A Mathematical Model for the Receptor Mediated Cellular Regulation of the Low Density Lipoprotein Metabolism

A prototype mathematical model for Brown and Goldstein’s pioneering studies on the LDL receptor mediated pathway for the regulation of the cellular content of cholesterol has been developed in this paper. In order to analyze the essential features of this complex system quantitatively and still reflect the framework of the total system, six important processes are considered in the model. They are: (1A, B) the hydrolysis and synthesis of the LDL receptor; (2) the binding of LDL to its receptors; (3) the hydrolysis of LDL; (4) the storage of cholesteryl esters; (5) the regulation of de novo synthesis of cholesterol; and (6) the efflux of free cholesterol to the external medium. All these processes form a system to let the cells take up enough cholesterol from the external medium for their utilization and yet avoid the excessive accumulation of the lipid within the cells. The validity of the model is tested by showing that it can predict many of experimental curves obtained for human fibroblasts in tissue culture studies. The main purpose of the model is to determine how the free cholesterol level in the cell is related to the external LDL concentration and the regulatory capacity of the cells to adapt to a changing LDL environment. In addition, the model reveals an important behavior of SMC, i.e., for a slowly increasing LDL concentration in the extracellular medium, the rate of intracellular degradation of LDL will first increase and then become saturated. It is proposed based on these results that the saturation of LDL degradation by SMCs and the subsequent increase in subendothelial LDL levels in regions of high macromolecular permeability might play a vital role in the formation of the early foam cell lesion.