Probing static disorder in Arrhenius kinetics by single-molecule force spectroscopy.
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 DeltaE, 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 DeltaE shows both force-dependent and independent components, where the force-dependent component scales with F(2), 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.
Department of Physics, Columbia University, New York, NY 10027, USA.
Tzu-Ling
TL
Kuo
Sergi
S
Garcia-Manyes
Jingyuan
J
Li
Itay
I
Barel
Hui
H
Lu
Bruce J
BJ
Berne
Michael
M
Urbakh
Joseph
J
Klafter
Julio M
JM
Fernández
D001671:Biochemistry / Q000379:methods*; D003198:Computer Simulation; D007700:Kinetics; D018625:Microscopy, Atomic Force / Q000379:methods*; D015233:Models, Statistical; D008968:Molecular Conformation; D011487:Protein Conformation; D017510:Protein Folding; D011506:Proteins / Q000737:chemistry; D013053:Spectrophotometry / Q000379:methods*; D013314:Stress, Mechanical; D013816:Thermodynamics; D025801:Ubiquitin / Q000737:chemistry*
D011506:Proteins; D025801:Ubiquitin