Astaburuaga2019 - ODE model of lysosomal ion homeostasis (LIH) including calcium pathways

To investigate the putative differential effect of chloride transport on lysosomal ion homeostasis,we generated an ODE mathematical model for this system. Our mathematical model builds upon a previously published model for lysosomal homeostasis (Grabe et al. 2001 J. Gen. Physiol, Ishida et al. 2013 J. Gen. Physiol), and further includes the (de)activation kinetics of the ClC-7 antiporter and Ca2+ uptake/release mechanisms. Our new model tracks the total number of ions within the lysosomal lumen over time. It considers different types of lysosomal ion channels and exchangers and two possible lysosomal Ca2+ transporters. The variation in the total number of each ion within the lysosome is described by an ordinary differential equation (ODE), and the rate of change is determined by the flux of the corresponding ion across the lysosomal membrane. The model considers different elements affecting lysosomal ion homeostasis, among which are: (i) the V-ATPase pump, (ii) a proton leak, (iii) the luminal proton buffering capacity, (iv) ClC-7 chloride/proton exchanger, (v) Ca2+ /proton exchanger (CAX), (vi) passive channels for K+ , Na+ , and Ca2+ , and (vii) Donnan particles, which are negatively charged particles or molecules trapped in the lysosomal lumen. It allows for the simulation of different scenarios mimicking the differential transport of chloride, its impact on Ca2+ uptake and release and ultimately on lysosomal homeostasis. We provide a Supplementary Information file (Astaburuaga et al. Cells 2019) with the full description of the mathematical model. The equations written in purple were newly developed, the other elements were retrieved from a previous mathematical model as indicated above.