Forces required of kinesin during processive transport through cytoplasm
ABSTRACT The purpose of this paper is to deduce whether the maximum force, steplike movement, and rate of ATP consumption of kinesin, as measured in buffer, are sufficient for the task of fast transport of vesicles in cells. Our results show that moving a 200-nm vesicle in viscoelastic COS7 cytoplasm, with the same steps as observed for kinesin-driven beads in buffer, required a maximum force of 16 pN and work per step of 1+/-0.7 ATP, if the drag force was assumed to decrease to zero between steps. In buffer, kinesin can develop a force of 6-7 pN while consuming 1 ATP/step, comparable to the required values. As an alternative to assuming that the force vanishes between steps, the measured COS7 viscoelasticity was extrapolated to zero frequency by a numerical fit. The force required to move the bead then exceeded 75 pN at all times and peaked briefly to 92 pN, well beyond the measured capabilities of a single kinesin in buffer. The work per step increased to 7+/-5 ATP, greatly exceeding the energy available to a single motor.
The motor protein kinesin transports organelles within cells. Especially within neurons, where transport distances along axons can be large, it has long been conjectured that the work of transport presents a significant energy cost to the cell. Although considerable progress has recently been made in understanding the force, velocity, and energy coupling as kinesin drags a latex bead along microtubules in solution, no quantitative connections have been made to the forces and work of fast transport in cells.
A single kinesin molecule in buffer can generate a steady force of no more than 7.5 pN while dragging an attached bead up the potential well of an optical trap (Svoboda and Block, 1994; Kojima et al., 1997; Visscher et al., 1999). When the constraining force is less than the stall force, a single kinesin can drag the bead at an average velocity of 800 nm/s in buffer. If the position of the latex bead is measured more carefully, it is found that kinesin moves along the microtubule in abrupt 8-nm steps, with each step coupled to the hydrolysis of 1 ATP. To achieve the observed time-averaged bead velocity of 800 nm/s, a single kinesin must carry out 100 such steps per second. Each step takes a mere 50 (mu)s in buffer (Nishiyama et al., 2001). Thus, a kinesin motor and its vesicle load in buffer are stationary 99.5% of the time, but when they move, their instantaneous velocity briefly exceeds 100,000 nm/s. Work is done only during the brief intervals when the bead moves.
In cells, the time-averaged velocity of fast axonal transport is 800-4500 nm/s (Howard 2001). However, kinesin molecules pulling a vesicle in a cell face a very different load. In the buffer-filled trap, the load is almost purely elastic, whereas in a cell, the load is almost purely viscous. The effect of viscous load has been explored in gliding assays (Hunt et al., 1994). The mobility decreases from 1.2 (mu)m/s in buffer to 0.2-0.5(mu)m/s in an increasingly viscous mixture of dextran, Ficoll, and trypsin inhibitor. The limiting average value of the force generated by kinesin in the viscous medium is 4.0-5.2 pN. Because the position of the microtubule was determined at intervals of 0.1-1.0 s, the individual steps were not resolved.
Recently, high-resolution optical tracking of the Brownian motion of intracellular particles has enabled researchers to measure, for the first time, the complex viscoelastic modulus G*(omega) within a living cell over a broad frequency range (Yamada et al., 2000). The modulus was determined for 0.5
The purpose of this paper is to calculate the drag force and work required to move a spherical vesicle within a cell from the measurements of G* in COS7 and the measurements of kinesin motion in an optical trap. It is assumed that kinesin moves in cytoplasm with the same quick steps as in an optical trap.
FORCE AND WORK IN A NEWTONIAN FLUID
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G. Holzwarth, Keith Bonin, and David B. Hill
Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109 USA
Submitted August 14, 2001, and accepted for publication January 14, 2002.
Address reprint requests to G. Holzwarth, Department of Physics, Wake Forest University, PO Box 7507, Winston-Salem. NC 27109. Tel.: 336– 758-5533; Fax: 336-758-6142; E-mail: email@example.com.
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