User:Johnsy/Lipoprotein Modelling/Bile Acid Biosynthesis

Background

We first start off with a diagram of the model that we wish to use for the bile acid biosyntheis pathway.

The Model

The equation governing the enzymatic degradation of cholesterol by the enzyme Cholesterol 7α Hydroxylase (C7H) is modeled using a simple Michaelis-Menten type equation as shown below. This equation will be combined with that from the de novo synthesis pathway to complete our hepatocyte model.

[math]\displaystyle{ \frac{d[IC]}{dt} = - \frac{k_3[C7H][IC]}{k_{m2} + [IC]} }[/math]

The equation for the synthesis of bile acids follows from the degradation of cholesterol assuming that in this model cholesterol is only degraded to bile acid.

[math]\displaystyle{ \frac{d[BA]}{dt} = \frac{k_3[C7H][IC]}{k_{m2} + [IC]} - d_3 \eta[BA] - r_1(1-\eta)[BA] + k_5[RBA] }[/math]