Mathematical aspects of apolipoprotein kinetics, with focus on metabolic diseases

Doctoral thesis, 2020

Biomathematics is a branch of science that aims at describing biological processes in mathematical terms to frame and solve otherwise unsolvable research questions in the biological and medical field. Cardiovascular diseases are the number one cause of death in the world. Metabolic diseases as metabolic syndrome and diabetes increase the risk of cardiovascular diseases, due to disrupted lipid metabolism. Apolipoproteins (apo) are particles attached to the lipid-carrying proteins (lipoproteins) and give them properties. ApoC-III inhibits lipoprotein lipase, therefore lowering down the release of the triglyceride from the lipoproteins to the tissues, apoE is a ligand involved in the uptake of lipoproteins from the liver and apoA4 influences insulin secretion. Studying how fast the apolipoproteins are formed and released in the blood (secretion rate (SR)) and how fast they are removed fromtheblood(fractionalcatabolicrate(FCR))enrichesourknowledgeonlipid metabolism. Apolipoprotein kinetics studies are only possible thanks to mathematical modelling. So far the three apolipoproteins had not being measured in the same study. We analyse the time series data generated from three experiments with the nonlinear mixed effects modelling framework. The novelty consists in having validated a structural model for all the apolipoproteins across three studies and having chosen statistical error model. A covariance-variance matrix for the random effects has been designed and it has been validated in 16 out of the 18 total occasions (three apolipoproteins with 2 occasions for 3 experiments). Applications of the mathematical framework to the kinetic studies has led to advancements in the realm of lipid metabolism. In Paper I and II apoC-III kinetics is studied before and after hypercaloric fructose treatment in abdominally-obese individuals. In Paper I the modelling framework developed in this thesis is presented and further applied to apoA4 and apoE kinetics; a strong bond has been uncovered between triglyceride levels and the SR and PS of apoC-III and an association has been found between apoC-III and apoE kinetic parameters. In Paper II the results for apoC-III are combined with lipoprotein kinetics analysis. Hypercaloric fructose intake leads to an increase in triglyceride levels, but the mechanism behind this phenomenon was so far unknown; in this work, results support the hypothesis that the increase in apoC-III SR causes a rise in the apoC-III concentration with subsequentincreaseintriglyceridelevel. InPaperIIIapoC-IIIandapoEkinetics are analysed before and after a PSK9-inhibitor-based drug treatment in type-IIdiabetic individuals. ApoE FCR increases consistently and apoE diminishes as a result of the treatment. Different elements suggest that the increase in apoE FCR might be related to an increase in VLDL2 FCR.