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.

Polysialic acid as a drug carrier: evaluation of a new polysialic acid–epirubicin conjugate and its comparison against established drug carriers

This paper explores the potential of polysialic acid (PSA) as a carrier for low molecular weight anticancer drugs. A PSA–epirubicin (Epi) conjugate was synthesized and compared against Epi conjugates containing established carriers, namely: N-(2-hydroxypropyl) methacrylamide (HPMA) copolymers, poly(ethylene glycol) (PEG) and polyglutamic acid (PGA). Biological assessments in the breast cancer cell line MCF-7 and in the anthracycline resistant MCF-7/DX showed that the PSA–Epi conjugate had the highest activity (40% and 30% cell death in the two cell lines at 1 mM Epi equiv., respectively). FACS studies confirmed internalization of all conjugates by cholesterol-dependent endocytosis. PSA–Epi showed release of Epi (40% at 5 h) when incubated with lysosome extracts. In vivo evaluation showed that all conjugates had a significantly longer half-life compared to free Epi. This study also allowed an investigation on the effect of the polymeric carrier on the biological activity of a conjugate, with the biodegradability of the carrier emerging as an important feature.