Template:ETH Modeling Formulas
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(Difference between revisions)
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k<sub>+1</sub> k<sub>2</sub> | k<sub>+1</sub> k<sub>2</sub> | ||
| - | X + E <==> X& | + | X + E <==> X•E --> P + E |
| - | k<sub> | + | k<sub>−1</sub> |
| - | d[X]/dt = | + | d[X]/dt = −k<sub>+1</sub>[X][E] + k<sub>−1</sub>[X•E] − d<sub>X</sub>[X] |
| - | d[E]/dt = | + | 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 = + k<sub>2</sub>[X•E] − d<sub>P</sub>[P] |
Revision as of 11:30, 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]
