hw1 - BE.430J/6.561J/2.795J/10.539J/HST.544J Fall 2004...

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BE.430J/6.561J/2.795J/10.539J/HST.544J Fall 2004 Homework 1 Due Wednesday (9/22) by 5pm 1. Oxygen Diffusion in Cells a) Oxygen is consumed by cells at a rate which is often nearly independent of the O 2 concentration. Assume that a cell is a sphere of radius a , and let k 0 and C 0 be the O 2 consumption rate per unit volume and the O 2 concentration just inside the cell membrane, respectively. Derive an expression for the steady-state O 2 concentration profile in the cell, C ( r ), assuming that the consumption rate is spatially uniform. Using the data given below, show that diffusion limitations at the single-cell level are unimportant. 2 Data: D 11 0 5 cm (O 2 diffusivity in cytoplasm) c s m = 0.2 pmol (typical O 2 consumption rate of mammalian cell) c h cell a 10 µ m C 0 = µ M (typical O 2 level in mixed venous blood or tissues) b) Consider now an aggregate of closely packed cells which is a sphere of radius b (>> a ). If b and k 0 are sufficiently large, no O 2
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This note was uploaded on 11/11/2011 for the course BIO 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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hw1 - BE.430J/6.561J/2.795J/10.539J/HST.544J Fall 2004...

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