Template:ETH Modeling Formulas
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(Difference between revisions)
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d[M]/dt = k<sub>tr</sub> − d<sub>M</sub>[M] | d[M]/dt = k<sub>tr</sub> − d<sub>M</sub>[M] | ||
| - | [M] : mRNA concentration | + | [M]<sub> </sub>: mRNA concentration |
| + | k<sub>tr</sub> : kinetic konstant (transcription) | ||
| + | d<sub>M </sub> : degradation konstant for mRNA | ||
| - | A transcriptional regulatory module can be described by the following | + | A transcriptional regulatory module can be described by the following ODE's: |
1 | 1 | ||
| - | d[M]/dt = k<sub>tr</sub> ( a + −−−−−−−−−−−− ) | + | d[M]/dt = k<sub>tr</sub> ( a + −−−−−−−−−−−−−− ) |
| - | 1 + (K/S)<sup>α•n</sup> | + | 1 + (K/[S])<sup>α•n</sup> |
| + | |||
| + | [M]<sub> </sub>: mRNA concentration | ||
| + | k<sub>tr</sub> : kinetic konstant (transcription) | ||
| + | a<sub> </sub> : constitutive portion, 0 ≤ a < 1 | ||
| + | [S]<sub> </sub>: inducer (α=+1) / repressor (α=−1) concentration | ||
| + | K<sub> </sub> : hill constant | ||
| + | n<sub> </sub> : hill coefficient | ||
| + | &alpha<sub> </sub> : α=+1 for induction, α=−1 for repression | ||
| + | d<sub>M </sub> : degradation konstant for mRNA | ||
Revision as of 12:00, 30 October 2006
To get our models into a form which can be simulated, we needed to transform the wiring diagrams into a set of ODE's (ordinary differential equations), which in our case will be non-linear.
For every concerned species X, we write
d[X]/dt = production - consumption
For enzymatic transformation of substrate X into product P (catalyzed by enzyme E), we write
k+1 k2
X + E <==> X•E --> P + E
k−1
d[X]/dt = −k+1[X][E] + k−1[X•E] − dX[X]
d[E]/dt = −k+1[X][E] + k−1[X•E] + k2[X•E] − dE[E]
d[P]/dt = + k2[X•E] − dP[P]
kinetic constants:
kk+1 : building enzyme-substrate complex (forward)
kk−1 : resolving enzyme-substrate complex (backward)
k2 : product formation
dXXX : degradation constants
For constitutive transcription, we have constant production rate and simply write
d[M]/dt = ktr − dM[M] [M] : mRNA concentration ktr : kinetic konstant (transcription) dM : degradation konstant for mRNA
A transcriptional regulatory module can be described by the following ODE's:
1
d[M]/dt = ktr ( a + −−−−−−−−−−−−−− )
1 + (K/[S])α•n
[M] : mRNA concentration
ktr : kinetic konstant (transcription)
a : constitutive portion, 0 ≤ a < 1
[S] : inducer (α=+1) / repressor (α=−1) concentration
K : hill constant
n : hill coefficient
&alpha : α=+1 for induction, α=−1 for repression
dM : degradation konstant for mRNA
