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BIOE 398BS: Quantitative Human Systems Physiology
Spring 2008
Bioengineering, University of Illinois at UrbanaChampaign
1
Two parts: First is paper problem.
Second is Matlab simulation.
Due: Feb. 01, 2008 at the beginning of class.
1.
*
We are going to calculate the size of a cell given the information below. Note that
the number of macromolecules and their average charge is not given, so use N to
represent the number of charges due to macromolecules.
Some of the solution will be
put in terms of N.
Include units in your answers.
Use the following data about a cell
g
Na
= 3.5
μ
mho/cm
2
,
g
K
= 250
μ
mho/cm
2
,
[Na
+
]
o
= 150
μ
mol / cm
3
,
(Note: this is 150 mM)
[K
+
]
o
= 5
μ
mol / cm
3
,
(Note: this is 5 mM)
q = 1.6 x 10
19
coulombs,
kT/q = 25 x 10
3
volts.
The external solution is electrically neutral, so [Na
+
]
o
+ [K
+
]
o
= [Cl

]
o
Let v = electric potential and V = cell size.
Note:
μ
mho = 10
6
(coulomb/sec)/volt, a mho is the basic unit of conductance (the
reciprocal of resistance, measured in ohms), the coloumb is a standard unit of charge, and
1
μ
mol = 10
6
x (6 x 10
23
) ions.
a.)
Assume that the pumping rate of the NA+/K+ pump is optimal (p
opt
), which given by
the following equation:
p
opt
= (kT/q
2
)(g
Na
g
K
/( g
Na
+ g
K
)) log(([Na
+
]
o
g
K
) / (g
Na
[K
+
]
o
).
This represents the optimal pumping rate to achieve the smallest cell volume, V, and
electrical potential, v.
Calculate the pumping rate and describe what it means.
b.)
Assuming that p=p
opt
, evaluate v, V, [NA
+
]
i
, [K
+
]
i
, [Cl

]
i
.
Note: some of the
solutions will be a function of N.
c.)
Which terms are a function of N and what does that mean about cell size versus
growth?
d.)
Calculate E
Na
, E
K
, E
Cl
.
*
Adapted from Hoppensteadt and Peskin text.
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View Full DocumentBIOE 398BS: Quantitative Human Systems Physiology
Spring 2007
Bioengineering, University of Illinois at UrbanaChampaign
2
2. Simulation of Action Potential
We will be simulating the electrical activity of a patch of membrane of a neuron in
response to a step change in voltage and an applied electrical current.
We will be
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 Fall '07
 BIOE
 Bioengineering

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