Mathematical Modelling of the Mitochondrial Dicarboxylate Carrier (SLC25A10).

The mitochondrial dicarboxylate carrier SLC25A10 mediates reversible exchange among succinate, malate, and phosphate, contributing to mitochondrial metabolic regulation. Structural studies establish a ping-pong mechanism, but most mathematical models still assume sequential binding, lacking mechanistic justification and overlooking the alternation of a single binding site. Here, we present the first mechanistically derived and thermodynamically consistent model of SLC25A10 based on a ping-pong framework. The model incorporates competitive binding of succinate, malate, and phosphate, heteroexchange, reversibility, and electroneutrality, and is calibrated using experimental datasets from intact mitochondria and reconstituted proteoliposomes. To estimate kinetic parameters and quantify their uncertainty, we employed Bayesian inference, enabling statistically rigorous calibration to uptake and competition assays. The model introduces new terms that quantify which substrate and from which side of the membrane is most likely to start the transport cycle. Beyond reproducing experimentally observed exchange kinetics, the model resolves non-equilibrium transport dynamics that are difficult to access directly in classical uptake assays. In particular, the simulations reveal a two-phase response in which an initial phosphate-driven high-flux uptake regime for malate and succinate is followed by a slower redistribution phase in which the two dicarboxylates continue to readjust primarily against each other. The model also predicts that mitochondrial morphology modulates early transport behaviour, with matrix swelling increasing and matrix condensation decreasing the initial SLC25A10 flux magnitude. More broadly, the framework provides a quantitative basis for studying how substrate competition, thermodynamic driving forces, and compartment geometry shape SLC25A10-mediated exchange, and it offers a transferable modelling strategy for other carriers in the SLC25 family.