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BME 100 Computer Project 3: Modeling a Genetic Oscillator
BME 100 Computer project 3:
Modeling a genetic oscillator: Repressilator
Nigel Chou
A)
Since units of
s
nM
=
dt
dM
i
,
therefore units of
s
1
,
s
nM
=
=
m
o
d
k
j
K
,
j
P
and
j
M
are nM (given)
The terms in
j
K
and
j
P
cancel out, therefore units of
s
nM
=
k
Since units of
s
nM
=
dt
dP
i
,
therefore units of
s
1
=
=
p
p
d
k
These results are summarized in table 1.
Table 1:
Dimensions of parameters
Parameter
Units
K
j
nM
P
j
nM
M
i
nM
k
nM s
1
k
0
nM s
1
d
m
s
1
k
p
s
1
d
p
s
1
B)
Let
m
m
d
d
dt
t
d
1
=
∴
=
τ
The units are
1
s
s
1
=
=

(dimensionless)
Let
j
j
j
K
P
p
=
dt
dP
K
dt
dp
i
j
i
1
=
∴
The units are
1
nM/nM
=
=
j
p
(dimensionless)
Let
j
i
p
p
i
K
M
d
k
m
=
1
dt
dM
K
dt
dm
i
j
i
1
=
∴
The units are,
1
nM/nM
=
=
j
m
(dimensionless)
1
The reason for this choice will is that it allows us to pull out a constant (β) from the second equation, as we shall
see later.
1
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View Full DocumentBME 100 Computer Project 3: Modeling a Genetic Oscillator
Also, K
i
= K
j
since all three reaction have the same kinetics
Equation 1
i
n
j
j
i
p
p
j
m
p
p
n
j
j
m
p
p
i
m
n
j
j
j
m
p
p
i
j
m
p
p
i
j
p
p
i
m
p
K
M
d
k
K
d
d
k
k
p
K
d
d
k
k
M
d
k
k
P
k
K
d
d
k
dt
dM
K
d
d
k
d
dt
dt
dM
K
d
k
d
dm

+
+
=

+
+
=

+
+
=
=
=
0
0
0
1
1
)
1
(
α
τ
By observing the above equation, we get:
j
m
p
p
K
d
d
k
k
=
and
j
m
p
p
K
d
d
k
k
0
0
=
The units are
1
nM
s
s
)
s
(nM
s
1
1
1
1
=
=




and
1
nM
s
s
)
s
(nM
s
1
1
1
1
0
=
=




, thus both are dimensionless
Equation 2
)
(
)
(
)
(
1
)
(
1
)
(
1
1
1
i
i
i
i
m
p
i
p
i
p
m
j
i
p
j
i
p
p
p
m
i
p
i
p
p
p
j
m
i
j
m
i
i
i
p
m
p
m
d
d
p
d
m
d
d
K
P
d
K
M
d
k
d
d
P
d
M
d
d
k
K
d
dt
dP
K
d
d
dt
dt
dP
K
d
dp

=

=

=
=

=

=
=
=
β
By observing the above equation, we get:
m
p
d
d
=
The units are
1
s
s
1
1
=
=


thus it is also dimensionless.
C)
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 Fall '07
 YUAN

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