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

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.

Comparison of methods for analysis of proteolysis by plasmin in milk

Sensitive methods that are currently used to monitor proteolysis by plasmin in milk are limited due to 7 their high cost and lack of standardisation for quality assurance in the various dairy laboratories. In 8 this study, four methods, trinitrobenzene sulphonic acid (TNBS), reverse phase high pressure liquid 9 chromatography (RP-HPLC), gel electrophoresis and fluorescamine, were selected to assess their 10 suitability for the detection of proteolysis in milk by plasmin. Commercial UHT milk was incubated 11 with plasmin at 37 °C for one week. Clarification was achieved by isoelectric precipitation (pH 4·6 12 soluble extracts)or 6% (final concentration) trichloroacetic acid (TCA). The pH 4·6 and 6% TCA 13 soluble extracts of milk showed high correlations (R2 > 0·93) by the TNBS, fluorescamine and 14 RP-HPLC methods, confirming increased proteolysis during storage. For gel electrophoresis,15 extensive proteolysis was confirmed by the disappearance of α- and β-casein bands on the seventh 16 day, which was more evident in the highest plasmin concentration. This was accompanied by the 17 appearance of α- and β-casein proteolysis products with higher intensities than on previous days, 18 implying that more products had been formed as a result of casein breakdown. The fluorescamine 19 method had a lower detection limit compared with the other methods, whereas gel electrophoresis 20 was the best qualitative method for monitoring β-casein proteolysis products. Although HPLC was the 21 most sensitive, the TNBS method is recommended for use in routine laboratory analysis on the basis 22 of its accuracy, reliability and simplicity.