User:Johnsy/Lipoprotein Modelling/Compartmental Modelling

We now wish to separate the model of the human body into three compartments to see the dynamics established within the body. These three compartments are the hepatocytes, the epithelial cells (and other cells in the body), and the blood plasma. Each have their own unique identities which require a slightly different model for each. Most importantly, the mode of cholesterol regulation is very different between hepatocytes and epithelial cells and each is able to control different aspects of cholesterol metabolism. What occurs within epithelial cells is crucial to the local control of cholesterol metabolism, while the functionality afforded in the hepatocytes enables a global control. The transmission mechanism between the two types of cells is, of course, the lipoproteins in the blood plamsa.

A Model of the Hepatocyte

The hepatocyte is unique amongst all other cells in terms of cholesterol metabolism since it is the only cells in the body that can excrete cholesterol from the body via bile acids. Although other cells in the body are capable of performing the bile acid synthesis pathway, it is within the liver cell that it predominates through the enzyme cholesterol 7α hydroxylase.

Furthermore, hepatocytes are also the major suppliers of VLDL and HDL nascent particles. VLDL acts as a method for redistributing cholesterol around the body through its conversion to IDL and further to LDL while HDL is responsible for reverse cholesterol transport, or moving excess cholesterol from peripheral cells back to the liver. In our model, we neglect the cholesterol output from the hepatocyte as the nascent particles do not contain significant amounts of cholesterol. Instead, we focus on the uptake of cholesterol from HDL molecules from either an endocytotic pathway where the entire lipoprotein is ingested or via selective removal of choelsterol without uptake of the whole particle.[1]

The figure below shows the main players in the cholesterol flux through the hepatocyte.

For this compartment, we will have three main equations governing the cell: intracellular cholesterol, LDL receptors, and bile acid.

The equations are shown below.

For Cholesterol

[math]\displaystyle{ \begin{alignat}{2} \frac{d[IC]}{dt} = & \frac{k_1}{d_1(b_1 + [IC])} \frac{k_2[HMG-CoA]}{k_{m1}+ [HMG-CoA] + \frac{k_{m1}}{k_i}[statin]} \\ & - \frac{k_4}{d_4(b_2 + \frac{r_1}{k_5}(1-\eta)[BA])} \frac{k_3[IC]}{k_{m2} + [IC]} \\ & + (d_I \frac{[IDL-C]}{\chi_I} + d_L \frac{[LDL-C]}{\chi_L})\phi_{LR} \\ & + d_5[LDL-C] - d_{HDL} \frac{[HDL-C]}{\chi_H}([IC]-p[HDL-C]) \\ \end{alignat} }[/math]

For Bile Acid

[math]\displaystyle{ \frac{d[BA]}{dt} = \frac{k_4}{d_4(b_2 + \frac{r_1}{k_5}(1-\eta)[BA])} \frac{k_3[IC]}{k_{m2} + [IC]} - d_3 \eta[BA] }[/math]

For LDL Receptors

[math]\displaystyle{ \frac{d[\phi_{LR}]}{dt} = -b(d_I \frac{[IDL-C]}{\chi_I} + d_L \frac{[LDL-C]}{\chi_L})\phi_{LR} + c\frac{1-\phi_{LR}}{b_3 + [IC]} }[/math]

References

1. Lewis GF and Rader DJ. New insights into the regulation of HDL metabolism and reverse cholesterol transport. Circ Res. 2005 Jun 24;96(12):1221-32. DOI:10.1161/01.RES.0000170946.56981.5c |