Problem set/conference #1

Background: What is the difference between molarity and molality (osmolarity and osmolarity)? If you don't know, ask your facilitator.

Directions: For the first two questions, determine whether the statement is true or false.

1. When a cell is placed in an aqueous solution in which the osmolality of the solution differs from that of the cell, the volume of the cell changes rapidly in response to rapid movement of K⁺, Na⁺, and Cl^- across the cell membrane.

2. When a red blood cell is placed in a large volume of an aqueous ionic solution containing only impermeant ions, the final intracellular osmolality of the red blood cell will be equal to the osmolality of the extracellular solution.

At time zero, a cell that has an osmolarity of 300 mOsm/L due to the presence of impermeant intracellular ions (reflection coefficient, σ = 1) is placed in a large volume of an aqueous test solution described below in 3-9. In response to immersion in the test solutions, the volume of the cell changes (or fails to change) in a characteristic manner. For each test solution, select a letter that MOST closely depicts the change (or lack of change) of volume that will occur in the test-cell. Letters may be used once, more than once, or not at all. Unless otherwise indicated, consider all dissolved substances in the test solutions to be impermeants, σ = 1. When the cell volume exceeds 1.5 times its initial volume of 1.0, it will burst as indicated by the star *.

Aqueous test-solutions:

3. 100 mM MgCl²

4. 100 mM NaCl

5. 1200 mOsM urea (σ = 0.25)

6. 100 mM NaCl, 1200 mOsM urea (σ = 0.25)

7. zero omosmolar water

8. 300 mM NaCl

9. 300 mM sucrose

Select the SINGLE BEST answer.

10. Two liters of cells containing an initial impermeant solute concentration of 300 mosm/l and an initial permeant solute concentration of 400 mosm/l (ρ = 0.25) is placed in four liters of solution containing 150 mosm/l of impermeant solutes and 400 mosm/l of permeant solutes (ρ = 0.25).

• A. Will the cells initially shrink or swell?
• B. What will the final volume of the cells be?
• C. What will the final osmolarity of the extracellular solution be?

11. The endothelium of systemic capillaries (in muscle for example) is permeable to water, ions, and to low molecular weight solutes, but the endothelium is impermeable to large proteins (>70,000 Daltons). Assume that the interstitial fluid surrounding cells near the venous end of a capillary has the same solute-composition as plasma ,but that plasma also contains enough protein - in fact, enough protein to produce an osmotic pressure of 10 mmHg. (The osmotic pressure produced by proteins is often called oncotic pressure.) Knowing this, the total oncotic pressure of the plasma at the venous end of the capillary will have what effect on net water movement?

• A. It will promote flow of water into the capillary from the interstitial fluid.
• B. It will promote flow of water into the interstitial fluid from the capillary.

12. If the intracellular and the extracellular concentrations of a particular ion are known, the Nernst equation can then be used to:

• A. calculate the conductance of that particular ion across the cell membrane.
• B. calculate the equilibrium potential for that particular ion.
• C. calculate the resting transmembrane potential of the cell.
• D. determine the direction a particular ion is moving when the cell is voltage-clamped at the equilibrium potential of that particular ion.

13. A membrane separates two compartments i and o containing solution of different ionic composition. Assuming the usual convention that compartment o is at the reference (ground) potential, calculate the equilibrium (Nernst) potential given that the ion concentrations in i and o (respectively) are the following:

(Assume that 2.3 RT/F = 60 mV and that log 3 = 0.5)

• A. 150 mM K_i / 15 mM K_o EK = ?
• B. 300 mM K_i / 30 mM K_o EK = ?
• C. 15 mM Na_i / 150 mM Na_o ENa = ?
• D. 9 mM Cl_i / 90 mM Cl_o ECl = ?
• E. 10-6 M Ca²⁺_i/10-3 M Ca²⁺_o ECa = ?

READ THE FOLLOWING CASE AND ANSWER THE QUESTIONS REGARDING IT. Your facilitator will discuss this case.

14. Before being forced to drink the 3 glasses of water, Casandra's extracellular fluid volume (ECF) was 5 L and the osmolarity of her ECF was 290 milliosmoles/L. The 3 glasses of tap water that Casandra drank and absorbed had a volume of 1 liter. The water contained essentially no electrolytes (osmoles). For simplicity in calculation, assume that for a few minutes all of the absorbed water remained in the ECF (i.e. did not enter cells). What would the new volume and osmolarity of Casandra's ECF be?

15. If, prior to diffusion of the absorbed water, the osmolality of the intracellular fluid (ICF) of the brain was 290 millosmoles/L, in what direction would water move? (from brain ECF to brain ICF, or vice versa)? How would this affect volume of the brain?

16. Rapid swelling of liver cells or muscle cells is not fatal. Why is rapid swelling of brain cells fatal?