Question

Careful measurements have been performed that examine the dependence of motor velocity on ATP concentration. Under certain conditions, the hydrolysis reaction performed by a molecular motor can be described using the Michaelis-Menten model. In the particular case of kinesin, its stepping is strongly coupled to its ATPase activity, which translates into relatively constant step sizes. Finally, its high processivity allows for a clear definition of speed, since kinesin takes many steps before falling off the microtubule. a) Relate the reaction speed (the rate of ATP hydrolysis) to the maximum stepping speed of kinesin and determine its dependence on ATP concentration. To do this, consider the motor as a simple Michaelis-Menten process characterized by a kinetic scheme of the form E + S ⇌ ES → E + P. b) Fit your model to the data by Schnitzer and Block (1997) provided in a separate file. Obtain Vmax and Km. c) Work out what change in substrate concentration is needed to increase the reaction rate from 0.1 Vmax to 0.9 Vmax. Data from Schnitzer, M. J. and M. Block (1997). Kinesin hydrolyzes one ATP per 8-nm step. Nature 388(6640): 386-90. x = ATP concentration (μM) Y = speed (nm/s) 13 19 50 95 260 410 650 650 10 40 100 400 1000

          Careful measurements have been performed that examine the dependence of motor velocity on ATP concentration. Under certain conditions, the hydrolysis reaction performed by a molecular motor can be described using the Michaelis-Menten model. In the particular case of kinesin, its stepping is strongly coupled to its ATPase activity, which translates into relatively constant step sizes. Finally, its high processivity allows for a clear definition of speed, since kinesin takes many steps before falling off the microtubule.

a) Relate the reaction speed (the rate of ATP hydrolysis) to the maximum stepping speed of kinesin and determine its dependence on ATP concentration. To do this, consider the motor as a simple Michaelis-Menten process characterized by a kinetic scheme of the form E + S ⇌ ES → E + P.

b) Fit your model to the data by Schnitzer and Block (1997) provided in a separate file. Obtain Vmax and Km.

c) Work out what change in substrate concentration is needed to increase the reaction rate from 0.1 Vmax to 0.9 Vmax.

Data from Schnitzer, M. J. and M. Block (1997). Kinesin hydrolyzes one ATP per 8-nm step. Nature 388(6640): 386-90.

x = ATP concentration (μM)
Y = speed (nm/s)
13 19 50 95 260 410 650 650
10 40 100 400 1000

Added by Cathy D.

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