Simple mechanochemistry describes the dynamics of kinesin molecules

doi:10.1073/pnas.141080498

Simple mechanochemistry describes the dynamics of kinesin molecules

^*Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742; and ^‡Department of Chemistry, MS60, Rice University, 6100 Main Street, Houston, TX 77005-1892

Edited by Thomas D. Pollard, The Salk Institute for Biological Studies, La Jolla, CA, and approved May 9, 2001 (received for review February 16, 2001)

Abstract

Recently, Block and coworkers [Visscher, K., Schnitzer, M. J., & Block, S. M. (1999) Nature (London) 400, 184–189 and Schnitzer, M. J., Visscher, K. & Block, S. M. (2000) Nat. Cell Biol. 2, 718–723] have reported extensive observations of individual kinesin molecules moving along microtubules in vitro under controlled loads, F = 1 to 8 pN, with [ATP] = 1 μM to 2 mM. Their measurements of velocity, V, randomness, r, stalling force, and mean run length, L, reveal a need for improved theoretical understanding. We show, presenting explicit formulae that provide a quantitative basis for comparing distinct molecular motors, that their data are satisfactorily described by simple, discrete-state, sequential stochastic models. The simplest (N = 2)-state model with fixed load-distribution factors and kinetic rate constants concordant with stopped-flow experiments, accounts for the global (V, F, L, [ATP]) interdependence and, further, matches relative acceleration observed under assisting loads. The randomness, r(F,[ATP]), is accounted for by a waiting-time distribution, ψ $\text{[math]}$ (t), [for the transition(s) following ATP binding] with a width parameter ν ≡ 〈t〉 ²/〈(Δt)²〉≃2.5, indicative of a dispersive stroke of mechanicity ≃0.6 or of a few (≳ν − 1) further, kinetically coupled states: indeed, N = 4 (but not N = 3) models do well. The analysis reveals: (i) a substep of d ₀ = 1.8–2.1 nm on ATP binding (consistent with structurally based suggestions); (ii) comparable load dependence for ATP binding and unbinding; (iii) a strong load dependence for reverse hydrolysis and subsequent reverse rates; and (iv) a large (≳50-fold) increase in detachment rate, with a marked load dependence, following ATP binding.

Footnotes

↵ † To whom reprint requests should be addressed.
This paper was submitted directly (Track II) to the PNAS office.
↵ § We remark that backward steps of kinesin on MTs are seen near stall conditions (7, 8). These may be envisaged as resulting from ADP and P_i associated with kinesins and the MT in a successor complex for which the overall solution concentrations, [ADP] and [P_i], may have relatively little direct relevance.
Abbreviation:

MT,

microtubule