Theory, analysis, and interpretation of single-molecule force spectroscopy experiments

Abstract

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...

Biasing effects of receptor-ligand complexes on protein-unfolding statistics

“…The standard theoretical framework treats protein unfolding or bond dissociation as thermally driven escape over a free energy barrier that is modulated by an external force F [11][12][13][14]. This description leads to a general expression for the distribution of unfolding or rupture forces in a pulling experiment,…”

Lipid-dependent conformational dynamics underlie the functional versatility of T-cell receptor

“…In addition to the 400 nm/s pulling speed, we also performed experiments at another two pulling speeds, which increased the dynamic force range for the total data set. The data at the three different pulling speeds (i.e., 400, 1 000 and 2 000 nm/s) followed the same trend when being converted to lifetime-force relationships using the method introduced by Dudko and coworkers [67] (Supplementary information, Figure S7). The extracted free energy from force spectroscopy data depends on the theoretical model used to describe the shape of the free energy landscape.…”

Polymer Mechanochemistry

“…The same idea was subsequently applied by Bell to cell adhesion [18] and extended to time-varying single-chain force by Evans [19], who derived it within the Kramers formulation of chemical kinetics. This Evans model has probably become the most widely used variant of mechanochemical kinetics because it enabled rationalization of single-molecule force experiments and has been elaborated extensively since its publication [20][21][22]. By replacing the force with stress, the Eyringansatz was extended from the single-chain level to a polymer solid [10,23], albeit at the cost of further obscuring the molecular origin of the proportionality between the control parameter (stress) and reaction rates.…”