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Cai W, Jäger M, Bullerjahn JT, Hugel T, Wolf S, Balzer BN. Anisotropic Friction in a Ligand-Protein Complex. NANO LETTERS 2023; 23:4111-4119. [PMID: 36948207 DOI: 10.1021/acs.nanolett.2c04632] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The effect of an externally applied directional force on molecular friction is so far poorly understood. Here, we study the force-driven dissociation of the ligand-protein complex biotin-streptavidin and identify anisotropic friction as a not yet described type of molecular friction. Using AFM-based stereographic single molecule force spectroscopy and targeted molecular dynamics simulations, we find that the rupture force and friction for biotin-streptavidin vary with the pulling angle. This observation holds true for friction extracted from Kramers' rate expression and by dissipation-corrected targeted molecular dynamics simulations based on Jarzynski's identity. We rule out ligand solvation and protein-internal friction as sources of the angle-dependent friction. Instead, we observe a heterogeneity in free energy barriers along an experimentally uncontrolled orientation parameter, which increases the rupture force variance and therefore the overall friction. We anticipate that anisotropic friction needs to be accounted for in a complete understanding of friction in biomolecular dynamics and anisotropic mechanical environments.
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Affiliation(s)
- Wanhao Cai
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104 Freiburg, Germany
| | - Miriam Jäger
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Jakob T Bullerjahn
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Str. 3, 60438 Frankfurt am Main, Germany
| | - Thorsten Hugel
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Bizan N Balzer
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110 Freiburg, Germany
- Freiburg Materials Research Center (FMF), University of Freiburg, Stefan-Meier-Str. 21, 79104 Freiburg, Germany
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Kuznets-Speck B, Limmer DT. Inferring equilibrium transition rates from nonequilibrium protocols. Biophys J 2023; 122:1659-1664. [PMID: 36964656 PMCID: PMC10183322 DOI: 10.1016/j.bpj.2023.03.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Revised: 01/08/2023] [Accepted: 03/21/2023] [Indexed: 03/26/2023] Open
Abstract
We develop a theory for inferring equilibrium transition rates from trajectories driven by a time-dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution function in terms of the equilibrium distribution function and the excess dissipation, we formulate a nonequilibrium transition state theory to estimate the rate enhancement over the equilibrium rate due to the nonequilibrium protocol. We demonstrate the utility of our theory in examples of pulling of harmonically trapped particles in one and two dimensions, as well as a semiflexible polymer with a reactive linker in three dimensions. We expect our purely thermodynamic approach will find use in both molecular simulation and force spectroscopy experiments.
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Affiliation(s)
| | - David T Limmer
- Chemistry Department, University of California, Berkeley, Berkeley, California; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California; Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California; Kavli Energy NanoSciences Institute, University of California, Berkeley, Berkeley, California.
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Cai W, Bullerjahn JT, Lallemang M, Kroy K, Balzer BN, Hugel T. Angle-dependent strength of a single chemical bond by stereographic force spectroscopy. Chem Sci 2022; 13:5734-5740. [PMID: 35694336 PMCID: PMC9117962 DOI: 10.1039/d2sc01077a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Accepted: 04/13/2022] [Indexed: 11/21/2022] Open
Abstract
A wealth of chemical bonds and polymers have been studied with single-molecule force spectroscopy, usually by applying a force perpendicular to the anchoring surface. However, the direction-dependence of the bond strength lacks fundamental understanding. Here we establish stereographic force spectroscopy to study the single-bond strength for various pulling angles. Surprisingly, we find that the apparent bond strength increases with increasing pulling angle relative to the anchoring surface normal, indicating a sturdy mechanical anisotropy of a chemical bond. This finding can be rationalized by a fixed pathway for the rupture of the bond, resulting in an effective projection of the applied pulling force onto a nearly fixed rupture direction. Our study is fundamental for the molecular understanding of the role of the direction of force application in molecular adhesion and friction. It is also a prerequisite for the nanoscale tailoring of the anisotropic strength of bottom-up designed materials. Stereographic force spectroscopy reveals that a chemical bond ruptures along a fixed pathway such that the apparent bond strength strongly depends on the angle of force application.![]()
