Mathematical models of mitochondrial bioenergetics provide powerful analytical tools to help interpret experimental data and facilitate experimental design for elucidating the supporting biochemical and physical processes. As a next step towards constructing a complete physiologically faithful mitochondrial bioenergetics model, a mathematical model was developed targeting the cardiac mitochondrial bioenergetic based upon previous efforts, and corroborated using both transient and steady state data. The model consists of several modified rate functions of mitochondrial bioenergetics, integrated calcium dynamics and a detailed description of the K+-cycle and its effect on mitochondrial bioenergetics and matrix volume regulation. Model simulations were used to fit 42 adjustable parameters to four independent experimental data sets consisting of 32 data curves. During the model development, a certain network topology had to be in place and some assumptions about uncertain or unobserved experimental factors and conditions were explicitly constrained in order to faithfully reproduce all the data sets. These realizations are discussed, and their necessity helps contribute to the collective understanding of the mitochondrial bioenergetics.

Competing models of mitochondrial energy metabolism in the heart are highly disputed. In addition, the mechanisms of reactive oxygen species (ROS) production and scavenging are not well understood. To deepen our understanding of these processes, a computer model was developed to integrate the biophysical processes of oxidative phosphorylation and ROS generation. The model was calibrated with experimental data obtained from isolated rat heart mitochondria subjected to physiological conditions and workloads. Model simulations show that changes in the quinone pool redox state are responsible for the apparent inorganic phosphate activation of complex III. Model simulations predict that complex III is responsible for more ROS production during physiological working conditions relative to complex I. However, this relationship is reversed under pathological conditions. Finally, model analysis reveals how a highly reduced quinone pool caused by elevated levels of succinate is likely responsible for the burst of ROS seen during reperfusion after ischemia.

Under high Ca 2+ load conditions, Ca 2+ concentrations in the extra-mitochondrial and mitochondrial compartments do not display reciprocal dynamics. This is due to a paradoxical increase in the mitochondrial Ca 2+ buffering power as the Ca 2+ load increases. Here we develop and characterize a mechanism of the mitochondrial Ca 2+ sequestration system using an experimental data set from isolated guinea pig cardiac mitochondria. The proposed mechanism elucidates this phenomenon and others in a mathematical framework and is integrated into a previously corroborated model of oxidative phosphorylation including the Na + /Ca 2+ cycle. The integrated model reproduces the Ca 2+ dynamics observed in both compartments of the isolated mitochondria respiring on pyruvate after a bolus of CaCl 2 followed by ruthenium red and a bolus of NaCl. The model reveals why changes in mitochondrial Ca 2+ concentration of Ca 2+ loaded mitochondria appear significantly mitigated relative to the corresponding extra-mitochondrial Ca 2+ concentration changes after Ca 2+ efflux is initiated. The integrated model was corroborated by simulating the set-point phenomenon. The computational results support the conclusion that the Ca 2+ sequestration system is composed of at least two classes of Ca 2+ buffers. The first class represents prototypical Ca 2+ buffering, and the second class encompasses the complex binding events associated with the formation of amorphous calcium phosphate. With the Ca 2+ sequestration system in mitochondria more precisely defined, computer simulations can aid in the development of innovative therapeutics aimed at addressing the myriad of complications that arise due to mitochondrial Ca 2+ overload.

In cardiac mitochondria, matrix free Ca2+ ([Ca2+]m) is primarily regulated by Ca2+ uptake and release via the Ca2+ uniporter (CU) and Na+/Ca2+ exchanger (NCE) as well as by Ca2+ buffering. Although experimental and computational studies on the CU and NCE dynamics exist, it is not well understood how matrix Ca2+ buffering affects these dynamics under various Ca2+ uptake and release conditions, and whether this influences the stoichiometry of the NCE. To elucidate the role of matrix Ca2+ buffering on the uptake and release of Ca2+, we monitored Ca2+ dynamics in isolated mitochondria by measuring both the extra-matrix free [Ca2+] ([Ca2+]e) and [Ca2+]m. A detailed protocol was developed and freshly isolated mitochondria from guinea pig hearts were exposed to five different [CaCl2] followed by ruthenium red and six different [NaCl]. By using the fluorescent probe indo-1, [Ca2+] and [Ca2+e]m were spectrofluorometrically quantified, and the stoichiometry of the NCE was determined. In addition, we measured NADH, membrane potential, matrix volume and matrix pH to monitor Ca2+-induced changes in mitochondrial bioenergetics. Our [Ca2+]e and [Ca2+]m measurements demonstrate that Ca2+ uptake and release do not show reciprocal Ca2+ dynamics in the extra-matrix and matrix compartments. This salient finding is likely caused by a dynamic Ca2+ buffering system in the matrix compartment. The Na+ - induced Ca2+ release demonstrates an electrogenic exchange via the NCE by excluding an electroneutral exchange. Mitochondrial bioenergetics were only transiently affected by Ca2+ uptake in the presence of large amounts of CaCl2, but not by Na+- induced Ca2+ release.

NADH: ubiquinone oxidoreductase (Complex I) is a proton pump in the electron transport chain that can produce a significant amounts of superoxide and hydrogen peroxide. While the flavin mononucleotide (FMN) is the putative site for hydrogen peroxide generation, sites responsible for superoxide are less certain. Here, data on Complex I kinetics and ROS generation are analyzed using a computational model to determine the sites responsible for superoxide. The analysis includes all the major redox centers: the FMN, iron-sulfur cluster N2, and semiquinone. Analysis reveals that the fully reduced FMN and semiquinone are the primary sources of superoxide, and the iron-sulfur cluster N2 produces none. The FMN radical only produces ROS when the quinone reductase site is blocked. Model simulations reveal ROS generation is maximized during reverse electron transport with both the FMN and semiquin one producing similar amounts of superoxide. In addition, the model successfully predicts the increase in ROS generation when the membrane potential is high and matrix pH is alkaline. Of the total ROS produced by Complex I, the majority originates from the FMN.