Team:TU Munich/model/andgate

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Model

The model for our AND-Gate is based on the model of the iGEM team PKU Beijing 2009 for their AND-Gate1. We modified the equations such that the change in tRNA and Aa-tRNA does not include the degradation of the mRNA which caused negativity of some concentrations in our model.[1]
For more details see the paper by Anderson [2].
The dye output was an adaption of the model proposed in the paper by Yildirim[3].
image: 9_Users_schaluck_Desktop_andgate.png

Equations

tRNA x ˙ 1 = k t ( OmpR-P K1 ) 2 ( 1+ OmpR-P K1 ) 2 - ( γ 1 + k a ) x 1 + γ 2p x 2 +2 k 7p x 3 ( γ 3 k 7m ) ( x 1 γ 0 + x 1 ) 2 Aa-tRNA x ˙ 2 = k a x 1 -2 k 7p x 3 ( γ 3 k 7m ) ( x 1 γ 0 + x 1 ) 2 - γ 2 x 2 T7RNA P mRNA x ˙ 3 = k 7m ( 1- ( YcgE K3 ) 2 ( 1+ YcgE K3 ) 2 )- γ 3 x 3 T7RNAP x ˙ 4 = k 7p x 3 ( γ 3 k 7m ) ( x 1 γ 0 + x 1 ) 2 - γ 4 x 4 lac Z mRNA x ˙ 5 = α M ( 1- ( x 4 K5 ) 2 ( 1+ x 4 K5 ) 2 )- γ M x 5 β -Galactosidase x ˙ 6 = α B x 5 - γ B x 6 dye x ˙ 7 = α A x 6

Parameters

Parameter
Value
Unit
Name
Source
k t
46.67 60
nM s
max transcription rate tRNA
[1]
k a
0.08 60
1 s
synthesis rate Aa-tRNA
[1]
k 7p
1.5625 60
nM s
max transcription rate T7RNAP
[1]
k 7m
268*0.05 60
1 s
max translation rate T7RNAP
[1]
k S
0.3
1 nM
AND Gate rate
[1]
γ 0
1
-
threshold Aa-tRNA
guessed
γ 1
1 60*60
1 s
degradation of tRNA
[1]
γ 2
1 40*60
1 s
degradation of Aa-tRNA
[1]
γ 3
1 4.4*60
1 s
degradation of T7RNAP mRNA
[1]
γ 4
46.67 40*60
1 s
degradation of T7RNAP
[1]
K1
5
nM
response param. OmpR-P,tRNA
guessed
K3
600
nM
response param. YcgE,T7RNAP
guessed
K5
k7p 4* γ 4
nM
response param T7RNAP,lacZ
guessed
α M
0.997 60
nM s
max transcription rate lacZ
[3]
α B
1.661e-5 60
1 s
max translation rate lacZ
[3]
α A
20 60
1 s
enzymatic reaction rate
[3]
γ M
0.411 60
1 s
degradation lacZ mRNA
[3]
γ B
8.331e-4 60
1 s
degradation β -Galactosidase
[3]

Initial Data

Name
Variable
Initial Value
Comment
Source
tRNA
x 1
0
Aa-tRNA
x 2
0
T7RNA P mRNA
x 3
0
T7RNAP
x 4
0
lac Z mRNA
x 5
0
β -Galactosidase
x 6
0
dye
x 7
0

Simulation

Since the AND-Gate is only an intermediate part, no additional simulation was done here.

References

1. PKU Beijing 2009, 'AND Gate 1' (2009).
2. Anderson, J Christopher and Voigt, Christopher A and Arkin, Adam P, 'Environmental signal integration by a modular AND gate', Mol Syst Biol (2007).
3. Yildirim, N and Santillan, M and Horike, D and Mackey, MC, 'Dynamics and bistability in a reduced model of the lac operon', CHAOS (2004), 279-292.