Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics

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.Author Summary: Mathematically modeling biological systems challenges our current understanding of the physical and biochemical events contributing to the observed dynamics. It requires careful consideration of hypothesized mechanisms, model development assumptions and details regarding the experimental conditions. We have adopted a modeling approach to translate these factors that explicitly considers the thermodynamic constraints, biochemical states and reaction mechanisms during model development. Such models have numerous constant parameters that must be determined. Integrating thermodynamics and detailed mechanistic representation of the principal phenomena help constrain these parameter values; therefore, only a handful of the total number of model parameters (∼10%) must be adjusted during parameter estimation through model simulations. Additionally, all models must undergo some form of corroboration prior to application. In practice, this corroboration should challenge all possible dynamics of the model, but it is recognized that in this data rich world, we are surprisingly data poor. Eventually such developed and corroborated models are capable of supporting current hypotheses, guiding experimental designs and contributing to the overall knowledge base of biological processes.