Intrinsic rates and activation free energies from single-molecule pulling experiments.
TL;DR: By analyzing simulated data, it is shown 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.
Abstract: 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 overinterpretation of experiments.
Citations
More filters
TL;DR: The purpose of this review is to broadly survey the mechanical to chemical relationships between synthetic polymers, and to consider the I-O relationship as an energy transduction process for designing stimuli-responsive materials.
Abstract: Engineering applications of synthetic polymers are widespread due to their availability, processability, low density, and diversity of mechanical properties (Figure 1a). Despite their ubiquitous nature, modern polymers are evolving into multifunctional systems with highly sophisticated behavior. These emergent functions are commonly described as “smart” characteristics whereby “intelligence” is rooted in a specific response elicited from a particular stimulus. Materials that exhibit stimuli-responsive functions thus achieve a desired output (O, the response) upon being subjected to a specific input (I, the stimulus). Given that mechanical loading is inevitable, coupled with the wide range of mechanical properties for synthetic polymers, it is not surprising that mechanoresponsive polymers are an especially attractive class of smart materials. To design materials with stimuli-responsive functions, it is helpful to consider the I-O relationship as an energy transduction process. Achieving the desired I-O linkage thus becomes a problem in finding how to transform energy from the stimulus into energy that executes the desired response. The underlying mechanism that forms this I-O coupling need not be a direct, one-step transduction event; rather, the overall process may proceed through a sequence of energy transduction steps. In this regard, the network of energy transduction pathways is a useful roadmap for designing stimuli-responsive materials (Figure 1b). It is the purpose of this review to broadly survey the mechanical to chemical * To whom correspondence should be addressed. Phone: 217-244-4024. Fax: 217-244-8024. E-mail: jsmoore@illinois.edu. † Department of Chemistry and Beckman Institute. ‡ Department of Materials Science and Engineering and Beckman Institute. § Department of Aerospace Engineering and Beckman Institute. Chem. Rev. XXXX, xxx, 000–000 A
1,081 citations
TL;DR: The cornerstone of the method is a transformation of the rupture-force histograms obtained at different force-loading rates into the force-dependent lifetimes measurable in constant-force experiments, and a generalization of Bell's formula is derived that is formally exact within the framework of Kramers theory.
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 force-loading 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.
619 citations
Cites background or methods from "Intrinsic rates and activation free..."
...This mapping follows directly from the quasi-adiabatic assumption (22, 26) and is independent of the nature of the underlying free-energy surface....
[...]
...Indeed, the same functional relation, with a numerical coefficient that differs by <10%, can be derived from the highly non-Gaussian rupture-force distributions (22) that correspond to τ (F) in Eq....
[...]
...For several simple one-dimensional free-energy profiles, the lifetime τ (F) calculated from Kramers theory can then be written as (22):...
[...]
...Explicit expressions for the rupture-force distributions enable the use of powerful maximum-likelihood or Bayesian inference methods in the analysis of experiments (22)....
[...]
...Recently (22), we have made the phenomenological model, based on Bell’s assumption, more realistic while retaining its mathematical simplicity....
[...]
TL;DR: An integrated view of hierarchical folding in an aptamer is provided, demonstrating how complex folding can be resolved into constituent parts, and further insights into tertiary structure formation are supplied.
Abstract: Riboswitches regulate genes through structural changes in ligand-binding RNA aptamers. With the use of an optical-trapping assay based on in situ transcription by a molecule of RNA polymerase, single nascent RNAs containing pbuE adenine riboswitch aptamers were unfolded and refolded. Multiple folding states were characterized by means of both force-extension curves and folding trajectories under constant force by measuring the molecular contour length, kinetics, and energetics with and without adenine. Distinct folding steps correlated with the formation of key secondary or tertiary structures and with ligand binding. Adenine-induced stabilization of the weakest helix in the aptamer, the mechanical switch underlying regulatory action, was observed directly. These results provide an integrated view of hierarchical folding in an aptamer, demonstrating how complex folding can be resolved into constituent parts, and supply further insights into tertiary structure formation.
