Mathematical model for low density lipoprotein (LDL) endocytosis by hepatocytes

Individuals with elevated levels of plasma low density lipoprotein (LDL) cholesterol (LDL-C) are considered to be at risk of developing coronary heart disease. LDL particles are removed from the blood by a process known as receptor-mediated endocytosis, which occurs mainly in the liver. A series of classical experiments delineated the major steps in the endocytotic process; apolipoprotein B-100 present on LDL particles binds to a specific receptor (LDL receptor, LDL-R) in specialized areas of the cell surface called clathrin-coated pits. The pit comprising the LDL-LDL-R complex is internalized forming a cytoplasmic endosome. Fusion of the endosome with a lysosome leads to degradation of the LDL into its constituent parts (that is, cholesterol, fatty acids, and amino acids), which are released for reuse by the cell, or are excreted. In this paper, we formulate a mathematical model of LDL endocytosis, consisting of a system of ordinary differential equations. We validate our model against existing in vitro experimental data, and we use it to explore differences in system behavior when a single bolus of extracellular LDL is supplied to cells, compared to when a continuous supply of LDL particles is available. Whereas the former situation is common to in vitro experimental systems, the latter better reflects the in vivo situation. We use asymptotic analysis and numerical simulations to study the longtime behavior of model solutions. The implications of model-derived insights for experimental design are discussed.

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.

Effects of phthalic acid esters on the liver and thyroid

The effects, over periods from 3 days to 9 months of administration, of diets containing di-2-ethylhexyl phthalate are very similar to those observed in rats administered diets containing hypolipidemic drugs such as clofibrate. Changes occur in a characteristic order commencing with alterations in the distribution of lipid within the liver, quickly followed by proliferation of hepatic peroxisomes and induction of the specialized P-450 isoenzyme(s) catalyzing omega oxidation of fatty acids. There follows a phase of mild liver damage indicated by induction of glucose-6-phosphatase activity and a loss of glycogen, eventually leading to the formation of enlarged lysosomes through autophagy and the accumulation of lipofuscin. Associated changes are found in the kidney and thyroid. The renal changes are limited to the proximal convoluted tubules and are generally similar to changes found in the liver. The effects on the thyroid are more marked. Although the levels of thyroxine in plasma fail to about half normal values, serum triiodothyronine remains close to normal values while the appearance of the thyroid varies, very marked hyperactivity being noted 7 days after commencement of treatment, this is less marked at 14 days, but even after 9 months treatment there is clear cut evidence for hyperactivity with colloid changes which indicate this has persisted for some time. Straight chain analogs of di-2-ethylhexyl phthalate, di-n-hexyl phthalate and di-n-oxtyl phthalate differ entirely in their short-term effects on the liver and kidney but have similar effects on the thyroid. The short-term in vivo hepatic effects of the three phthalate esters can be reproduced in hepatocytes in tissue culture. All three phthalate esters, as well as clofibrate, have early marked effects on the metabolism of fatty acids in isolated hepatocytes. The nature of these changes is such as to increase storage of lipid in the liver. A hypothesis is presented to explain the progress from these initial metabolic effects to the final formation of liver tumors.

Interactions between uncoupling protein 2 gene polymorphisms, obesity and alcohol intake on liver function: a large meta-analysed population-based study

BACKGROUND AND OBJECTIVE: Given the role of uncoupling protein 2 (UCP2) in the accumulation of fat in the hepatocytes and in the enhancement of protective mechanisms in acute ethanol intake, we hypothesised that UCP2 polymorphisms are likely to cause liver disease through their interactions with obesity and alcohol intake. To test this hypothesis, we investigated the interaction between tagging polymorphisms in the UCP2 gene (rs2306819, rs599277 and rs659366), alcohol intake and obesity traits such as BMI and waist circumference (WC) on alanine aminotransferase (ALT) and gamma glutamyl transferase (GGT) in a large meta-analysis of data sets from three populations (n=20 242). DESIGN AND METHODS: The study populations included the Northern Finland Birth Cohort 1966 (n=4996), Netherlands Study of Depression and Anxiety (n=1883) and LifeLines Cohort Study (n=13 363). Interactions between the polymorphisms and obesity and alcohol intake on dichotomised ALT and GGT levels were assessed using logistic regression and the likelihood ratio test. RESULTS: In the meta-analysis of the three cohorts, none of the three UCP2 polymorphisms were associated with GGT or ALT levels. There was no evidence for interaction between the polymorphisms and alcohol intake on GGT and ALT levels. In contrast, the association of WC and BMI with GGT levels varied by rs659366 genotype (Pinteraction=0.03 and 0.007, respectively; adjusted for age, gender, high alcohol intake, diabetes, hypertension and serum lipid concentrations). CONCLUSION: In conclusion, our findings in 20 242 individuals suggest that UCP2 gene polymorphisms may cause liver dysfunction through the interaction with body fat rather than alcohol intake.

Chemotherapeutic agents and gene expression in cardiac myocytes

It is becoming apparent that anti-cancer chemotherapies are increasingly associated with cardiac dysfunction or even congestive heart failure (Minotti et al., 2004; Eliott, 2006; Suter et al., 2004; Ren, 2005). Our data suggest that one of the contributing factors to the cardiotoxicitiy of these drugs may be the activation of the AhR-response (including the increased expression of Cyp1a1) and/or other detoxification program in cardiac myocytes themselves. The induction of such responses may have secondary effects (e.g. to increase the level of intracellular oxidative stress), which may influence the contractility or even survival of cardiac myocytes. Furthermore, the specific response of cardiac myocytes, both with respect to the metabolizing enzymes and the export channels, potentially differs from other cells (e.g. we failed to detect any increase in expression of other “classical” AhR-responsive genes, Ugt1a1 and Ugt1a6). This could account for, for example, the observation that doxoribicinol (the 13-hydroxy form of doxorubicin) accumulates in cardiac myocytes but not in hepatocytes (Del Tacca et al., 1985; Olson et al., 1988). Given the vulnerability of the heart and the almost irreparable damage that can be done by severe oxidative stress, further studies would seem to be merited specifically on the effects of chemotherapeutic agents on cardiac myocytes.