A mathematical model of calcium signals around laser-induced epithelial wounds

Cells around epithelial wounds must first become aware of the wound's presence in order to initiate the wound-healing process. An initial response to an epithelial wound is an increase in cytosolic calcium followed by complex calcium-signaling events. While these calcium signals are driven by both physical and chemical wound responses, cells around the wound will all be equipped with the same cellular components to produce and interact with the calcium signals. Here we have developed a mathematical model in the context of laser ablation of the Drosophila pupal notum that integrates tissue-level damage models with a cellular calcium-signaling toolkit. The model replicates experiments in the contexts of control wounds as well as knockdowns of specific cellular components, but it also provides new insights that are not easily accessible experimentally. The model suggests that cell-cell variability is necessary to produce calcium-signaling events observed in experiments; it quantifies calcium concentrations during wound-induced signaling events, and it shows that intercellular transfer of the molecule IP₃ is required to coordinate calcium signals across distal cells around the wound. The mathematical model developed here serves as a framework for quantitative studies in both wound signaling and calcium signaling in the Drosophila system.