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 P15-6B). 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.

Swimming of an organism.
A cylindrical shaped object representing a small organism is shown. The organism consists of three parts which include head, midpiece, and tail. At the two ends of the organism, head and tail are present. The food is consumed by the organism through its head. At the midpiece, ADP (adenosine diphosphate) is converted to ATP (adenosine triphosphate). The reactants involved in the conversion include Glucose and Oxygen, and the products produced include Carbon dioxide and water. The length of the tail is L and here, the ATP is converted back to ADP with the release of needed energy for swimming. Actually, the tail has a converged end but in this model, the cross-sectional area of the tail is taken to be a rectangle.

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?

Transcribed Image Text:

Food- Gluc 0₂- Head ADP CO, HO ATP Midpiece ATP-ADP Tail Model Actual