November 3rd 2008. BIOP-401 2nd 1-hr exam Name:
1
1. (10 points) A typical kinesin couples the energy of ATP hydrolysis with directional movement
along microtubules. In the presence of microtubules, it hydrolyzes ATP with the kcat and KM of 115 s-1
and 30µM, respectively. Estimate the translocation rate for this kinesin at
1.1 1 mM ATP
Solution:
Translocation rate = 115 s-1*8 nm ≈ 920 nm*s-1
1.2 100 nM ATP
Solution:
Translocation rate = 0.38 s-1*8 nm ≈ 3 nm*s-1
(assume that ADP and Pi are at very low concentrations and do not inhibit ATP hydrolysis; Mg2+ is
present in sufficiently high concentration to saturate all ATP)
Bonus 10 points: Why (and under what circumstances) the answer you obtained may represent a
drastic underestimation or overestimation of the actual kinesin velocity?
Solution:
Underestimation: Because the ATPase activity was measured at the steady-state situation, it averages
ATP hydrolysis of actively moving as that of the motor that has dissociated from the track and has to
rebound to it. If the latter state takes up a significant portion of the overall cycle of the motor, and the
ATPase activity in the detached motor is low, the kcat of ATP hydrolysis will be an underestimation of
the ATP hydrolysis rate by actively walking motor.
Overestimation: We assumed that 1 ATP molecule is hydrolyzed per one step and that all steps are
forward. Imperfect coupling and/or sliding or backward stepping will result in overestimation of the
velocity.
2. (total 30 points) For a chemical reaction whose
reaction coordinate is depicted on the right (T=300K), find:
2.1 (5 points) The ratio of Product to Substrate at
equilibrium
2.2 (5 points) k forward (forward rate constant)
2.3 (5 points) k reverse (reverse rate constant)
