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Key points: A computational model of P2X channel activation in microglia was developed that includes downfield Ca2+‐dependent signalling pathways.This model provides quantitative insights into how diverse signalling pathways in microglia converge to control microglial function. Microglia function is orchestrated through highly coupled signalling pathways that depend on calcium (Ca2+). In response to extracellular ATP, transient increases in intracellular Ca2+ driven through the activation of purinergic receptors, P2X and P2Y, are sufficient to promote cytokine synthesis. Although the steps comprising the pathways bridging purinergic receptor activation with transcriptional responses have been probed in great detail, a quantitative model for how these steps collectively control cytokine production has not been established. Here we developed a minimal computational model that quantitatively links extracellular stimulation of two prominent ionotropic purinergic receptors, P2X4 and P2X7, with the graded production of a gene product, namely the tumour necrosis factor α (TNFα) cytokine. In addition to Ca2+ handling mechanisms common to eukaryotic cells, our model includes microglia‐specific processes including ATP‐dependent P2X4 and P2X7 activation, activation of nuclear factor of activated T‐cells (NFAT) transcription factors, and TNFα production. Parameters for this model were optimized to reproduce published data for these processes, where available. With this model, we determined the propensity for TNFα production in microglia, subject to a wide range of ATP exposure amplitudes, frequencies and durations that the cells could encounter in vivo. Furthermore, we have investigated the extent to which modulation of the signal transduction pathways influence TNFα production. Our results suggest that pulsatile stimulation of P2X4 via micromolar ATP may be sufficient to promote TNFα production, whereas high‐amplitude ATP exposure is necessary for production via P2X7. Furthermore, under conditions that increase P2X4 expression, for instance, following activation by pathogen‐associated molecular factors, P2X4‐associated TNFα production is greatly enhanced. Given that Ca2+ homeostasis in microglia is profoundly important to its function, this computational model provides a quantitative framework to explore hypotheses pertaining to microglial physiology. Key points: A computational model of P2X channel activation in microglia was developed that includes downfield Ca2+‐dependent signalling pathways.This model provides quantitative insights into how diverse signalling pathways in microglia converge to control microglial function. [ABSTRACT FROM AUTHOR]