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Affiliation(s)
- Wanhao Cai
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104, Freiburg, Germany
| | - Jakob T. Bullerjahn
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Straße 3, 60438, Frankfurt am Main, Germany
| | - Max Lallemang
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104, Freiburg, Germany
- Cluster of Excellence livMatS@FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110, Freiburg, Germany
| | - Klaus Kroy
- Institute for Theoretical Physics, Leipzig University, Brüderstraße 16, 04103, Leipzig, Germany
| | - Bizan N. Balzer
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104, Freiburg, Germany
- Cluster of Excellence livMatS@FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110, Freiburg, Germany
- Freiburg Materials Research Center (FMF), University of Freiburg, Stefan-Meier-Str. 21, 79104, Freiburg, Germany
| | - Thorsten Hugel
- Institute of Physical Chemistry, University of Freiburg, Albertstr. 21, 79104, Freiburg, Germany
- Cluster of Excellence livMatS@FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110, Freiburg, Germany
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Bullerjahn JT, Sturm S, Kroy K. Theory of rapid force spectroscopy. Nat Commun 2014; 5:4463. [PMID: 25079911 PMCID: PMC4124868 DOI: 10.1038/ncomms5463] [Citation(s) in RCA: 63] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2014] [Accepted: 06/19/2014] [Indexed: 12/19/2022] Open
Abstract
In dynamic force spectroscopy, single (bio-)molecular bonds are actively broken to assess their range and strength. At low loading rates, the experimentally measured statistical distributions of rupture forces can be analysed using Kramers’ theory of spontaneous unbinding. The essentially deterministic unbinding events induced by the extreme forces employed to speed up full-scale molecular simulations have been interpreted in mechanical terms, instead. Here we start from a rigorous probabilistic model of bond dynamics to develop a unified systematic theory that provides exact closed-form expressions for the rupture force distributions and mean unbinding forces, for slow and fast loading protocols. Comparing them with Brownian dynamics simulations, we find them to work well also at intermediate pulling forces. This renders them an ideal companion to Bayesian methods of data analysis, yielding an accurate tool for analysing and comparing force spectroscopy data from a wide range of experiments and simulations. Dynamic force spectroscopy is widely applied to probe molecular interactions by forcible bond breaking, but it currently lacks an analytical theory that spans the divide between experiment and simulation. Here, such a unified framework is developed and shown to be accurate for slow and fast loading.
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Affiliation(s)
- Jakob T Bullerjahn
- Universität Leipzig, Institut für theoretische Physik, 04103 Leipzig, Germany
| | - Sebastian Sturm
- Universität Leipzig, Institut für theoretische Physik, 04103 Leipzig, Germany
| | - Klaus Kroy
- Universität Leipzig, Institut für theoretische Physik, 04103 Leipzig, Germany
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Lamprecht C, Hinterdorfer P, Ebner A. Applications of biosensing atomic force microscopy in monitoring drug and nanoparticle delivery. Expert Opin Drug Deliv 2014; 11:1237-53. [PMID: 24809228 DOI: 10.1517/17425247.2014.917078] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
INTRODUCTION The therapeutic effects of medicinal drugs not only depend on their properties, but also on effective transport to the target receptor. Here we highlight recent developments in this discipline and show applications of atomic force microscopy (AFM) that enable us to track the effects of drugs and the effectiveness of nanoparticle delivery at the single molecule level. AREAS COVERED Physiological AFM imaging enables visualization of topographical changes to cells as a result of drug exposure and allows observation of cellular responses that yield morphological changes. When we upgrade the regular measuring tip to a molecular biosensor, it enables investigation of functional changes at the molecular level via single molecule force spectroscopy. EXPERT OPINION Biosensing AFM techniques have generated powerful tools to monitor drug delivery in (living) cells. While technical developments in actual AFM methods have simplified measurements at relevant physiological conditions, understanding both the biological and technical background is still a crucial factor. However, due to its potential impact, we expect the number of application-based biosensing AFM techniques to further increase in the near future.
