Homework #5
ChE 361
Spring 2010
Problem 1. Consider the following dynamic model for sustained oscillations in yeast glycolysis:
dG
dt
=
V
in

k
1
GA
=
f
1
(
G, A
)
dA
dt
=
2
k
1
GA

k
p
A
K
m
+
A
=
f
2
(
G, A
)
where
G
and
A
are the intracellular concentrations of glucose and ATP, respectively,
V
in
= 0.36
is the constant flux of glucose into the yeast cell,
k
1
= 0.02 is an enzyme activity, and the
parameters
k
p
= 6.0 and
K
m
= 13.0 determine the kinetics of ATP degradation. Consider the
following steadystate solution:
¯
G
= 10.15,
¯
A
= 1.77.
1. Derive the linearized model
dx
dt
=
Ax
at this steadystate point.
2. Determine the stability of the steady state by computing the eigenvalues of the
A
matrix.
Verify your answer with Matlab.
What can be claimed about stability away from this
steadystate point?
Problem 2. Consider the batch operation of a flash drum for separating a binary liquid mixture.
The drum has liquid molar holdup
M
and liquid mole fraction of the more volatile component
x
. A constant rate of heat
Q
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 Spring '10
 HENSON
 Thermodynamics, Enzyme, Steady State, Trigraph

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