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.

In hepatocytes, cholesterol is converted to bile acids to be excreted into the intestine via the action of the enzyme cholesterol 7α hydroxylase (C7H). The bile acid is excreted and stored in the gall bladder and is pooled until hormonal changes within the body signal to contract and excrete the bile acid into the gut during feeding. Bile acids are key to increasing the solubility of ingested lipids. Approximately 95% of the bile acids are returned to the circulation through the ileum (termed enterohepatic circulation). The returned bile acids then inhibit the gene expression of C7H through a complex unknown pathway, but modeled simply as a direct inhibitor as seen below. The returned bile acids are returned to the bile acid pool in the hepatocytes with a certain rate constant.

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]

Individual terms are described below:

• [math]\displaystyle{ d_3 \eta[BA] }[/math] - This term describes the excretion of bile acids of which a fraction η is not returned to the liver (η is usually about 5% of the excreted bile acids).

• [math]\displaystyle{ r_1(1-\eta)[BA] }[/math] - This term describes the excretion of bile acids which are recycled to the blood stream and are converted to "Returned Bile Acids" (RBA). This was done for the convenience since the gene expression of C7H is dependent on the returned bile acid pool and not the bile acid pool already present in the hepatocyte.

• [math]\displaystyle{ k_5[RBA] }[/math] - This term describes the conversion of Returned Bile Acids to the Bile Acid pool.

The equation governing the production of the enzyme C7H is described below. This is a genetically controlled production and will be justified and described further below. The justification follows similar lines to the genetic justification for the production of HMGR in the de novo synthesis pathway.

[math]\displaystyle{ \frac{d[C7H]}{dt} = \frac{k_4}{b_2 + [RBA]} - d_4[C7H] }[/math]

And finally, the equation relating to the returned bile acids is shown below.

[math]\displaystyle{ \frac{d[RBA]}{dt} = r_1(1-\eta)[BA] - k_5[RBA] }[/math]