We present a unified framework for extracting kinetic information from single-molecule pulling experiments at constant force or constant pulling speed. Our procedure provides estimates of not only (i) the intrinsic rate coefficient and (ii) the location of the transition state but also (iii) the free energy of activation. By analyzing simulated data, we show that the resulting rates of force-induced rupture are significantly more reliable than those obtained by the widely used approach based on Bell's formula. We consider the uniqueness of the extracted kinetic information and suggest guidelines to avoid over-interpretation of experiments.

Dynamic force spectroscopy probes the kinetic and thermodynamic properties of single molecules and molecular assemblies. Here, we propose a simple procedure to extract kinetic information from such experiments. The cornerstone of our method is a transformation of the rupture-force histograms obtained at different forceloading rates into the force-dependent lifetimes measurable in constant-force experiments. To interpret the force-dependent lifetimes, we derive a generalization of Bell's formula that is formally exact within the framework of Kramers theory. This result complements the analytical expression for the lifetime that we derived previously for a class of model potentials. We illustrate our procedure by analyzing the nanopore unzipping of DNA hairpins and the unfolding of a protein attached by flexible linkers to an atomic force microscope. Our procedure to transform rupture-force histograms into the force-dependent lifetimes remains valid even when the molecular extension is a poor reaction coordinate and higher-dimensional free-energy surfaces must be considered. In this case the microscopic interpretation of the lifetimes becomes more challenging because the lifetimes can reveal richer, and even nonmonotonic, dependence on the force. atomic force microscope | optical tweezers | nanopore unzipping Kramers theory | rupture force distribution M echanical forces play an increasingly recognized role in biology at the molecular level. Many biological macromolecules have a load-bearing function in living cells. Proteins such as titin in the skeletal and cardiac muscle sarcomere, fibronectin in the extracellular matrix, and spectrin in erythrocytes provide resistance under mechanical stress. Other biomolecules such as higher-order nucleic acid complexes are unraveled in a controlled way by mechanical forces before being processed by polymerases, helicases, and ribosomes (1).The controlled application of mechanical forces on single molecules provides a powerful tool to study their structure, dynamics, and function. Remarkable advances in single-molecule manipulation have made it possible to measure the forces and strains that develop during many processes in a cell in real time. Moreover, the exertion of external forces modify these processes in a controlled way (2). In such experiments, a molecule or molecular complex is attached to an atomic force microscope (AFM) or laser optical tweezer, often through flexible molecular linkers. Pulling at a constant speed or at a constant force builds up mechanical tension, eventually culminating in a molecular transition such as ligand-receptor dissociation (3, 4), unfolding of a protein (5-10), or unzipping of nucleic acids (11,12). When performed at constant force, these experiments directly probe the force-dependent lifetime of the system, τ (F). In contrast, the distribution of rupture forces measured in experiments at a constant pulling speed needs to be processed to provide information about τ (F).The standard theory of irreversible rupture induced by an external t...

