Computer simulation of metabolism in palmitate-perfused rat heart. II. Behavior of complete model

Identifying Site-Specific Superoxide and Hydrogen Peroxide Production Rates From the Mitochondrial Electron Transport System Using a Computational Strategy

Mitochondrial reactive oxygen species (ROS) play important roles in cellular signaling; however, certain pathological conditions such as ischemia/reperfusion (I/R) injury disrupt ROS homeostasis and contribute to cell death. A major impediment to developing therapeutic measures against oxidative stress-induced cellular damage is the lack of a quantitative framework to identify the specific sources and regulatory mechanisms of mitochondrial ROS production. We developed a thermodynamically consistent, mass-and-charge balanced, kinetic model of mitochondrial ROS homeostasis focused on redox sites of electron transport chain complexes I, II, and III. The model was calibrated and corroborated using comprehensive data sets relevant to ROS homeostasis. The model predicts that complex I ROS production dominates other sources under conditions favoring a high membrane potential with elevated nicotinamide adenine dinucleotide (NADH) and ubiquinol (QH₂) levels. In general, complex I contributes to significant levels of ROS production under pathological conditions, while complexes II and III are responsible for basal levels of ROS production, especially when QH₂ levels are elevated. The model also reveals that hydrogen peroxide production by complex I underlies the non-linear relationship between ROS emission and O₂ at low O₂ concentrations. Lastly, the model highlights the need to quantify scavenging system activity under different conditions to establish a complete picture of mitochondrial ROS homeostasis. In summary, we describe the individual contributions of the electron transport system complex redox sites to total ROS emission in mitochondria respiring under various combinations of NADH- and Q-linked respiratory fuels under varying workloads.

Skeletal muscle mitochondria of NDUFS4-/- mice display normal maximal pyruvate oxidation and ATP production

Mitochondrial ATP production is mediated by the oxidative phosphorylation (OXPHOS) system, which consists of four multi-subunit complexes (CI-CIV) and the FoF1-ATP synthase (CV). Mitochondrial disorders including Leigh Syndrome often involve CI dysfunction, the pathophysiological consequences of which still remain incompletely understood. Here we combined experimental and computational strategies to gain mechanistic insight into the energy metabolism of isolated skeletal muscle mitochondria from 5-week-old wild-type (WT) and CI-deficient NDUFS4-/- (KO) mice. Enzyme activity measurements in KO mitochondria revealed a reduction of 79% in maximal CI activity (Vmax), which was paralleled by 45-72% increase in Vmax of CII, CIII, CIV and citrate synthase. Mathematical modeling of mitochondrial metabolism predicted that these Vmax changes do not affect the maximal rates of pyruvate (PYR) oxidation and ATP production in KO mitochondria. This prediction was empirically confirmed by flux measurements. In silico analysis further predicted that CI deficiency altered the concentration of intermediate metabolites, modestly increased mitochondrial NADH/NAD+ ratio and stimulated the lower half of the TCA cycle, including CII. Several of the predicted changes were previously observed in experimental models of CI-deficiency. Interestingly, model predictions further suggested that CI deficiency only has major metabolic consequences when its activity decreases below 90% of normal levels, compatible with a biochemical threshold effect. Taken together, our results suggest that mouse skeletal muscle mitochondria possess a substantial CI overcapacity, which minimizes the effects of CI dysfunction on mitochondrial metabolism in this otherwise early fatal mouse model.

Microarray and proteomic analysis of the cardioprotective effects of cold blood cardioplegia in the mature and aged male and female

