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.

The competitive ability of pea-barley intercrops against weeds and the interactions with crop productivity and soil N availability

Grain legumes, such as peas (Pisum sativum L.), are known to be weak competitors against weeds when grown as the sole crop. In this study, the weed-suppression effect of pea–barley (Hordeum vulgare L.)intercropping compared to the respective sole crops was examined in organic field experiments across Western Europe (i.e., Denmark, the United Kingdom, France, Germany and Italy). Spring pea (P) and barley(B) were sown either as the sole crop, at the recommended plant density (P100 and B100, respectively), or in replacement (P50B50) or additive (P100B50)intercropping designs for three seasons (2003–2005). The weed biomass was three times higher under the pea sole crops than under both the intercrops and barley sole crops at maturity. The inclusion of joint experiments in several countries and various growing conditions showed that intercrops maintain a highly asymmetric competition over weeds, regardless of the particular weed infestation (species and productivity), the crop biomass or the soil nitrogen availability. The intercropping weed suppression was highly resilient, whereas the weed suppression in pea sole crops was lower and more variable. The pea–barley intercrops exhibited high levels of weed suppression, even with a low percentage of barley in the total biomass. Despite a reduced leaf area in the case of a low soil N availability, the barley sole crops and intercrops displayed high weed suppression, probably because of their strong competitive capability to absorb soil N. Higher soil N availabilities entailed increased leaf areas and competitive ability for light, which contributed to the overall competitive ability against weeds for all of the treatments. The contribution of the weeds in the total dry matter and soil N acquisition was higher in the pea sole crop than in the other treatments, in spite of the higher leaf areas in the pea crops.