Template:ETH Modeling Formulas
From 2006.igem.org
(Difference between revisions)
| Line 27: | Line 27: | ||
d<sub>M </sub> : degradation konstant for mRNA | 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 and ODE of the following form: |
1 | 1 | ||
| - | d[M]/dt = k<sub>tr</sub> ( a + −−−−−−−−−−−−−− ) | + | d[M]/dt = k<sub>tr</sub> ( a + −−−−−−−−−−−−−− ) − d<sub>M</sub>[M] |
1 + (K/[S])<sup>α•n</sup> | 1 + (K/[S])<sup>α•n</sup> | ||
| Line 40: | Line 40: | ||
α<sub> </sub> : α=+1 for induction, α=−1 for repression | α<sub> </sub> : α=+1 for induction, α=−1 for repression | ||
d<sub>M </sub> : degradation konstant for mRNA | d<sub>M </sub> : degradation konstant for mRNA | ||
| + | |||
| + | Finally, translation is usually modelled like this: | ||
| + | d[P]/dt = k<sub>tl</sub>[M] − d<sub>P</sub>[P] | ||
| + | |||
| + | [P]<sub> </sub>: product (protein) concentration | ||
| + | [M]<sub> </sub>: mRNA concentration | ||
| + | k<sub>tl</sub> : kinetic konstant (translation) | ||
| + | d<sub>P </sub> : degradation konstant for protein P | ||
Revision as of 12:05, 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 and ODE of the following form:
1
d[M]/dt = ktr ( a + −−−−−−−−−−−−−− ) − dM[M]
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
α : α=+1 for induction, α=−1 for repression
dM : degradation konstant for mRNA
Finally, translation is usually modelled like this:
d[P]/dt = ktl[M] − dP[P] [P] : product (protein) concentration [M] : mRNA concentration ktl : kinetic konstant (translation) dP : degradation konstant for protein P
