Theoretical calculation methods for kinesin in fast axonal transport

Theoretical formalism for bead movement powered by single two-headed motors in a motility assay

Kinesins and dyneins are protein motors that can use the free energy of ATP hydrolysis to carry a cargo and move uni-directionally along a microtubule filament. The purpose of this paper is to derive the formalism connecting the ATP-driven translocation reactions of these motors on microtubule filaments and the movement of the bead carried by the motor in a motility assay in which the bead is clamped at an arbitrary constant force. The formalism is thus useful in elucidating the load-dependent kinetic mechanism of the free-energy transduction of the motor using the mechanical data obtained from the motility assay. The formalism is also useful in assessing the effect on the measured motility data of various physical and hydrodynamic parameters of the assay, such as the size of the bead, the viscosity of the medium, the stiffness of the elastic element connecting the motor and the bead, etc. In a previous paper [Biophys. J. 67 (2000) 313] (hereafter referred to as paper I), we have derived the formalism for the case that the motor in the assay has only one head. In this paper we extend the derivation to the case that the motor is two-headed. The formalism is derived based on a simple two-state hand-over-hand model for the movement of the motor on microtubule, but can be easily extended to more complicated kinetic models. Effects of various hydrodynamic parameters on the velocity of the bead are studied with numerical calculations of the model. The difference between the formalism presented in this paper and the widely used "chemical" formalism, in which the movement of the kinesin and the bead is described by pure chemical reactions, is discussed.

Theoretical formalism for kinesin motility I. Bead movement powered by single one-headed kinesins

The directional movement on a microtubule of a plastic bead connected elastically to a single one-headed kinesin motor is studied theoretically. The kinesin motor can bind and unbind to periodic binding sites on the microtubule and undergo conformational changes while catalyzing the hydrolysis of ATP. An analytic formalism relating the dynamics of the bead and the ATP hydrolysis cycle of the motor is derived so that the calculation of the average velocity of the bead can be easily carried out. The formalism was applied to a simple three-state biochemical model to investigate how the velocity of the bead movement is affected by the external load, the diffusion coefficient of the bead, and the stiffness of the elastic element connecting the bead and the motor. The bead velocity was found to be critically dependent on the diffusion coefficient of the bead and the stiffness of the elastic element. A linear force-velocity relation was found for the model no matter whether the bead velocity was modulated by the diffusion coefficient of the bead or by the externally applied load. The formalism should be useful in modeling the mechanisms of chemimechanical coupling in kinesin motors based on in vitro motility data.

How do selectins mediate leukocyte rolling in venules?

At the onset of inflammation, 20-80% of all leukocytes passing postcapillary venules roll along the endothelium. Recent blocking experiments with antibodies and soluble adhesion receptor molecules, as well as in vitro reconstitution experiments, suggest that leukocyte rolling is mediated by adhesion molecules that belong to the selectin family. What differentiates a selectin-counterreceptor interaction that leads to leukocyte rolling from others that mediate firm adhesion after static incubation but no adhesion when incubated under flow conditions? Here, we explore this question by introducing a quantitative biophysical model that is compatible with the laws of mechanics as applied to rolling leukocytes and the present biochemical and biophysical data on selectin mediated interactions. Our computational experiments point to an adhesion mechanism in which the rate of bond formation is high and the detachment rate low, except at the rear of the contact area where the stretched bonds detach at a high uniform rate. The bond length and bond flexibility play a critical role in enhancing leukocyte rolling at a wide range of fluid shear rates.

Dynamics of single-motor molecules: the thermal ratchet model

We present a model for single-motor molecules--myosin, dynein, or kinesin--that is powered either by thermal fluctuations or by conformational change. In the thermally driven model, the cross-bridge fluctuates about its equilibrium position against an elastic restoring force. The attachment and detachment of the cross-bridge are determined by modeling the electrostatic attraction between the cross-bridge and the fiber binding sites, so that binding depends on the strain in the cross-bridge and its velocity with respect to the fiber. The model correctly predicts the empirical force-velocity characteristics for populations of motor molecules. For a single motor, the apparent cross-bridge step size per ATP hydrolysis depends nonlinearly on the load. When the elastic energy driving the cross-bridge is generated by a conformational change, the velocity and duty cycle are much larger than is observed experimentally for myosin.

Copurification of kinesin polypeptides with microtubule-stimulated Mg-ATPase activity and kinetic analysis of enzymatic properties

Determination of kinetic properties for kinesin adenosine triphosphatase (ATPase), a proposed motor for transport of membranous organelles, requires adequate amounts of kinesin with a consistent level of enzymatic activity. A purification procedure is detailed that produces approximately 2 mg of kinesin at up to 96% purity from 800 g of bovine brain. This protocol consists of a microtubule affinity step using 5'-adenylylimidodiphosphate (AMP-PNP); followed by gel filtration, ion exchange, and hydroxylapatite chromatography; and then sucrose density gradient centrifugation. The microtubule-activated ATPase activity of kinesin coeluted with kinesin polypeptides throughout the purification. Highly purified kinesin had a Vmax of 0.31 mumol/min/mg in the presence of microtubules, with a Km for ATP of 0.20 mM. The kinetic constants obtained in these studies compare favorably with physiological levels of ATP and microtubules. Variations in buffer conditions for the assay were found to affect ATPase activity significantly. A study of the ability of kinesin to utilize a variety of cation-ATP complexes indicated that kinesin is a microtubule-stimulated Mg-ATPase, but kinesin is able to hydrolyze Ca-ATP, Mn-ATP, and Co-ATP as well as Mg-ATP in the presence of microtubules. In the absence of microtubules, Ca-ATP appears to be the best substrate. Studies with several inhibitors of ATPases determined that vanadate inhibited kinesin ATPase at the lowest concentrations of inhibitor, but significant inhibition of the ATPase also occurred with submillimolar concentrations of AMP-PNP. Other inhibitors of kinesin include N-ethylmaleimide, adenosine diphosphate (ADP), pyrophosphate, and tripolyphosphate. Further characterization of the kinetic properties of the kinesin ATPase is important for understanding the molecular mechanisms for transport of membranous organelles along microtubules.