Kinetic Model for Ca²⁺-induced Permeability Transition in Energized Liver Mitochondria Discriminates between Inhibitor Mechanisms*

Abstract

Cytotoxicity associated with pathophysiological Ca²⁺ overload (e.g. in stroke) appears mediated by an event termed the mitochondrial permeability transition (mPT). We built and solved a kinetic model of the mPT in populations of isolated rat liver mitochondria that quantitatively describes Ca²⁺-induced mPT as a two-step sequence of pre-swelling induction followed by Ca²⁺-driven, positive feedback, autocatalytic propagation. The model was formulated as two differential equations, each directly related to experimental parameters (Ca²⁺ flux/mitochondrial swelling). These parameters were simultaneously assessed using a spectroscopic approach to monitor multiple mitochondrial properties. The derived kinetic model correctly identifies a correlation between initial Ca²⁺ concentration and delay interval prior to mPT induction. Within the model's framework, Ru-360 (a ruthenium complex) and Mg²⁺ were shown to compete with the Ca²⁺-stimulated initiation phase of mPT induction, consistent with known inhibition at the phenomenological level of the Ca²⁺ uniporter. The model further reveals that Mg²⁺, but not Ru-360, inhibits Ca²⁺-induced effects on a downstream stage of mPT induction at a site distinct from the uniporter. The analytical approach was then applied to promethazine, an FDA-approved drug previously shown to inhibit both mPT and ischemia-reperfusion injury. Kinetic analysis revealed that promethazine delayed mPT induction in a manner qualitatively distinct from that of lower concentrations of Mg²⁺. In summary, we have developed a kinetic model to aid in the quantitative characterization of mPT induction. This model is consistent with/informative about the biochemistry of several mPT inhibitors, and its success suggests that this kinetic approach can aid in the classification of agents or targets that modulate mPT induction.