Integrated rate laws for processive and distributive enzymatic turnover.

Recently derived steady-state differential rate laws for the catalytic turnover of molecules containing two substrate sites are reformulated as integrated rate laws. The analysis applies to a broad class of Markovian dynamic models, motivated by the varied and often complex mechanisms associated with DNA modifying enzymes. Analysis of experimental data for the methylation kinetics of DNA by Dam (DNA adenine methyltransferase) is drastically improved through the use of integrated rate laws.

Lipid diffusion in the distal and proximal leaflets of supported lipid bilayer membranes studied by single particle tracking.

Supported lipid bilayers (SLBs) have been studied extensively as simple but powerful models for cellular membranes. Yet, potential differences in the dynamics of the two leaflets of a SLB remain poorly understood. Here, using single particle tracking, we obtain a detailed picture of bilayer dynamics.

Specificity versus Processivity in the Sequential Modification of DNA: A Study of DNA Adenine Methyltransferase.

A detailed analysis is carried out on both published experimental results and new experiments for the methylation kinetics of two-site DNA substrates (with site separations between 100 and 800 bp) catalyzed by bacterial DNA adenine methyltransferase (Dam). A previously reported rate enhancement for the second methylation event (relative to that of the first methylation) is shown to result from elevated substrate specificity for singly methylated DNA over that of unmethylated DNA and not processive turnover of both sites by the same copy of Dam. An elementary model is suggested that cleanly fits the experimental data over a broad range of intersite separations.

On the generality of Michaelian kinetics.

The reversible Michaelis-Menten equation is shown to follow from a very broad class of steady-state kinetic models involving enzymes that adopt a unique free (i.e., not complexed to substrate/product) state in solution.

Extracting enzyme processivity from kinetic assays.

A steady-state analysis for the catalytic turnover of molecules containing two substrate sites is presented. A broad class of Markovian dynamic models, motivated by the action of DNA modifying enzymes and the rich variety of translocation mechanisms associated with these systems (e.g.

Friction through reversible jumps of surface atoms.

We propose a microscopic model that incorporates the effect of thermally activated motion of surface atoms on nanoscopic friction. Our calculations demonstrate that the stick-slip motion of the tip is governed by two competing processes: (i) jumps of the surface atoms to the tip which tend to inhibit sliding, and (ii) jumps back to the sample which give rise to sliding. The energy dissipated during the reversible jumps of the surface atoms between the sample and tip contributes significantly to the friction force, and leads to a nonmonotonic dependence of friction on temperature, which has been observed in recent friction force microscopy experiments for different material classes.

Probing and tuning frictional aging at the nanoscale.

Time-dependent increase of frictional strength, or frictional aging, is a widely observed phenomenon both at macro and nanoscales. The frictional aging at the nanoscale may result from nucleation of capillary bridges and strengthening of chemical bonding, and it imposes serious constraints and limitations on the performance and lifetime of micro- and nanomachines. Here, by analytical model and numerical simulations, we investigate the effect of inplane oscillations on friction in nanoscale contacts which exhibit aging.

Formation and rupture of capillary bridges in atomic scale friction.

While formation of capillary bridges significantly contributes to the adhesion and friction at micro- and nanoscales, many key aspects of dynamics of capillary condensation and its effect on friction forces are still not well understood. Here, by analytical model and numerical simulations, we address the origin of reduction of friction force with velocity and increase of friction with temperature, which have been experimentally observed under humid ambient conditions. These observations differ significantly from the results of friction experiments carried out under ultrahigh vacuum, and disagree with predictions of thermal Prandtl-Tomlinson model of friction.

Slow cracklike dynamics at the onset of frictional sliding.

We propose a friction model which incorporates interfacial elasticity and whose steady state sliding relation is characterized by a generic nonmonotonic behavior, including both velocity weakening and strengthening branches. In 1D and upon the application of sideway loading, we demonstrate the existence of transient cracklike fronts whose velocity is independent of sound speed, which we propose to be analogous to the recently discovered slow interfacial rupture fronts. Most importantly, the properties of these transient inhomogeneously loaded fronts are determined by steady state front solutions at the minimum of the sliding friction law, implying the existence of a new velocity scale and a "forbidden gap" of rupture velocities.

Stabilizing stick-slip friction.

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes.

Probing static disorder in Arrhenius kinetics by single-molecule force spectroscopy.

The widely used Arrhenius equation describes the kinetics of simple two-state reactions, with the implicit assumption of a single transition state with a well-defined activation energy barrier DeltaE, as the rate-limiting step. However, it has become increasingly clear that the saddle point of the free-energy surface in most reactions is populated by ensembles of conformations, leading to nonexponential kinetics. Here we present a theory that generalizes the Arrhenius equation to include static disorder of conformational degrees of freedom as a function of an external perturbation to fully account for a diverse set of transition states.

Multibond dynamics of nanoscale friction: the role of temperature.

The main challenge in predicting sliding friction is related to the complexity of highly nonequilibrium processes, the kinetics of which are controlled by the interface temperature. Our experiments reveal a nonmonotonic enhancement of dry nanoscale friction at cryogenic temperatures for different material classes. Concerted simulations show that it emerges from two competing processes acting at the interface: the thermally activated formation as well as rupturing of an ensemble of atomic contacts.