please answer question 16.3. provided on the book\'s website. Does your analysis
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please answer question 16.3.
provided on the book's website. Does your analysis support the hand-over-hand mechanism? What value of k do you obtain? - 16.3 Kinesin as an ATP-hydrolyzing enzyme As described in the chapter, 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 introduced in Section 15.2.7 (p. 596). 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 a speed, since kinesin takes many steps before falling off the microtubule. Relate the reaction speed (the rate of ATP hydrolysis) to the maximum stepping speed of kinesin and determine its dependence on ATP concentration. Fit your model to the data by Schnitzer and Block (1997) shown in Figure 16.54 and provided on the book's website. Then work out what change in substrate concentration is needed to increase the reaction rate from 0.1 Vmax to 0.9Vmax 16.4 Kinetics of two-state motors In the chapter, in order to obtain the velocity of a two-state motor, we made use of a trick to circumvent solving the master equation directly. Here we take up this task and in the process also derive an expression for the diffusion constant. (a) Consider a trial solution of the system of equations for Po (n, t) and p1(n, 0), given by Equations 16.33 and 16.34, 678Explanation / Answer
A key goal in the study of the function of ATP-driven motor enzymes is to quantify the movement produced from consumption of one ATP molecule1,2,3. Discrete displacements of the processive motor kinesin along a microtubule have been reported as 5 and/or 8 nm (refs 4, 5). However, analysis of nanometre-scale movements is hindered by superimposed brownian motion. Moreover, because kinesin is processive and turns over stochastically, some observed displacements must arise from summation of smaller movements that are too closely spaced in time to be resolved. To address both of these problems, we used light microscopy instrumentation6 with low positional drift (<39 pm s?1) to observe single molecules of a kinesin derivative moving slowly (?2.5 nm s?1) at very low (150 nM) ATP concentration, so that ATP-induced displacements were widely spaced in time.
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