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Affiliation(s)
- Constanze Lamprecht
- University of Kiel, Institute of Materials Science Biocompatible Nanomaterials , Kaiserstr.2, 24143 Kiel , Germany
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Brucale M, Schuler B, Samorì B. Single-molecule studies of intrinsically disordered proteins. Chem Rev 2014; 114:3281-317. [PMID: 24432838 DOI: 10.1021/cr400297g] [Citation(s) in RCA: 112] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Marco Brucale
- Institute for the Study of Nanostructured Materials (ISMN), Italian National Council of Research (CNR) , Area della Ricerca Roma1, Via Salaria km 29.3 00015 Monterotondo (Rome), Italy
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Effect of viscoelasticity on the analysis of single-molecule force spectroscopy on live cells. Biophys J 2012; 103:137-45. [PMID: 22828340 DOI: 10.1016/j.bpj.2012.05.044] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2012] [Revised: 04/30/2012] [Accepted: 05/24/2012] [Indexed: 10/28/2022] Open
Abstract
Single-molecule force spectroscopy is used to probe the kinetics of receptor-ligand bonds by applying mechanical forces to an intermediate media on which the molecules reside. When this intermediate media is a live cell, the viscoelastic properties can affect the calculation of rate constants. We theoretically investigate the effect of media viscoelasticity on the common assumption that the bond force is equal to the instantaneous applied force. Dynamic force spectroscopy is simulated between two cells of varying micromechanical properties adhered by a single bond with a constant kinetic off-rate. We show that cell and microvilli deformation, and hydrodynamic drag contribute to bond forces that can be 28-90% lower than the applied force for loading rates of 10(3)-10(7) pN/s, resulting in longer bond lifetimes. These longer bond lifetimes are not caused by changes in bond kinetics; rather, they are due to the mechanical response of the intermediate media on which the bonds reside. Under the assumption that the instantaneous bond force is equal to the applied force--thereby ignoring viscoelasticity--leads to 14-39% error in the determination of off-rates. We present an approach that incorporates viscoelastic properties in calculating the instantaneous bond force and kinetic dissociation parameter of the intermolecular bond.
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Walhorn V, Schäfer C, Schröder T, Mattay J, Anselmetti D. Functional characterization of a supramolecular affinity switch at the single molecule level. NANOSCALE 2011; 3:4859-4865. [PMID: 22009325 DOI: 10.1039/c1nr10912j] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Surface-immobilized and switchable resorcin[4]arene receptor molecules were quantitatively investigated with atomic force microscopy (AFM) and AFM-single molecule force spectroscopy (AFM-SMFS). The upper rim of the supramolecular receptor cavities was modified with two photodimerizable anthracene moieties. The molecular constitution can be externally switched and controlled by exposure to ultraviolet (UV) light and heat. The topography as well as the complexation affinity against small ammonium guest ions of the two isomers were investigated at the single molecule level. Our results demonstrate the feasibility to externally control the supramolecular receptor's affinity and simultaneously quantify and associate these binding properties with the structural change of the resorcin[4]arenes structure on the basis of the measured molecule corrugation height.
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Affiliation(s)
- Volker Walhorn
- Experimental Biophysics and Applied Nanoscience, Department of Physics, Bielefeld University, Universitätsstraße 25, 33615, Bielefeld, Germany
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Kaur P, Fuhrmann A, Ros R, Kutner LO, Schneeweis LA, Navoa R, Steger K, Xie L, Yonan C, Abraham R, Grace MJ, Lindsay S. Antibody-unfolding and metastable-state binding in force spectroscopy and recognition imaging. Biophys J 2011; 100:243-50. [PMID: 21190677 DOI: 10.1016/j.bpj.2010.11.050] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2010] [Revised: 11/12/2010] [Accepted: 11/23/2010] [Indexed: 11/18/2022] Open
Abstract
Force spectroscopy and recognition imaging are important techniques for characterizing and mapping molecular interactions. In both cases, an antibody is pulled away from its target in times that are much less than the normal residence time of the antibody on its target. The distribution of pulling lengths in force spectroscopy shows the development of additional peaks at high loading rates, indicating that part of the antibody frequently unfolds. This propensity to unfold is reversible, indicating that exposure to high loading rates induces a structural transition to a metastable state. Weakened interactions of the antibody in this metastable state could account for reduced specificity in recognition imaging where the loading rates are always high. The much weaker interaction between the partially unfolded antibody and target, while still specific (as shown by control experiments), results in unbinding on millisecond timescales, giving rise to rapid switching noise in the recognition images. At the lower loading rates used in force spectroscopy, we still find discrepancies between the binding kinetics determined by force spectroscopy and those determined by surface plasmon resonance-possibly a consequence of the short tethers used in recognition imaging. Recognition imaging is nonetheless a powerful tool for interpreting complex atomic force microscopy images, so long as specificity is calibrated in situ, and not inferred from equilibrium binding kinetics.
