Template:ETH Modeling Formulas
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(Difference between revisions)
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d[X]/dt = −k<sub>+1</sub>[X][E] + k<sub>−1</sub>[X•E] − d<sub>X</sub>[X] | d[X]/dt = −k<sub>+1</sub>[X][E] + k<sub>−1</sub>[X•E] − d<sub>X</sub>[X] | ||
d[E]/dt = −k<sub>+1</sub>[X][E] + k<sub>−1</sub>[X•E] + k<sub>2</sub>[X•E] − d<sub>E</sub>[E] | d[E]/dt = −k<sub>+1</sub>[X][E] + k<sub>−1</sub>[X•E] + k<sub>2</sub>[X•E] − d<sub>E</sub>[E] | ||
| - | d[P]/dt = | + | d[P]/dt = <sub> </sub> + k<sub>2</sub>[X•E] − d<sub>P</sub>[P] |
| + | |||
| + | kinetic constants: | ||
| + | k<sub>k+1</sub> : building enzyme-substrate complex (forward) | ||
| + | k<sub>k−1</sub> : resolving enzyme-substrate complex (backward) | ||
| + | k<sub>2 </sub> : product formation | ||
| + | d<sub>XXX</sub> : degradation constants | ||
| + | |||
| + | For constitutive transcription, we have constant production rate and simply write | ||
| + | d[M]/dt = k<sub>tr</sub> − d<sub>M</sub>[M] | ||
| + | |||
| + | [M] : mRNA concentration | ||
| + | |||
| + | A transcriptional regulatory module can be described by the following ODEs: | ||
| + | 1 | ||
| + | d[M]/dt = k<sub>tr</sub> ( a + −−−−−−−−−−−− ) | ||
| + | 1 + (K/S)<sup>α•n</sup> | ||
Revision as of 11:51, 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
A transcriptional regulatory module can be described by the following ODEs:
1
d[M]/dt = ktr ( a + −−−−−−−−−−−− )
1 + (K/S)α•n
