Rectified Brownian motion and kinesin motion along microtubules.

The mechanism of rectified Brownian movement is used to analyze measured data for kinesin motion along microtubules. A key component of the mechanism is the diffusive movement of the microtubule binding heads of kinesin during the adenosine triphosphate ~ATP! cycle. The first-passage time distribution for this step is analyzed in detail and is shown to be responsible for observed load-velocity profiles. The ATPase activity of the kinesin heads is that of a nucleotide switch and not that of a direct chemomechanical energy converter. Experimental data acquisition, rate constants, and alternative explanations are discussed. The mechanism described in this paper is fundamental to the nanobiology of intracellular processes. In an earlier paper @1#, the mechanism of rectified Brown- ian movement was described and used to explain several chemomechanical energy conversions in molecular and cel- lular biology. The cases covered in that paper were ubiquinone transport across lipid membranes in electron transport chains, allosteric conformation changes in proteins, P-type ATPase ion transporters, several rotary arm enzyme complexes, and the dynamics of actin-myosin cross bridges in muscle fibers. The fundamental idea of rectified Brownian movement is that the metabolic free-energy currency of ad- enosine triphosphate ~ATP! does no mechanical work di- rectly, but instead is responsible for biasing boundary condi- tions for thermal diffusion. All work is done by thermal energy that is harnessed at the expense of metabolic free energy through the switching on and off of asymmetric boundary conditions. This idea, in various forms, has a long history in the literature @2,3#. In the present paper, this mechanism is used to analyze experimental data gathered on the behavior of kinesin as it moves along microtubules. Several kinds of data have been gathered. Rate constant data have been obtained and refined @4#, new structural information has been elaborated very re- cently @5#, and load-velocity profiles have been determined @6#, most recently by means of improved optical tweezers techniques @7#. These data show that kinesin is capable of velocities as high as 1000 nanometers per second ~nm/s! at low loads, decreasing to zero velocity with increased loads with a stall force of about 5-6 piconewtons ~pN! .I n our model, this behavior is captured by the first-passage time distribution for the diffusive motion of a free kinesin head from one microtubule binding site to the next binding site. A number of subtle issues arise with this analysis. These are addressed in this paper. In Sec. II, a biophysical descrip- tion of the kinesin microtubule system is presented. In Sec. III, the basic steps of the ATP cycle are described. In Sec. IV, the rectified Brownian movement model is presented and analyzed. This analysis focuses on the first-passage time dis- tribution function. Analytic and numerical results are pre- sented. In Sec. V, problems with the measured load-velocity profiles and with reported rate constants are addressed. A discussion of alternative perspectives is given. These include Brownian ratchet mechanisms @8#, a model invoking an ATP driven ''power stroke'' @9#, and a model in which the load influences reaction rates directly @10#. The rectified Brownian movement model implies that the ATPase activity of the kinesin heads is that of a switch, like that of its ancestral protein, and not that of a direct chemo- mechanical energy converter.