Modelling the ATP production in mitochondria

TL;DR

This paper revises a mathematical model of mitochondrial ATP production by correcting flux rate approximations, analyzing its dynamical behavior, and exploring how calcium and FBP influence mitochondrial stability and response times.

Contribution

It introduces improved flux rate approximations in the BPLS model and analyzes the resulting dynamical properties and physiological responses.

Findings

The enhanced BPLS model has a unique stable fixed point under physiological conditions.

Calcium and FBP saturation effects are confirmed in the model.

Response times increase significantly at high calcium and FBP concentrations.

Abstract

We revisit here the mathematical model for ATP production in mitochondria introduced recently by Bertram, Pedersen, Luciani, and Sherman (BPLS) as a simplification of the more complete but intricate Magnus and Keizer's model. We identify some inaccuracies in the BPLS original approximations for two flux rates, namely the adenine nucleotide translocator rate $J_{\rm ANT}$ and the calcium uniporter rate $J_{\rm uni}$. We introduce new approximations for such flux rates and then analyze some of the dynamical properties of the model. We infer, from exhaustive numerical explorations, that the enhanced BPLS equations have a unique attractor fixed point for physiologically acceptable ranges of mitochondrial variables and respiration inputs, as one would indeed expect from homeostasis. We determine, in the stationary regime, the dependence of the mitochondrial variables on the respiration inputs, namely the cytosolic concentration of calcium ${\rm Ca}_{\rm c}$ and the substrate fructose 1,6-bisphosphate FBP. The same dynamical effects of calcium and FBP saturations reported for the original BPLS model are observed here. We find out, however, a novel non-stationary effect which could be, in principle, physiologically interesting: some response times of the model tend to increase considerably for high concentrations of calcium and/or FBP. In particular, the larger the concentrations of ${\rm Ca}_{\rm c}$ and/or FBP, the larger the necessary time to attain homeostasis.