BSCI 426 BIOL 622    Fall '14 Problem Set 4

assigned:     9/25/14
due:            10/02/14

1. Calculate the diffusion time for a small molecule to travel across the following distances:
(please convert to useful units such as nsec, min, days, years...)
i) through a 5 nm long aqueous channel through a membrane
ii) from one end to the other of the inside of a red blood cell (8 µm).
iii) from the cell body of a spinal neuron to the nerve terminal 1 meter away
iv) from your brain to your toes (2 meters)
v) from the top of the ocean to a point 10 km down

2. The diffusion of oxygen from the cell surface to a mitochondrion can limit the rate of energy production.  Muscle cells consume large amounts of energy and those designed to work aerobically have myoglobin in the cytosol to help carry oxygen to the mitochondrion.
i) How can something that diffuses more slowly that oxygen help carry oxygen?
ii) What concentration of oxygenated myoglobin would be needed to accelerate the oxygen flux by a factor of 10? (you should make simplifying assumptions to answer this)

Hints: Consider that the blood supply keeps the [oxygen] outside the cell at a constant value. Consider that the mitochondrion is an oxygen sink.

Information:

a. At 37 C, oxygen solubility in water is 0.0032 g O₂/ 100 ml water if the O₂ pressure is 760 mm Hg.  However, air is only 20% O₂ and, in a mammal, at the cell surface the O₂ partial pressure is likely to be only 40 mm Hg.  Thus you should scale down the concentration in solution accordingly.
b. Assume the diffusion constants in the cell are:
for O₂: 5 x 10^-5 cm² sec^-1
for myoglobin: 6 x 10^-7 cm² sec^-1