Mechanistic mathematical model of kinesin under time and space fluctuating loads

• Published in: Nonlinear dynamics 2008-09, Vol.53 (4), p.303-320
• Main Authors: Hendricks, Adam G., Epureanu, Bogdan I., Meyhöfer, Edgar
• Format: Article
• Language: English
• Subjects: Automotive Engineering; Brownian motion; Classical Mechanics; Control; Coupling (molecular); Domains; Dynamical Systems; Engineering; Load fluctuation; Loads (forces); Mathematical analysis; Mathematical models; Mechanical Engineering; Mechanical properties; Molecular motors; Original Paper; Vibration
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-007-9315-1

Kinesin-1 is a processive molecular motor that converts the energy from ATP hydrolysis and Brownian motion into directed movement. Single-molecule techniques have allowed the experimental characterization of single kinesins in vitro at a range of loads and ATP concentrations, and shown that each kinesin molecule moves processively along microtubules by alternately advancing each of its motor domains in a hand-over-hand fashion. Existing models of kinesin movement focus on time and space invariant loads, and hence are not well suited to describing transient dynamics. However, kinesin must undergo transient dynamics when external perturbations (e.g., interactions with other kinesin molecules) cause the load on each motor to change in time. We have developed a mechanistic model that describes, deterministically, the average motion of kinesin under time and space varying loads. The diffusion is modeled using a novel approach inspired by the classical closed form solution for the mean first-passage time. In the new approach, the potential in which the free motor domain diffuses is time varying and updated at each instant during the motion. The mechanistic model is able to predict experimental force-velocity data over a wide range of ATP concentrations (1 μM–10 mM). This mechanistic approach to modeling the mechanical behavior of the motor domains of kinesin allows rational and efficient characterization of the mechanochemical coupling, and provides predictions of kinesin with time-varying loads, which is critical for modeling coordinated transport involving several kinesin molecules.