The whole-cell kinetic metabolic model of the pH regulation mechanisms in human erythrocytes

Abstract

Mathematical modeling in recent years helped to obtain answers to questions that were difficult or even impossible to answer experimentally, to predict several unexpected connections in cell metabolism and to understand and importance of certain biochemical reactions. Due to the complexity and variety of processes underlying the mechanisms of intracellular pH (pHi) regulation, mathematical modeling and metabolome analysis are powerful tools for their analysis. In this regard, a mathematical metabolic model for human erythrocytes was created, which combines cellular metabolism with acid-base processes and gas exchange. The model consists of the main metabolic pathways, such as glycolysis, the pentose phosphate pathway, some membrane transport systems, and interactions between hemoglobin and metabolites. The Jacobs-Stewart cycle, which is fundamental in gas exchange and pH regulation, was included to these pathways. The model was created in the COPASI environment, consisted of 85 reactions, the rate of which is based on accurate kinetic equations. The time dependences of reaction flows and metabolite concentrations, as an outcome of calculations, allowed us to reproduce the behaviour of the metabolic system after its disturbance in vitro and to establish the recovery mechanisms or approximation to stationary states. The COPASI simulation environment provides model flexibility by reproducing any experimental design by optimizing direct quantitative comparisons between measured and predicted results. Thus, the procedure of parameters optimization (Parameter Estimation) followed by the solution of the model’s differential equations (Time Course procedure) was used to predict the behaviour of all measured and unmeasured variables over time. The initial intracellular concentrations of CO2, HCO3– in human erythrocytes used for incubation in a phosphate buffer medium were calculated. Changes in CO2, HCO3– content over time were shown. It was established that the regulation of pH in erythrocytes placed in a buffer medium takes place with the participation of two types of processes – fast (takes place in 1.3 s) and slow. It is shown that fast processes are aimed at restoring the intracellular balance between CO2 and HCO3–, slow processes are aimed at establishing the balance of H+ between the cell and the extracellular environment. The role of carbonic anhydrase (CA) and hemoglobin in the processes of pH stabilization is shown and analyzed. The physiological role of the metabolon between band 3 protein (AE1), CA, aquaporin and hemoglobin in maintaining pH homeostasis in the conditions of in vitro experiments are discussed.