Simple mechanochemistry describes the dynamics of kinesin molecules

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 microM 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, psi(1)(+)(t), [for the transition(s) following ATP binding] with a width parameter nu identical with (2)/<(Delta t)(2)> approximately 2.5, indicative of a dispersive stroke of mechanicity approximately 0.6 or of a few ( greater than or similar to nu - 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 ( greater than or similar to 50-fold) increase in detachment rate, with a marked load dependence, following ATP binding.