Probing static disorder in Arrhenius kinetics by single-molecule force spectroscopy

Tzu Ling Kuo, Sergi Garcia-Manyes, Jingyuan Li, Itay Barel, Hui Lu, Bruce J. Berne, Michael Urbakh, Joseph Klafter, Julio M. Fernández

Research output: Contribution to journalArticlepeer-review


The widely used Arrhenius equation describes the kinetics of simple two-state reactions, with the implicit assumption of a single transition state with a well-defined activation energy barrier ΔE, as the rate-limiting step. However, it has become increasingly clear that the saddle point of the free-energy surface in most reactions is populated by ensembles of conformations, leading to nonexponential kinetics. Here we present a theory that generalizes the Arrhenius equation to include static disorder of conformational degrees of freedom as a function of an external perturbation to fully account for a diverse set of transition states. The effect of a perturbation on static disorder is best examined at the single-molecule level. Here we use force-clamp spectroscopy to study the nonexponential kinetics of single ubiquitin proteins unfolding under force. We find that the measured variance in ΔE shows both force-dependent and independent components, where the forcedependent component scales with F2, in excellent agreement with our theory. Our study illustrates a novel adaptation of the classical Arrhenius equation that accounts for the microscopic origins of nonexponential kinetics, which are essential in understanding the rapidly growing body of single-molecule data.

Original languageEnglish
Pages (from-to)11336-11340
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number25
StatePublished - 22 Jun 2010


  • Molecular dynamics simulations
  • Protein unfolding
  • Single-molecule force-clamp spectroscopy
  • Ubiquitin


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