model of muscle contraction. Based on your understanding of the sliding-filament model and the structure of a sarcomere, propose a molecular explanation for the relationship of tension to sarcomere length in the portions of Figure Q16–1 marked I, II, III, and IV. (In this muscle, the length of the myosin filament is 1.6 μm, and the lengths of the actin thin filaments that project from the Z discs are 1.0 μm.) 16–6 At 1.4 mg/mL pure tubulin, microtubules grow at a rate of about 2 μm/min. At this growth rate, how many αβ-tubulin dimers (8 nm in length) are added to the ends of a microtubule each second?
Figure Q16–2 Model for microtubule nucleation by pure αβ-tubulin dimers (Problem 16–7).
16–7 A solution of pure αβ-tubulin dimers is thought to nucleate microtubules by forming a linear protofilament about seven dimers in length. At that point, the probabilities that the next αβ-dimer will bind laterally or to the end of the protofilament are about equal. The critical event for microtubule formation is thought to be the first lateral association (Figure Q16–2). How does lateral association promote the subsequent rapid formation of a microtubule?
16–8 How does a centrosome “know” when it has found the center of the cell?
16–9 The movements of single motor-protein molecules can be analyzed directly. Using polarized laser light, it is possible to create interference patterns that exert a centrally directed force, ranging from zero at the center to a few piconewtons at the periphery (about 200 nm from the center). Individual molecules that enter the interference pattern are rapidly pushed to the center, allowing them to be captured and moved at the experimenter’s discretion.
Using such “optical tweezers,” single kinesin molecules can be positioned on a microtubule that is fixed to a coverslip. Although a single kinesin molecule cannot be seen optically, it can be tagged with a silica bead and tracked indirectly by following the bead (Figure Q16–3A). In the absence of ATP, the kinesin molecule remains at the center of the interference pattern, but with ATP it moves toward the plus end of the microtubule. As kinesin moves along the microtubule, it encounters the force of the interference pattern, which simulates the load kinesin carries during its actual function in the cell. Moreover, the pressure against the silica bead counters the effects of Brownian (thermal) motion, so that the position of the bead more accurately reflects the position of the kinesin molecule on the microtubule.
A trace of the movements of a kinesin molecule along a microtubule is shown in Figure Q16–3B.
A. As shown in Figure Q16–3B, all movement of kine-sin is in one direction (toward the plus end of the micro-tubule). What supplies the free energy needed to ensure a unidirectional movement along the microtubule?
b.
What is the average rate of movement of kinesin along the microtubule?
C.
What is the length of each step that a kinesin takes as it moves along a microtubule?
D.
From other studies it is known that kinesin has two globular domains that can each bind to β-tubulin, and that kinesin moves along a single protofilament in a microtubule. In each protofilament, the β-tubulin subunit repeats at 8-nm intervals. Given the step length and the interval between β-tubulin subunits, how do you suppose a kine-sin molecule moves along a microtubule?
E.
Is there anything in the data in Figure Q16–3B that tells you how many ATP molecules are hydrolyzed per step?