14. Look up the paper of Groebe (Biophysical Journal 68: 1246-1269) and follow his directions for writing a computer program for a more up-to-date model of oxygen diffusion from red blood cells into muscle tissue. Use this program to try to answer some of the questions raised in problem 10, above.

The next group of problems require information from the handout on Transport Processes.

15. Consider a cell with an elastic membrane that obeys the following relationship between cell volume, v, and pressure, P:
P = a(v-v0), where a/RT = 0.5 * 1012 moles liter-2.
The cell contains membrane-impermeant anions with an average charge of -5.0. Its volume is v0 when it is surrounded by a solution containing 0.15 M NaCl and 0.02 M sucrose. The cell membrane is freely permeable to Na+ and Cl- ions, and to water, but is impermeable to sucrose. When the cell is transferred to a solution containing 0.16 M NaCl and no sucrose, its volume comes to equilibrium at 2v0. At this new equilibrium point, calculate the diameter of the cell and the voltage across the cell membrane.

16. An animal cell is immersed in a medium containing 0.155 M Na+, 0.005 M K+, and 0.160 M Cl- ions. The cell contains a mixture of non-penetrating ions that cannot pass through the cell membrane; these molecules carry an average charge of -5.0.
a) Assume that the cell membrane is freely permeable to Na+ and Cl- ions, completely impermeable to K+ ions, and there is no K+ inside the cell. Assume that the cell membrane is not exerting any pressure on the cell contents. What concentration of non-penetrating ions inside the cell will be in electrochemical and osmotic equilibrium with the external medium? What will be the membrane potential difference at equilibrium?
b) Now assume instead that the cell membrane is freely permeable to K+ and Cl- ions, completely impermeable to Na+ ions, and there is no Na+ inside the cell. What will be the concentration of non-penetrating ions inside the cell, and the membrane voltage, at equilibrium?
What important conclusion do you draw from this comparison?
c) Under the conditions in (b), what will happen if the pH decreases, so that the average charge on the non-penetrating ions inside the cell is -4.0?

17. A cell is immersed in a medium containing 0.155 M NaCl and 0.008 M KCl, and its volume remains constant. Measurements show that the cell contains 0.005 M Na+, 0.24 M K+, and 0.06 M of non-permeant molecules. The Cl- concentration inside the cell, and the average charge on the non-permeant molecules, are not known. This cell does not have a pressure-resistant membrane.
The relative passive permeabilities of the cell membrane to ions have been found to be Cl- = 100 and Na+ = 1.
Which of the following hypotheses are consistent with these measurements? (Explain!)
a) The only active transport occuring in the cell membrane is an active extrusion of Na+ ions.
b) The cell membrane carries out a 3:2 coupled Na:K exchange transport.

18) Under the conditions of problem (17), if case b is true, how much energy (Kcal/mole or KJ/mole) is required to extrude 3 Na+ ions and take up 2 K+ ions?
Is it reasonable to suggest that this is done by dephosphorylating just one ATP molecule for each transport cycle?

19) Under the conditions of problem (17), case b, assume that the external solution also contains 1 mM Ca++. What will be the internal concentration of free Ca++ if equilibrium is maintained by a 3Na+/Ca++ exchange transporter?
How much will this change the energy requirement calculated in problem (18)?

20) Consider an epithelium that is actively transporting Na+ ions from the apical medium to the basolateral medium. Cl- ions are passively transported, probably through Cl- channels, so that there is no electrical current flow. Assume that the passive permeability of the basolateral membrane to Na+ ions is negligible. Assume that for a distance of 100 Ám from the basolateral surface, the basolateral medium is unstirred. Movement of Na+ and Cl- ions through this region depends upon diffusion. Beyond 100 Ám, the basolateral medium is vigorously stirred so that the result is that the Na+ and Cl- concentrations at 100 Ám are constant and equal to 0.15 mM.
If the NaCl transport rate is 2 moles/min/cm2 of membrane, what will be the Na+ and Cl- concentrations at the surface of the basolateral membrane? (Start by neglecting the difference in the transport coefficients of Na+ and Cl- ions. If you want, you can then look up real values and calculate the effect.)
Now, describe what will happen if the epithelial membranes are highly permeable to water molecules.

21. EAP says (page 594) that the maximum glucose uptake by the human kidneys is Tm=320 mg/min. What is the reason for this maximum?
a) Not enough glucose carrier in the tubule membranes (as stated in EAP), or
b) Not enough energy available to transport more glucose.
You will need to make a calculation to justify your conclusion.

22. What percentage oxygen extraction from the blood flowing through the kidney is required to recover 3 mg/ml of glucose from the filtrate? (You will need some additional information.)

23. Do you expect the percentage oxygen extraction from the blood flowing through the kidney to increase if the plasma glucose concentration increases from 1 mg/ml to 3 mg/ml? How much, or why not?

24. Consider a standard 70 kg human ingesting glucose at a rate of 2400 kcal/day. [This is a very unreasonable diet, of course, but I don't think you will learn more here by bothering with a realistic diet.] Oxidative metabolism of glucose is used to generate ATP, which is used to perform external work, with an average work output of 40 pN nm per molecule of ATP used. The rest of the energy of glucose oxidation is converted to heat. Respiration is tightly controlled, allowing only the minimum respiration that is needed to obtain the oxygen for glucose oxidation. The oxygen extraction is 27%. Assume that the body is well insulated, so that the only heat loss results from:
a) drinking water at 10oC.
b) urination at 37oC.
c) evaporation of water, including metabolic water, from the lungs.

What is the required rate of drinking (liters/day) to maintain a constant body temperature?

Here are some assumptions and data that you can use:

  1. Inhaled and exhaled air are both at 30 C. The inhaled air is at 20% RH and the exhaled air is at 100% RH. The vapor pressure of water at 30oC is 31.9 mm Hg.

  2. Energy change of glucose oxidation = -686 kcal/mole.
  3. 582 kcal/gm for the heat of vaporization of water.
If you get an unreasonable answer, you can then calculate how much water should be evaporated by panting and/or sweating in order to reduce the water intake rate to a reasonable value. If the rate of drinking is exactly equal to the rate of water loss by panting and sweating, calculate the drinking rate and the urine flow rate.