Dynamic force spectroscopy of single molecules is described by a model that predicts a distribution of rupture forces, the corresponding mean rupture force, and variance, which are all amenable to experimental tests. The distribution has a pronounced asymmetry, which has recently been observed experimentally. The mean rupture force follows a (lnV) 2/3 dependence on the pulling velocity, V, and differs from earlier predictions. Interestingly, at low pulling velocities, a rebinding process is obtained whose signature is an intermittent behavior of the spring force, which delays the rupture. An extension to include conformational changes of the adhesion complex is proposed, which leads to the possibility of bimodal distributions of rupture forces.S ingle molecule spectroscopy is by now an established approach that can report on distributions of molecular properties, and can provide kinetic information on conformational changes, such as folding and unfolding of molecules without the ''scrambling'' that occurs due to ensemble averaging (1). Such information could be valuable in particular for biomolecules, where rare events might have functional significance, but which can be masked in an ensemble approach. Dynamic force spectroscopy (DFS) has been introduced as a spectroscopic tool to probe the complex relationships between ''force-lifetime and chemistry'' in single molecules bound in an adhesion complex (2-4), and to reveal details of molecular scale energy landscapes and adhesion strength.The rupture force in DFS is quantified by the maximum extension of a spring, the linker, which is followed by a rapid recoil of the spring to its rest position. This behavior resembles the stick-to-slip transition in studies on friction. The unbinding process of a single molecule is studied one molecule at a time, which means that one measures a collection of independent random rupture events. This type of measurement leads to a distribution of rupture forces. In addition, measurements of rupture forces over a wide range of pulling velocities, from very slow to extremely fast, are used to explore the energy landscape of the bound complex.In DFS experiments, an adhesion bond is driven away from its equilibrium by a spring pulled at a given velocity. Rupture of adhesion bonds occurs by means of thermally assisted escape from the bound state across an activation barrier. The latter diminishes as the applied force increases, so the rupture force is determined by an interplay between the rate of escape in the absence of the external force and the pulling velocity (loading rate). Thus, the measured forces are not an intrinsic property of the bound complex, but rather, they depend on the mechanical setup and loading rate applied to the system.In this article, we discuss an approach to describe unbinding processes measured by DFS, which goes beyond previous models and methods of analysis (2-11). As we show, our approach (i) proposes a possible mechanism of rupture; (ii) emphasizes the importance of investigating the distribution function...

SUMMARY During B lymphocyte development, immunoglobulin heavy chain variable (VH), diversity (DH) and joining (JH) segments assemble to generate a diverse antigen receptor repertoire. Here we have marked the distal VH and DH-JH-Eμ regions with Tet-operator binding sites and traced their 3D-trajectories in pro-B cells transduced with a retrovirus encoding Tet-repressor-EGFP. We found that these elements displayed fractional Langevin motion (fLm) due to the viscoelastic hindrance from the surrounding network of proteins and chromatin fibers. Using fractional Langevin dynamics modeling, we found that, with high probability, DHJH elements reach a VH element within minutes. Spatial confinement emerged as the dominant parameter that determined the frequency of such encounters. We propose that the viscoelastic nature of the nuclear environment causes coding elements and regulatory elements to bounce back and forth in a spring-like fashion until specific genomic interactions are established and that spatial confinement of topological domains largely controls first-passage times for genomic interactions.

Background: Drosophila melanogaster females have two X chromosomes and two autosome sets (XX;AA), while males have a single X chromosome and two autosome sets (X;AA). Drosophila male somatic cells compensate for a single copy of the X chromosome by deploying male-specific-lethal (MSL) complexes that increase transcription from the X chromosome. Male germ cells lack MSL complexes, indicating that either germline X-chromosome dosage compensation is MSL-independent, or that germ cells do not carry out dosage compensation.

We explore emergent effects of multidimensionality of the free energy landscape on single-molecule kinetics under constant force. The proposed minimal model reveals the existence of a spectrum of unusual scenarios for the force-dependent lifetime, all of which are shown to occur on a free energy landscape with a single transition state. We present an analytical solution that governs single-molecule responses to a constant force and relates them to microscopic parameters of the system.

Single-molecule force experiments provide powerful new tools to explore biomolecular interactions. Here, we describe a systematic procedure for extracting kinetic information from force-spectroscopy experiments, and apply it to nanopore unzipping of individual DNA hairpins. Two types of measurements are considered: unzipping at constant voltage, and unzipping at constant voltage-ramp speeds. We perform a global maximum-likelihood analysis of the experimental data at low-to-intermediate ramp speeds. To validate the theoretical models, we compare their predictions with two independent sets of data, collected at high ramp speeds and at constant voltage, by using a quantitative relation between the two types of measurements. Microscopic approaches based on Kramers theory of diffusive barrier crossing allow us to estimate not only intrinsic rates and transition state locations, as in the widely used phenomenological approach based on Bell's formula, but also free energies of activation. The problem of extracting unique and accurate kinetic parameters of a molecular transition is discussed in light of the apparent success of the microscopic theories in reproducing the experimental data.

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.