The swimming rate of a small organism [J. Theoret. Biol., 26, 11 (1970)] is related to the...

The swimming rate of a small organism [J. Theoret. Biol., 26, 11 (1970)] is related to the energy released by the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP). The rate of hydrolysis is equal to the rate of diffusion of ATP from the midpiece to the tail (see Figure 5). The diffusion coefficient of ATP in the midpiece and tail is 3.6 × 10-6 cm2/s. ADP is converted to ATP in the midsection, where its concentration is 4.36 × 10-5 mol/cm3. The cross-sectional area of the tail is 3 × 10-10 cm2.

Figure 5 Swimming of an organism.

(a) Derive an equation for diffusion and reaction in the tail.

(b) Derive an equation for the effectiveness factor in the tail.

(c) Taking the reaction in the tail to be of zero order, calculate the length of the tail. The rate of reaction in the tail is 23 × 10-18 mol/s.

(d) Compare your answer with the average tail length of 41 μm. What are possible sources of error?