Recently we have shown that the cardioprotection afforded by cardioplegia is modulated by age and gender and is significantly decreased in the aged female. In this report we use microarray and proteomic analyses to identify transcriptomic and proteomic alterations affecting cardioprotection using cold blood cardioplegia in the mature and aged male and female heart. Mature and aged male and female New Zealand White rabbits were used for in situ blood perfused cardiopulmonary bypass. Control hearts received 30 min sham ischemia and 120 min sham reperfusion. Global ischemia (GI) hearts received 30 min of GI achieved by cross-clamping of the aorta. Cardioplegia (CP) hearts received cold blood cardioplegia prior to GI. Following 30 min of GI the hearts were reperfused for 120 min and then used for RNA and protein isolation. Microarray and proteomic analyses were performed. Functional enrichment analysis showed that mitochondrial dysfunction, oxidative phosphorylation and calcium signaling pathways were significantly enriched in all experimental groups. Glycolysis/gluconeogenesis and the pentose phosphate pathway were significantly changed in the aged male only (P < 0.05), while glyoxylate/dicarboxylate metabolism was significant in the aged female only (P < 0.05). Our data show that specific pathways associated with the mitochondrion modulate cardioprotection with CP in the aged and specifically in the aged female. The alteration of these pathways significantly contributes to decreased myocardial functional recovery and myonecrosis following ischemia and may be modulated to allow for enhanced cardioprotection in the aged and specifically in the aged female.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

Detailed kinetics and regulation of mammalian 2-oxoglutarate dehydrogenase

Background

Mitochondrial 2-oxoglutarate (α-ketoglutarate) dehydrogenase complex (OGDHC), a key regulatory point of tricarboxylic acid (TCA) cycle, plays vital roles in multiple pathways of energy metabolism and biosynthesis. The catalytic mechanism and allosteric regulation of this large enzyme complex are not fully understood. Here computer simulation is used to test possible catalytic mechanisms and mechanisms of allosteric regulation of the enzyme by nucleotides (ATP, ADP), pH, and metal ion cofactors (Ca²⁺ and Mg²⁺).

Results

A model was developed based on an ordered ter-ter enzyme kinetic mechanism combined with con-formational changes that involve rotation of one lipoic acid between three catalytic sites inside the enzyme complex. The model was parameterized using a large number of kinetic data sets on the activity of OGDHC, and validated by comparison of model predictions to independent data.

Conclusions

The developed model suggests a hybrid rapid-equilibrium ping-pong random mechanism for the kinetics of OGDHC, consistent with previously reported mechanisms, and accurately describes the experimentally observed regulatory effects of cofactors on the OGDHC activity. This analysis provides a single consistent theoretical explanation for a number of apparently contradictory results on the roles of phosphorylation potential, NAD (H) oxidation-reduction state ratio, as well as the regulatory effects of metal ions on ODGHC function.

Detailed kinetics and regulation of mammalian NAD-linked isocitrate dehydrogenase

A mathematical model is presented to describe the catalytic mechanism of mammalian NAD-linked isocitrate dehydrogenase (NAD-IDH), a highly regulated enzyme in the tricarboxylic acid cycle, a crucial pathway in energy metabolism and biosynthesis. The mechanism accounts for allosteric regulation by magnesium-bound isocitrate and EGTA and calcium-bound ATP and ADP. The developed model is used to analyze kinetic data for the cardiac enzyme and to estimate kinetic parameter values. Since the kinetic mechanism is expressed in terms of chemical species (rather than biochemical reactants), the model explicitly accounts for the effects of biochemical state (ionic strength, pH, temperature, and metal cation concentration) on the kinetics. Because the substrate isocitrate competes with allosteric activators (ATP and ADP) and an inhibitor (EGTA) for metal ion cofactors (Ca(2+) and Mg(2+)), the observed kinetic relationships between reactants, activator and inhibitor concentrations, and catalytic flux are complex. Our analysis reveals that under physiological conditions, the ADP/ATP ratio plays a more significant role than Ca(2+) concentration in regulating the enzyme's activity. In addition, the enzyme is highly sensitive to Mg(2+) concentration in the physiological range, pointing to a potential regulatory role of [Mg(2+)] in mitochondrial energy metabolism.

Extraction of elementary rate constants from global network analysis of E. coli central metabolism

Background

As computational performance steadily increases, so does interest in extending one-particle-per-molecule models to larger physiological problems. Such models however require elementary rate constants to calculate time-dependent rate coefficients under physiological conditions. Unfortunately, even when in vivo kinetic data is available, it is often in the form of aggregated rate laws (ARL) that do not specify the required elementary rate constants corresponding to mass-action rate laws (MRL). There is therefore a need to develop a method which is capable of automatically transforming ARL kinetic information into more detailed MRL rate constants.

