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 correct some inaccuracies in the BPLS original approximations and 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  . 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 effect of calcium saturation reported for the original BPLS model is observed here. We find out, however, an interesting non-stationary effect : the inertia of the model tends to increase considerably for high concentrations of calcium {\rm   .
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 .
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