Template:ETH Modeling Formulas

From 2006.igem.org

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