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Affiliation(s)
- Parminder Kaur
- Biodesign Institute, Arizona State University, Tempe, Arizona, USA
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Huang S, He J, Chang S, Zhang P, Liang F, Li S, Tuchband M, Fuhrmann A, Ros R, Lindsay S. Identifying single bases in a DNA oligomer with electron tunnelling. NATURE NANOTECHNOLOGY 2010; 5:868-73. [PMID: 21076404 PMCID: PMC4121130 DOI: 10.1038/nnano.2010.213] [Citation(s) in RCA: 196] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2010] [Accepted: 10/04/2010] [Indexed: 05/21/2023]
Abstract
It has been proposed that single molecules of DNA could be sequenced by measuring the physical properties of the bases as they pass through a nanopore. Theoretical calculations suggest that electron tunnelling can identify bases in single-stranded DNA without enzymatic processing, and it was recently experimentally shown that tunnelling can sense individual nucleotides and nucleosides. Here, we report that tunnelling electrodes functionalized with recognition reagents can identify a single base flanked by other bases in short DNA oligomers. The residence time of a single base in a recognition junction is on the order of a second, but pulling the DNA through the junction with a force of tens of piconewtons would yield reading speeds of tens of bases per second.
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Affiliation(s)
- Shuo Huang
- Biodesign Institute, Arizona State University, Tempe, Arizona 85287, USA
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Fuhrmann A, Ros R. Single-molecule force spectroscopy: a method for quantitative analysis of ligand–receptor interactions. Nanomedicine (Lond) 2010; 5:657-66. [DOI: 10.2217/nnm.10.26] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
The quantitative analysis of molecular interactions is of high interest in medical research. Most methods for the investigation of ligand–receptor complexes deal with huge ensembles of biomolecules, but often neglect interactions with low affinity or small subpopulations with different binding properties. Single-molecule force spectroscopy offers fascinating possibilities for the quantitative analysis of ligand–receptor interactions in a wide affinity range and the sensitivity to detect point mutations. Furthermore, this technique allows one to address questions about the related binding energy landscape. In this article, we introduce single-molecule force spectroscopy with a focus on novel developments in both data analysis and theoretical models for the technique. We also demonstrate two examples of the capabilities of this method.
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Affiliation(s)
- Alexander Fuhrmann
- Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA
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Aioanei D, Samorì B, Brucale M. Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:061916. [PMID: 20365199 DOI: 10.1103/physreve.80.061916] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2009] [Indexed: 05/29/2023]
Abstract
Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.
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Affiliation(s)
- Daniel Aioanei
- Department of Biochemistry G Moruzzi, University of Bologna, Via Irnerio 48, 40126 Bologna, Italy.
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Tshiprut Z, Urbakh M. Exploring hysteresis and energy dissipation in single-molecule force spectroscopy. J Chem Phys 2009; 130:084703. [DOI: 10.1063/1.3077867] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fuhrmann A, Anselmetti D, Ros R, Getfert S, Reimann P. Refined procedure of evaluating experimental single-molecule force spectroscopy data. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031912. [PMID: 18517427 DOI: 10.1103/physreve.77.031912] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2007] [Revised: 11/09/2007] [Indexed: 05/26/2023]
Abstract
Dynamic force spectroscopy is a well-established tool to study molecular recognition in a wide range of binding affinities on the single-molecule level. The theoretical interpretation of these data is still very challenging and the models describe the experimental data only partly. In this paper we reconsider the basic assumptions of the models on the basis of an experimental data set and propose an approach of analyzing and quantitatively evaluating dynamic force spectroscopy data on single ligand-receptor complexes. We present our procedure to process and analyze the force-distance curves, to detect the rupture events in an automated manner, and to calculate quantitative parameters for a biophysical characterization of the investigated interaction.
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Affiliation(s)
- Alexander Fuhrmann
- Experimental Biophysics, Physics Department, Bielefeld University, 33615 Bielefeld, Germany
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