390 citations
TL;DR: The principles and applications of advanced FD-based AFM tools for the quantitative multiparametric characterization of complex cellular and biomolecular systems under physiological conditions are discussed.
Abstract: A current challenge in the life sciences is to understand how biological systems change their structural, biophysical and chemical properties to adjust functionality. Addressing this issue has been severely hampered by the lack of methods capable of imaging biosystems at high resolution while simultaneously mapping their multiple properties. Recent developments in force-distance (FD) curve–based atomic force microscopy (AFM) now enable researchers to combine (sub)molecular imaging with quantitative mapping of physical, chemical and biological interactions. Here we discuss the principles and applications of advanced FD-based AFM tools for the quantitative multiparametric characterization of complex cellular and biomolecular systems under physiological conditions.
384 citations
TL;DR: How advanced experimental, computational and theoretical methods can be used to assess structure-process-property relations and to monitor and predict mechanisms associated with failure of protein materials are discussed.
Abstract: Biological protein materials feature hierarchical structures that make up a diverse range of physiological materials. The analysis of protein materials is an emerging field that uses the relationships between biological structures, processes and properties to probe deformation and failure phenomena at the molecular and microscopic level. Here we discuss how advanced experimental, computational and theoretical methods can be used to assess structure-process-property relations and to monitor and predict mechanisms associated with failure of protein materials. Case studies are presented to examine failure phenomena in the progression of disease. From this materials science perspective, a de novo basis for understanding biological processes can be used to develop new approaches for treating medical disorders. We highlight opportunities to use knowledge gained from the integration of multiple scales with physical, biological and chemical concepts for potential applications in materials design and nanotechnology.
340 citations
References
More filters
46,339 citations
TL;DR: In this article, a particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.
7,289 citations
TL;DR: The force required to separate two cells is shown to be greater than the expected electrical forces between cells, and of the same order of magnitude as the forces required to pull gangliosides and perhaps some integral membrane proteins out of the cell membrane.
Abstract: A theoretical framework is proposed for the analysis of adhesion between cells or of cells to surfaces when the adhesion is mediated by reversible bonds between specific molecules such as antigen and antibody, lectin and carbohydrate, or enzyme and substrate. From a knowledge of the reaction rates for reactants in solution and of their diffusion constants both in solution and on membranes, it is possible to estimate reaction rates for membrane-bound reactants. Two models are developed for predicting the rate of bond formation between cells and are compared with experiments. The force required to separate two cells is shown to be greater than the expected electrical forces between cells, and of the same order of magnitude as the forces required to pull gangliosides and perhaps some integral membrane proteins out of the cell membrane.
4,058 citations
TL;DR: How Brownian dynamics can help bridge the gap between molecular dynamics and probe tests is described, which shows that bond strength progresses through three dynamic regimes of loading rate.
2,401 citations
TL;DR: The implementation and test of Jarzynski's equality provides the first example of its use as a bridge between the statistical mechanics of equilibrium and nonequilibrium systems, and extends the thermodynamic analysis of single molecule manipulation data beyond the context of equilibrium experiments.
Abstract: Recent advances in statistical mechanical theory can be used to solve a fundamental problem in experimental thermodynamics. In 1997, Jarzynski proved an equality relating the irreversible work to the equilibrium free energy difference, DeltaG. This remarkable theoretical result states that it is possible to obtain equilibrium thermodynamic parameters from processes carried out arbitrarily far from equilibrium. We test Jarzynski's equality by mechanically stretching a single molecule of RNA reversibly and irreversibly between two conformations. Application of this equality to the irreversible work trajectories recovers the DeltaG profile of the stretching process to within k(B)T/2 (half the thermal energy) of its best independent estimate, the mean work of reversible stretching. The implementation and test of Jarzynski's equality provides the first example of its use as a bridge between the statistical mechanics of equilibrium and nonequilibrium systems. This work also extends the thermodynamic analysis of single molecule manipulation data beyond the context of equilibrium experiments.
1,086 citations