Statistics of reversible bond dynamics observed in force-clamp spectroscopy

We present a detailed analysis of two-state trajectories obtained from force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the unique possibility to vary the equilibrium constant in two-state kinetics, for instance the unfolding and refolding of biomolecules, over many orders of magnitude due to the force dependency of the respective rates. We discuss two different kinds of counting statistics, the event-counting usually employed in the statistical analysis of two-state kinetics and additionally the so-called cycle-counting. While in the former case all transitions are counted, cycle-counting means that we focus on one type of transitions. This might be advantageous in particular if the equilibrium constant is much larger or much smaller than unity because in these situations the temporal resolution of the experimental setup might not allow to capture all transitions of an event-counting analysis. We discuss how an analysis of FCS data for complex systems exhibiting dynamic disorder might be performed yielding information about the detailed force-dependence of the transition rates and about the time scale of the dynamic disorder. In addition, the question as to which extent the kinetic scheme can be viewed as a Markovian two-state model is discussed.Comment: 25 pages, 10 figures, Phys. Rev. E, in pres

Force-clamp spectroscopy of reversible bond breakage

We consider reversible breaking of adhesion bonds or folding of proteins under the influence of a constant external force. We discuss the stochastic properties of the unbinding/rebinding events and analyze their mean number and their variance in the framework of simple two-state models. In the calculations, we exploit the analogy to single molecule fluorescence and particularly between unbinding/rebinding and photon emission events. Environmental fluctuation models are used to describe deviations from Markovian behavior. The second moment of the event-number distribution is found to be very sensitive to possible exchange processes and can thus be used to identify temporal fluctuations of the transition rates.Comment: 8 pages, 4 figure

Dynamic force spectroscopy: analysis of reversible bond-breaking dynamics

The problem of diffusive bond-dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e. under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach each other as the system reaches equilibrium. We investigate the dependence of the rupture force distributions and mean rupture forces on external parameters like cantilever stiffness and influence of a soft linker. We find that depending on the implementation of a soft linker the equilibrium rupture force is either unaffected by the presence of the linker or changes in a predictable way with the linker-compliance. Additionally, we show that it is possible to extract the equilibrium constant of the on- and off-rates from the determination of the equilibrium rupture forces.Comment: 32 pages, 14 figure

Hydrophobic mismatch sorts SNARE proteins into distinct membrane domains

The clustering of proteins and lipids in distinct microdomains is emerging as an important principle for the spatial patterning of biological membranes. Such domain formation can be the result of hydrophobic and ionic interactions with membrane lipids as well as of specific protein–protein interactions. Here using plasma membrane-resident SNARE proteins as model, we show that hydrophobic mismatch between the length of transmembrane domains (TMDs) and the thickness of the lipid membrane suffices to induce clustering of proteins. Even when the TMDs differ in length by only a single residue, hydrophobic mismatch can segregate structurally closely homologous membrane proteins in distinct membrane domains. Domain formation is further fine-tuned by interactions with polyanionic phosphoinositides and homo and heterotypic protein interactions. Our findings demonstrate that hydrophobic mismatch contributes to the structural organization of membranes

Size Matters: Problems and Advantages Associated with Highly Miniaturized Sensors

There is no doubt that the recent advances in nanotechnology have made it possible to realize a great variety of new sensors with signal transduction mechanisms utilizing physical phenomena at the nanoscale. Some examples are conductivity measurements in nanowires, deflection of cantilevers and spectroscopy of plasmonic nanoparticles. The fact that these techniques are based on the special properties of nanostructural entities provides for extreme sensor miniaturization since a single structural unit often can be used as transducer. This review discusses the advantages and problems with such small sensors, with focus on biosensing applications and label-free real-time analysis of liquid samples. Many aspects of sensor design are considered, such as thermodynamic and diffusion aspects on binding kinetics as well as multiplexing and noise issues. Still, all issues discussed are generic in the sense that the conclusions apply to practically all types of surface sensitive techniques. As a counterweight to the current research trend, it is argued that in many real world applications, better performance is achieved if the active sensor is larger than that in typical nanosensors. Although there are certain specific sensing applications where nanoscale transducers are necessary, it is argued herein that this represents a relatively rare situation. Instead, it is suggested that sensing on the microscale often offers a good compromise between utilizing some possible advantages of miniaturization while avoiding the complications. This means that ensemble measurements on multiple nanoscale sensors are preferable instead of utilizing a single transducer entity