Mathematical modelling of competitive LDL/VLDL binding and uptake by hepatocytes

Abstract

Elevated levels of low-density-lipoprotein cholesterol (LDL-C) in the plasma are a well-established risk factor for the development of coronary heart disease. Plasma LDL-C levels are in part determined by the rate at which LDL particles are removed from the bloodstream by hepatic uptake. The uptake of LDL by mammalian liver cells occurs mainly via receptor-mediated endocytosis, a process which entails the binding of these particles to specific receptors in specialised areas of the cell surface, the subsequent internalization of the receptor–lipoprotein complex, and ultimately the degradation and release of the ingested lipoproteins’ constituent parts. We formulate a mathematical model to study the binding and internalization (endocytosis) of LDL and VLDL particles by hepatocytes in culture. The system of ordinary differential equations, which includes a cholesterol-dependent pit production term representing feedback regulation of surface receptors in response to intracellular cholesterol levels, is analysed using numerical simulations and steady-state analysis. Our numerical results show good agreement with in vitro experimental data describing LDL uptake by cultured hepatocytes following delivery of a single bolus of lipoprotein. Our model is adapted in order to reflect the in vivo situation, in which lipoproteins are continuously delivered to the hepatocyte. In this case, our model suggests that the competition between the LDL and VLDL particles for binding to the pits on the cell surface affects the intracellular cholesterol concentration. In particular, we predict that when there is continuous delivery of low levels of lipoproteins to the cell surface, more VLDL than LDL occupies the pit, since VLDL are better competitors for receptor binding. VLDL have a cholesterol content comparable to LDL particles; however, due to the larger size of VLDL, one pit-bound VLDL particle blocks binding of several LDLs, and there is a resultant drop in the intracellular cholesterol level. When there is continuous delivery of lipoprotein at high levels to the hepatocytes, VLDL particles still out-compete LDL particles for receptor binding, and consequently more VLDL than LDL particles occupy the pit. Although the maximum intracellular cholesterol level is similar for high and low levels of lipoprotein delivery, the maximum is reached more rapidly when the lipoprotein delivery rates are high. The implications of these results for the design of in vitro experiments is discussed.

Mathematical modelling of hepatic lipid metabolism

“…A more in-depth model of VLDL assembly has been proposed by Shorten and Upreti [50] in which the lipid composition of secreted VLDLs can be determined from uptake of individual free fatty acids after elongation and desaturation by liver enzymes. Another area of mathematical modelling is the hepatic uptake and metabolism of lipoproteins, and the competition between subclasses within this process [46,58].…”

Evaluating computational models of cholesterol metabolism

“…Furthermore, the model accounts for a proportion of unbound (other than those occluded) receptors being internalized upon endocytosis. Pearson et al [51] also studied competition between lipoproteins for binding to the LDL-receptor, but in contrast to Tindall et al [50] who assumed a continuous distribution of receptors over the plasma membrane, explicitly modeled the number of free and occupied pits [50,51]. Finally, Bhattacharya et al (2014) expanded on the model of Wattis et al (2008) by including a detailed model of regulation of intracellular cholesterol synthesis [52].…”

“…In the models based on that of Wattis et al [49][50][51] an important assumption made is that the cholesterol concentration is controlled around a set point and that the rate of either synthesis or efflux of cholesterol is assumed to be linearly dependent on the offset from this set point. Given a sufficiently large synthesis/efflux-rate (lambda) this results in the production rate of free receptor being determined by the fixed cholesterol set point.…”

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

“…Thus all quantities can now be written as a function of I * , only T * m still depend on other quantities, and these can be eliminated using other expressions in (33), for example, T * m = f 8 (I * ,f 6 (I * )).…”

“…There are also models focusing on the metabolism of a variety of lipoproteins in the body and the transport of and conversion between them [30]. Other models describe specific types of lipoprotein and their competitive uptake in the liver [31][32][33]. Models of skeletal muscle metabolism, particularly in terms of energy balance, have also been proposed [34,35] however these are restricted to skeletal muscle and ignore the rest of the body.…”