Mathematical Modelling of Material Transfer to High-Density Lipoprotein (HDL) upon Triglyceride Lipolysis by Lipoprotein Lipase: Relevance to Cardioprotective Role of HDL

Figures

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  Figure 1. Kinetics of HDL content of CE (A), FC (B), TC (C), PL (D) and apoA-I (E) during VLDL lipolysis by LPL in the presence of HDL. Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25]. Initial concentrations: HDL, 5 (blue circles), 10 (red squares), 20 (green diamonds) and 40 (purple triangles) mg total mass/dL; VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 2. Kinetics of the accumulation in HDL of CE (A), FC (B), TC (C), PL (D) and apoA-I (E) during VLDL lipolysis by LPL in the presence of HDL. Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25]. In order to calculate accumulation in HDL of a given component, its content at baseline (t = 0) was subtracted from the results of the modelling. Initial concentrations: HDL, 5 (blue circles), 10 (red squares), 20 (green diamonds) and 40 (purple triangles) total mass/dL; VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 3. Dose-dependences of the accumulation in HDL of CE (A), FC (B), TC (C), PL (D) and apoA-I (E) during VLDL lipolysis by LPL in the presence of HDL. Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25] for the reaction time of 1 (blue circles), 2 (red squares) and 3 (green diamonds) h. In order to calculate accumulation in HDL of a given component, its content at baseline (t = 0) was subtracted from the results of the modelling. Initial concentrations: HDL, 5, 10, 20 and 40 mg total mass/dL; VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 4. Comparison of the kinetics of accumulation in HDL of FC (A–D) and TC (E–H) with experimental data obtained for HDL isolated by ultracentrifugation or by apoB precipitation [25]. Experimental data for HDL isolated by ultracentrifugation and apoB precipitation are shown as green diamonds and red squares, respectively, whereas modelling results are presented as black circles for FC and blue triangles for TC. As the experimental data do not distinguish between TC and FC and are expressed relative to the initial content of FC in TGRL, all the data are expressed as a percentage of the initial TGRL-FC. Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25]. In order to calculate accumulation in HDL of FC or TC, its content at baseline (t = 0) was subtracted from the results of the modelling and expressed as a percentage of the initial VLDL content of FC, according to [25]. Initial concentrations: HDL, 5 (A,E), 10 (B,F), 20 (C,G) and 40 (D,H) mg total mass/dL (shown in the upper left corner of each panel); VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 5. Dose-dependences of contributions to HDL-FC provided by individual processes, including LCAT-mediated formation of CE from FC in large, lipid-rich, spherical HDL (A), LCAT-mediated formation of CE from FC in small, lipid-poor, discoidal HDL (B), FC transfer from VLDL to HDL under the action of FC concentration gradient (C), FC transfer to HDL upon collisions between VLDL and HDL particles (D) and FC transfer to HDL upon fusion of lipid-poor apoA-I with lipid-rich HDL (E). Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25] for the reaction time of 1 (blue circles), 2 (red squares) and 3 (green diamonds) h. In order to calculate accumulation of FC in HDL, its content at baseline (t = 0) was subtracted from the results of the modelling. Initial concentrations: VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 6. Kinetics of contributions to HDL-FC provided by individual processes, including LCAT-mediated formation of CE from FC in large, lipid-rich, spherical HDL (purple), LCAT-mediated formation of CE from FC in small, lipid-poor, discoidal HDL (brown), FC transfer from VLDL to HDL under the action of FC concentration gradient (red), FC transfer to HDL upon collisions between VLDL and HDL particles (green) and FC transfer to HDL upon fusion of lipid-poor and lipid-rich HDL (blue). Results are separately shown for HDL concentrations of 5 (A), 10 (B), 20 (C) and 40 (D) mg total mass/dL (indicated in the upper left corner of each panel). Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25]. In order to calculate accumulation of FC in HDL, its content at baseline (t = 0) was subtracted from the results of the modelling. Initial concentrations: VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 7. Relative contributions to HDL-FC provided by individual processes, including LCAT-mediated formation of CE from FC in large, lipid-rich, spherical HDL (purple), LCAT-mediated formation of CE from FC in small, lipid-poor, discoidal HDL (brown), FC transfer from VLDL to HDL under the action of FC concentration gradient (red), FC transfer to HDL upon collisions between VLDL and HDL particles (green) and FC transfer to HDL upon fusion of lipid-poor apoA-I with lipid-rich HDL (blue). All negative contributions were converted into positive and relative contributions of all processes were calculated as percentages of their sum. For the sake of simplicity, data are only shown for two HDL concentrations of 5 and 20 mg/dL. Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25]. In order to calculate accumulation of FC in HDL, its content at baseline (t = 0) was subtracted from the results of the modelling. Initial concentrations: VLDL-TG, 30 mg/dL; LPL, 190 U/mL.

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  Figure 8. Influence of LCAT (A) and CETP (B) activities on the accumulation of cholesterol in HDL. Mathematical modelling was performed under conditions of in vitro TGRL lipolysis described elsewhere [25] for the reaction time of 1 (blue circles), 2 (red squares) and 3 (green diamonds) h (A). In order to calculate accumulation of cholesterol in HDL, its content at baseline (t = 0) was subtracted from the results of the modelling. Initial concentrations: VLDL-TG, 30 mg/dL; LPL, 190 U/mL. (A) HDL, 40 mg total mass/dL; (B) HDL, 5 (blue circles), 10 (red squares), 20 (green diamonds) and 40 (purple triangles) total mass/dL; reaction time, 2 h.

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  Figure 9. Schematic representation ofthe model oflipoprotein remodellingupon VLDL lipolysis by LPL in the presence of HDL. The arrows shown represent processes described in the text which are equally abbreviated in italics. The arrows are numbered according to the reaction numbers shown in Table 2. Gl, glycerol; FFA, free fatty acids; grad, gradient; diss, dissociation; coll, collision.