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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 steadystate 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 singlecell 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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 Spring '03
 RogerD.Kamm

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