10.4. Kinetics of real enzymes and machines[[Student version, January 17, 2003]] 383
of Section 10.4.1 should apply, with one modification: Since the average rate of stepping depends
on the free energy landscape along the valley, in particular it will depend on the applied load force
(the tilt in theβdirection), just as in Sections 10.2.1–10.2.3. In short, then, we expect that
Atightly coupled molecular motor, with at least one irreversible step in its
kinetics, should move at a speed governed by the Michaelis–Menten rule, with
parametersvmaxandKMdependent upon the load force.(10.22)
Areal molecular motor will, however, have some important differences from the “bumpy rubber
gears” imagined in Section 10.2.1. One difference is that we expect an enzyme’s free energy land-
scape to be even more rugged than the one shown in Figure 10.9. Activation barriers will give the
most important limit on the rate of stepping, not the viscous friction imagined in Section 10.2.1.
In addition, we have no reason to expect that the valleys in the energy landscape will be the sim-
ple diagonals imagined in Figure 10.9. More likely, they will zigzag from one corner to the other.
Some substeps may follow a path nearly parallel to theα-axis (a “purely chemical step”). The
landscape along such a substep is unaffected by tilting in theβdirection, so its rate will be nearly
independent of the applied load. Other substeps will follow a path at some angle to theα-axis (a
“mechanochemical step”); their rate will be sensitive to load.
Physical measurements can reveal details about the individual kinetic steps in a motor’s opera-
tion. This section will follow an analysis due to M. Schnitzer, K. Visscher, and S. Block. Building
on others’ ideas, these authors argued for a model of kinesin’s cycle similar to the one sketched in
Figure 10.21. The rest of this section will outline the evidence leading to this model and describe
the steps symbolized by the cartoons in the figure.
Clues from kinetics Conventional (or “two-headed”) kinesin forms a “homodimer,” an asso-
ciation of two identical protein subunits. This structure lets kinesin walk along its microtubule
track with aduty ratioof nearly 100%. The duty ratio is the fraction of the total cycle during
which the motor is bound to its track, and cannot slide freely along it; a high duty ratio lets the
motor move forward efficiently even when an opposing load force is applied. One way for kinesin
to achieve its high duty ratio could be by coordinating the detachment of its two identical heads
in a “hand-over-hand” manner, so that at any moment one is always attached while the other is
stepping.^10
Kinesin is also highlyprocessive.That is, it takes many steps (typically about one hundred)
before detaching from the microtubule. Processivity is a very convenient property for the exper-
imentalist seeking to study kinesin. Thanks to processivity, it’s possible to follow the progress of
amicron-size glass bead for many steps as it is hauled along a microtubule by a single kinesin
molecule. Using optical tweezers and a feedback loop, experimenters can also apply a precisely
known load force to the bead, then study the kinetics of kinesin stepping at various loads.
K. Svoboda and coauthors initiated a series of single-molecule motility assays of the type just
described in 1993. Using an interferometry technique, they resolved individual steps of a kinesin
dimer attached to a bead of radius 0. 5 μm,finding that each step was 8nmlong, exactly the distance
between successive kinesin binding sites on the microtubule track (see Figure 10.22). Moreover,
as shown in the figure, kinesin rarely takes backward steps, even under a significant backward load
force: In the terminology of Section 10.2.3, it is close to the “perfect ratchet” limit.
(^10) T 2 Recent work has cast doubt on the hand-over-hand picture, in which the two kinesin heads execute identical
chemical cycles (see Hua et al., 2002). Whatever the final model of kinesin stepping may be, however, it will have to
beconsistent with the experiments discussed in this section.