A mathematical model for the effect of malaria on arginine catabolism in endothelial cells

Background: Malaria is an infectious disease caused by protozoan parasites from the genus Plasmodium. P. falciparum infects red blood cells (RBCs) which thus adhere to the microvascular endothelium. The accumulation of infected RBCs cause the reduction of oxygen resulting in impaired perfusion and, eventually, organ damage [1]. The characteristics of severe malaria are decreased nitric oxide (NO) production [2], low extracellular concentration of L-arginine, the substrate of NO production [3], and increased cell free haemoglobin (Hb) concentration compared to healthy control subjects [4]. Arginine catabolism is part of the urea cycle. Aim The aim of this study is to develop a mathematical model based on data obtained from our previous study in Timika to describe arginine catabolism in endothelial cells in malaria. This model also aims to identify the optimal dosing schedule of arginine infusion in malaria.

Methods: The MontaƱez [5] (a steady state acyclic intracellular model) and Jeffers [6] (a model for NO quenching) models were used as the initial building blocks for a model for intracellular arginine catabolism and NO quenching, respectively. Subsequently, further model development was conducted to include intra and extracellular transport and cyclic catabolism as well as arginine supplementation in non-steady state conditions. Model development was undertaken in MATLAB. No estimation procedures were included. The optimal dosing schedule was determined by calculating the total number of NO molecules produced in the endothelial cell (or that reach the adjacent muscle cells) for any given dosing regimen of arginine.

Results: A full arginine catabolic model was developed that was able to describe available data. Modification of the maximum enzyme velocities was required for some enzymes, such as iNOS, suggesting induction in malaria. In addition some affinity constants for transporters were also required to be increased, suggesting that a pool of arginine may exist intracellularly which is inaccessible to the transporter. The cumulative NO molecules produced by endothelial cells is significantly increased with the supplementation of extracellular arginine. An increase in dose of arginine infusion leads only to a minimal increase in cumulative NO molecules. However, an increase in duration of the arginine infusion from 0.5 to 12 hours resulted in a significant increase in the cumulative NO molecules. Therefore, the administration of arginine is schedule-dependent. Additionally, an increase in cell free Hb decreases the cumulative number of NO molecules that reach muscle cells via an inverse relationship.

Conclusion: Our model represents adequately arginine catabolism in malaria and our findings are in agreement with the current in vivo data. The model hypothesizes that the most important determinant of the benefits seen with arginine is the duration of the infusion. Further work is required to test this hypothesis.


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