Here is a general framework for implementing Hill type reactions in CADET (volunteers sought).
\varphi_j = \varphi_{max_j} \prod_{i=0}^{N_{comp}-1}\frac{c^{h_{i,j}}_i}{K_{m,i,j}+c^{h_{i,j}}_i} \frac{1}{1+K_{I,i,j} c_i}
There can be several reactions j at the same time. As in the mass action law, a stoichiometric matrix S = (s_{i,j}) is required to define the net fluxes of the components that are consumed or produced by the reactions.
f_{react,i} = \sum_{j=0}^{N_{react}-1} s_{i,j} \varphi_i
The model is parameterized as follows:
- Components i that are not substrates of reaction j are indicated by h_{i,j}=0 and K_{m,i,j}=0.
- Components i that are not inhibitors of reaction j are indicated by K_{I,i,j}=0.
- If the Hill constants h_{i,j} are 1, this reduces to the Michaelis-Menten model (or Monod model, depending on the context).