Mathematical modelling of human P2X-mediated plasma membrane electrophysiology and calcium dynamics in microglia

Abstract

Regulation of cytosolic calcium (Ca2+) dynamics is fundamental to microglial function. Temporal and spatial Ca2+ fluxes are induced from a complicated signal transduction pathway linked to brain ionic homeostasis. In this paper, we develop a novel biophysical model of Ca2+ and sodium (Na+) dynamics in human microglia and evaluate the contribution of purinergic receptors (P2XRs) to both intracellular Ca2+ and Na+ levels in response to agonist/ATP binding. This is the first comprehensive model that integrates P2XRs to predict intricate Ca2+ and Na+ transient responses in microglia. Specifically, a novel compact biophysical model is proposed for the capture of whole-cell patch-clamp currents associated with P2X4 and P2X7 receptors, which is composed of only four state variables. The entire model shows that intricate intracellular ion dynamics arise from the coupled interaction between P2X4 and P2X7 receptors, the Na+/Ca2+ exchanger (NCX), Ca2+ extrusion by the plasma membrane Ca2+ ATPase (PMCA), and Ca2+ and Na+ leak channels. Both P2XRs are modelled as two separate adenosine triphosphate (ATP) gated Ca2+ and Na+ conductance channels, where the stoichiometry is the removal of one Ca2+ for the hydrolysis of one ATP molecule. Two unique sets of model parameters were determined using an evolutionary algorithm to optimise fitting to experimental data for each of the receptors. This allows the proposed model to capture both human P2X7 and P2X4 data (hP2X7 and hP2X4). The model architecture enables a high degree of simplicity, accuracy and predictability of Ca2+ and Na+ dynamics thus providing quantitative insights into different behaviours of intracellular Na+ and Ca2+ which will guide future experimental research. Understanding the interactions between these receptors and other membrane-bound transporters provides a step forward in resolving the qualitative link between purinergic receptors and microglial physiology and their contribution to brain pathology. Author summary Mathematical modelling and computer simulation are powerful tools by which we can analyse complex biological systems, particularly, neural phenomena involved in brain dysfunction. In this research, we develop a theoretical foundation for studying P2X-mediated calcium and sodium signalling in human microglial cells. Microglia, which are brain-resident macrophages, restructure their intracellular actin cytoskeleton to enable motility; this restructuring requires a complex molecular cascade involving a set of ionic channels, membrane-coupled receptors and cytosolic components. Recent studies highlight the importance for increasing our understanding of microglia physiology, since their functions play critical roles in both normal physiological and pathological dynamics of the brain. There is a need to develop reliable human cellular models to investigate the biology of microglia aimed at understanding the influence of purinergic signalling in brain dysfunction to provide novel drug discovery targets. In this work, a detailed mathematical model is built for the dynamics of human P2XRs in microglia. Subsequently, experimental whole-cell currents are used to derive P2X-mediated electrophysiology of human microglia (i.e. sodium and calcium dynamics, and membrane potential). Our predictions reveal new quantitative insights into P2XRs on how they regulate ionic concentrations in terms of physiological interactions and transient responses.