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

Regulation of cytosolic calcium (Ca(2+)) dynamics is fundamental to microglial function. Temporal and spatial Ca(2+) fluxes are induced from a complicated signal transduction pathway linked to brain ionic homeostasis. In this paper, we develop a novel biophysical model of Ca(2+) and sodium (Na(+)) dynamics in human microglia and evaluate the contribution of purinergic receptors (P2XRs) to both intracellular Ca(2+) and Na(+) levels in response to agonist/ATP binding. This is the first comprehensive model that integrates P2XRs to predict intricate Ca(2+) 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 P2X(4) and P2X(7) receptors, which is composed of only four state variables. The entire model shows that intricate intracellular ion dynamics arise from the coupled interaction between P2X(4) and P2X(7) receptors, the Na(+)/Ca(2+) exchanger (NCX), Ca(2+) extrusion by the plasma membrane Ca(2+) ATPase (PMCA), and Ca(2+) and Na(+) leak channels. Both P2XRs are modelled as two separate adenosine triphosphate (ATP) gated Ca(2+) and Na(+) conductance channels, where the stoichiometry is the removal of one Ca(2+) 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 P2X(7) and P2X(4) data (hP2X(7) and hP2X(4)). The model architecture enables a high degree of simplicity, accuracy and predictability of Ca(2+) and Na(+) dynamics thus providing quantitative insights into different behaviours of intracellular Na(+) and Ca(2+) 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.