  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.
