cluster lifetime are supported by numerical simulations for large number of bonds. Our study suggests that experiments measuring force-displacement relations could be useful in exploring the dynamics of adhesion clusters.

Scaling of the rupture dynamics of polymer chains pulled at one end at a constant rate

We consider the rupture dynamics of a homopolymer chain pulled at one end at a constant loading rate r . Compared to single bond breaking, the existence of the chain introduces two aspects into rupture dynamics: The non-Markovian aspect in the barrier crossing and the slow down of the force propagation to the breakable bond. The relative impact of both these processes is investigated, and the second one was found to be the most important at moderate loading rates. The most probable rupture force is found to decrease with the number of bonds as f{max} proportional, variant-[ln(const N/r)]2/3 and finally to approach a saturation value independent on N . All of our analytical findings are confirmed by extensive numerical simulations.

Lifetime of ligand-receptor clusters under external force

We present a theory for the lifetime T(N,f) of a ligand-receptor cluster with N bonds under constant external force F=fN , where f is force per bond. We show that there exists a critical force per bond f(c) such that at large N when f>f(c) the lifetime T(N,f) is independent of cluster size N ; when f>f(c) the lifetime scales as ln[T(N,f)] approximately N due to a free energy barrier with height approximately N along the dissociation path; when f=f(c), the lifetime scales as T(N,f) approximately N(1/3) due to strong fluctuation of a number of closed bonds. Our study shows that adhesion clusters with more bonds are more stable at small f but respond to external force as fast as smaller adhesion clusters at large f .

A hybrid polymer gel with controlled rates of cross-link rupture and self-repair

A family of hybrid polymer gels is described, in which covalent cross-links create a permanent, stiff scaffold onto which reversible metal-ligand coordinative cross-links are added. The reversible metal-ligand interactions are shown to bear mechanical stress within the hybrid gel, and relaxations in response to that applied stress are consistent with the stress-free kinetics of ligand exchange in systems that model the reversible cross-links. The stress-induced dissociation of a model metal-ligand complex is examined by a single-molecule force spectroscopy, and its mechanical response is compared with a previously studied complex. The mechanical response of the individual interactions is relevant to those found in the family of hybrid gels, and the modular platform is therefore suitable for the study of stress-induced molecular dissociations, and their subsequent repair, within a macroscopic material of fixed structure.

Bell's expression and the generalized Garg form for forced dissociation of a biomolecular complex

The dissociation of a biomolecular complex under the action of constant force, constant loading rate, and periodic force is studied theoretically. We show that the celebrated Bell expression provides a good approximation for the bond dissociation rate when F/F(c)<<1, where F(c) is the maxima slope of the binding potential along the reaction coordinate. When 1-F/F(c) <<1 the dissociation rate is better described by a generalized Garg form in which the potential derivative is expanded near F(c). We also show that a constant-force experiment is suitable for extracting the activation energy of the bond, a constant loading experiment is suitable to extract F(c), while time-periodic force can be applied to extract both bond dissociation rates at zero force and F(c).

Breaking bonds in the atomic force microscope: theory and analysis

A theoretical framework is developed to analyze molecular bond breaking in dynamic force spectroscopy using atomic force microscopy. An analytic expression of the observed bond breaking probability as a function of force is obtained in terms of the relevant physical parameters. The force-ramp mode is discussed in detail, which gives the best framework to extract the relevant physical parameters such as the potential depth and its width, if a set of widely different force-loading rates are used. We also show that the commonly used Ritchie-Evans model is incomplete and that it is only applicable for forces well below the maximum permitted by the potential. Statistical complications arising from the use of constant velocity experiments are discussed in detail.

Energy barrier scalings in driven systems

Energy landscape mappings are performed for two different molecular systems under mechanical loads. Barrier heights are observed to scale as Delta U approximately delta(3/2), where delta is a residual load. Catastrophe theory predicts that this scaling should arise for vanishing delta; however, this region is irrelevant in physical processes at finite temperature because thermal fluctuations cause the system to cross over the barrier before reaching the small-delta regime. Surprisingly, we find that the Delta U approximately delta(3/2), scaling is valid far beyond the vanishing delta regime described by catastrophe theory. We discuss how this scaling will therefore be relevant at finite temperatures and gives corrections to Eyring's theory for transition rates.