Mathematical Modeling of PI3K/Akt Pathway in Microglia.

The motility of microglia involves intracellular signaling pathways that are predominantly controlled by changes in cytosolic Ca2+ and activation of PI3K/Akt (phosphoinositide-3-kinase/protein kinase B). In this letter, we develop a novel biophysical model for cytosolic Ca2+ activation of the PI3K/Akt pathway in microglia where Ca2+ influx is mediated by both P2Y purinergic receptors (P2YR) and P2X purinergic receptors (P2XR). The model parameters are estimated by employing optimization techniques to fit the model to phosphorylated Akt (pAkt) experimental modeling/in vitro data. The integrated model supports the hypothesis that Ca2+ influx via P2YR and P2XR can explain the experimentally reported biphasic transient responses in measuring pAkt levels. Our predictions reveal new quantitative insights into P2Rs on how they regulate Ca2+ and Akt in terms of physiological interactions and transient responses. It is shown that the upregulation of P2X receptors through a repetitive application of agonist results in a continual increase in the baseline [Ca2+], which causes the biphasic response to become a monophasic response which prolongs elevated levels of pAkt.

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

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.