1. (a) Skeletal muscle and eukaryotic cilia derive their free energy from ATP hydrolysis; the bacterial flagellar motor uses a proton-motive force.

A47

(b) Skeletal muscle requires myosin and actin. Eukaryotic cilia require microtubules and dynein. The bacterial flagellar motor requires MotA, MotB, and FliG, as well as many ancillary components.

2. 6400 Å/80 Å = 80 body lengths per second. For a 10-foot automobile, this body-length speed corresponds to a speed of 80 × 10 feet = 800 feet per second, or 545 miles per hour.

3. 4pN = 8.8 × 10⁻¹³ pounds. The weight of a single motor domain is 100,000 g mol⁻¹/(6.023 × 10²³ molecules mol⁻¹) = 1.7 × 10⁻¹⁹ g = 3.7 × 10⁻²² pounds. Thus, a motor domain can lift (8.8 × 10⁻¹³/3.7 × 10⁻²²) = 2.4 = 10⁹ times its weight.

4. Both actin filaments and microtubules are built from subunits and these subunits bind and hydrolyze nucleoside triphosphates. Actin filaments are built of a single type of subunit and these subunits bind ATP. Microtubules are built of two different types of subunits and these subunits bind GTP.

5. The light chains in myosin stiffen the lever arm. The light chains in kinesin bind cargo to be transported.

6. After death, the ratio of ADP to ATP increases rapidly. In the ADP form, myosin motor domains bind tightly to actin. Myosin–actin interactions are possible because the drop in ATP concentration also allows the calcium concentration to rise, clearing the blockage of actin by tropomyosin through the action of the troponin complex.

7. Above its critical concentration, ATP-actin will polymerize. The ATP will hydrolyze through time to form ADP-actin, which has a higher critical concentration. Thus, if the initial subunit concentration is between the critical concentrations of ATP-actin and ADP-actin, filaments will form initially and then disappear on ATP hydrolysis.

8. A one-base step is approximately 3.4 Å = 3.4 × 10⁻⁴ µm. If a stoichiometry of one molecule of ATP per step is assumed, this distance corresponds to a velocity of 0.017 µm s⁻¹. Kinesin moves at a velocity of 6400 Å per second, or 0.64 µm s⁻¹.

9. A proton-motive force across the plasma membrane is necessary to drive the flagellar motor. Under conditions of starvation, this proton-motive force is depleted. In acidic solution, the pH difference across the membrane is sufficient to power the motor.

10. The mean distance between tumbles would be longer when the bacterium is moving up a gradient of a chemoattractant.

11. (a) 1.13 × 10⁻⁹ dyne

(b) 6.8 × 10¹⁴ erg

(c) 6.6 × 10⁻¹¹ erg per 80 molecules of ATP. A single kinesin motor provides more than enough free energy to power the transport of micrometer-size cargoes at micrometer-per-second velocities.

12. The spacing between identical subunits on microtubules is 8 nm. Thus, a kinesin molecule with a step size that is not a multiple of 8 nm would have to be able to bind at more than one type of site on the microtubule surface.

13. KIF1A must be tethered to an additional microtubule-binding element that retains an attachment to the microtubule when the motor domain releases.

14. Filaments built from subunits can be arbitrarily long, can be dynamically assembled and disassembled, and require only a small amount of genetic information to encode.

15. Protons still flow from outside to inside the cell. Each proton might pass into the outer half-channel of one MotA–MotB complex, bind to the MS ring, rotate clockwise, and pass into the inner half-channel of the neighboring MotA–MotB complex.

16. At a high concentration of calcium ion, Ca²⁺ binds to calmodulin. In turn, calmodulin binds to a protein kinase that phosphorylates myosin light chains and activates it. At low calcium ion concentration, the light chains are dephosphorylated by a Ca²⁺-independent phosphatase.

17. (a) The value of k_cat is approximately 13 molecules per second, whereas the K_M value for ATP is approximately 12 µM.

(b) The step size is approximately (380 − 120)/7 = 37 nm.

(c) The step size is very large, which is consistent with the presence of six light-chain-binding sites and, hence, very long lever arms. The rate of ADP release is essentially identical with the overall k_cat; so ADP release is rate limiting, which suggests that both motor domains can bind to sites 37 nm apart simultaneously. ADP release from the hindmost domain allows ATP to bind, leading to actin release and lever-arm motion.