Template:ETH Modeling Formulas

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''in progress''
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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.
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For every concerned species <tt>X</tt>, we write
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d[X]/dt = production - consumption
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For enzymatic transformation of substrate X into product P (catalyzed by enzyme E), we write
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        k<sub>+1</sub>      k<sub>2</sub>
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X + E <==> X&sdot;E --> P + E
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        k<sub>-1</sub>
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d[X]/dt = -k<sub>+1</sub>[X][E] + k<sub>-1</sub>[X&sdot;E]          - d<sub>X</sub>[X]
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d[E]/dt = -k<sub>+1</sub>[X][E] + k<sub>-1</sub>[X&sdot;E] + k<sub>2</sub>[X&sdot;E] - d<sub>E</sub>[E]
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d[P]/dt =                      + k<sub>2</sub>[X&sdot;E] - d<sub>P</sub>[P]

Revision as of 11:24, 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]
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