Red blood cells are in an isotonic aqueous solution with a volume much greater than the volume of blood cells. The solutes in the cells and in the bath do not cross the membranes of the cells. When a solute that can cross the membranes is added to the water bath, it is observed that the cells shrink at first. Then they slowly regain their original size (see the diagram; data from Macey and Oster, UC Berkeley). The initial molar concentration of impermeable solutes in the isotonic solution is 300 mole/m^3; additional solutes raise the concentration to 600 mole/m^3. A typical cell has an initial volume of 8.7·10–17 m^3 and a surface of about 1.4·10–10 m^2.
a. Which substances can flow across the cell membrane? Which cannot? b. Why does the volume of blood cells decrease initially? What is the condition for the volume to increase? (Hint: We assume that only the amount of water in a cell affects its volume.) c. If the substance added to the bath could not diffuse into the cells, what would happen to their volume? d. Write the laws of balance of the substances for a cell that flow across the membrane. e. Express the transports in your laws of balance by constitutive laws. f. Use the graph to determine the volume current of water at t = 0 s. Then determine the currents of mass and of amount of substance of water. | | 
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Data from Macey and Oster (UC Berkeley)
Use this to find the permeability of the cell walls for water. g. What can we say about the flow of water when the volume has reached its minimal value at t = 0.25 s? What does this mean for the total concentration of solutes in the cell? How much of the added substance has moved from the bath into a cell? Use this to estimate the permeability of the cell walls for the diffusing substance. h. Sketch the concentrations of impermeable and new solute inside a cell as functions of time. Sketch the total concentration inside and outside as functions of time. i. Sketch the currents of water and of perme- able solutes as functions of time. |
