Modeling the ATP production in mitochondria

DOI10.1007/S11538-013-9862-1zbMATH Open1311.92073arXiv1212.1194OpenAlexW3100866913WikidataQ45161958 ScholiaQ45161958MaRDI QIDQ372058

Alberto Saa, Kellen Manoela Siqueira

Publication date: 11 October 2013

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

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_{m A N T}

and the calcium uniporter rate

J_{m u n i}

. 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

{m C a}_{m 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

{m C a}_{m c}

and/or FBP, the larger the necessary time to attain homeostasis.

Full work available at URL: https://arxiv.org/abs/1212.1194

zbMATH Keywords

ATP mitochondria calcium

Mathematics Subject Classification ID

Biochemistry, molecular biology (92C40) Cell biology (92C37)