Results

By incorporating proteomic data related to enzyme abundance into an MRL modelling framework, here we present an efficient method operating at a global network level for extracting elementary rate constants from experiment-based aggregated rate law (ARL) models. The method combines two techniques that can be used to overcome the difficult properties in parameterization. The first, a hybrid MRL/ARL modelling technique, is used to divide the parameter estimation problem into sub-problems, so that the parameters of the mass action rate laws for each enzyme are estimated in separate steps. This reduces the number of parameters that have to be optimized simultaneously. The second, a hybrid algebraic-numerical simulation and optimization approach, is used to render some rate constants identifiable, as well as to greatly narrow the bounds of the other rate constants that remain unidentifiable. This is done by incorporating equality constraints derived from the King-Altman and Cleland method into the simulated annealing algorithm. We apply these two techniques to estimate the rate constants of a model of E. coli glycolytic pathways. The simulation and statistical results show that our innovative method performs well in dealing with the issues of high computation cost, stiffness, local minima and uncertainty inherent with large-scale non-convex nonlinear MRL models.

Conclusion

In short, this new hybrid method can ensure the proper solution of a challenging parameter estimation problem of nonlinear dynamic MRL systems, while keeping the computational effort reasonable. Moreover, the work provides us with some optimism that physiological models at the particle scale can be rooted on a firm foundation of parameters generated in the macroscopic regime on an experimental basis. Thus, the proposed method should have applications to multi-scale modelling of the real biological systems allowing for enzyme intermediates, stochastic and spatial effects inside a cell.

Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation, metabolite transport, and electrophysiology

A computational model of mitochondrial metabolism and electrophysiology is introduced and applied to analysis of data from isolated cardiac mitochondria and data on phosphate metabolites in striated muscle in vivo. This model is constructed based on detailed kinetics and thermodynamically balanced reaction mechanisms and a strict accounting of rapidly equilibrating biochemical species. Since building such a model requires introducing a large number of adjustable kinetic parameters, a correspondingly large amount of independent data from isolated mitochondria respiring on different substrates and subject to a variety of protocols is used to parameterize the model and ensure that it is challenged by a wide range of data corresponding to diverse conditions. The developed model is further validated by both in vitro data on isolated cardiac mitochondria and in vivo experimental measurements on human skeletal muscle. The validated model is used to predict the roles of NAD and ADP in regulating the tricarboxylic acid cycle dehydrogenase fluxes, demonstrating that NAD is the more important regulator. Further model predictions reveal that a decrease of cytosolic pH value results in decreases in mitochondrial membrane potential and a corresponding drop in the ability of the mitochondria to synthesize ATP at the hydrolysis potential required for cellular function.

The computational integrated myocyte: a view into the virtual heart

The presentation outlines an integrative approach for developing a computational model of cardiomyocytes. A modular approach is proposed, and strategies of linking the modules (intermediary metabolism, electrophysiology, and mechanics) of the model are presented. A strong recommendation is given toward an integrated system approach backed by experimental validation.

Control of mitochondrial beta-oxidation flux

The control of mitochondrial beta-oxidation, including the delivery of acyl moieties from the plasma membrane to the mitochondrion, is reviewed. Control of beta-oxidation flux appears to be largely at the level of entry of acyl groups to mitochondria, but is also dependent on substrate supply. CPTI has much of the control of hepatic beta-oxidation flux, and probably exerts high control in intact muscle because of the high concentration of malonyl-CoA in vivo. beta-Oxidation flux can also be controlled by the redox state of NAD/NADH and ETF/ETFH(2). Control by [acetyl-CoA]/[CoASH] may also be significant, but it is probably via export of acyl groups by carnitine acylcarnitine translocase and CPT II rather than via accumulation of 3-ketoacyl-CoA esters. The sharing of control between CPTI and other enzymes allows for flexible regulation of metabolism and the ability to rapidly adapt beta-oxidation flux to differing requirements in different tissues.

Cardiac energy metabolism: models of cellular respiration

The heart requires a large amount of energy to sustain both ionic homeostasis and contraction. Under normal conditions, adenosine triphosphate (ATP) production meets this demand. Hence, there is a complex regulatory system that adjusts energy production to meet this demand. However, the mechanisms for this control are a topic of active debate. Energy metabolism can be divided into three main stages: substrate delivery to the tricarboxylic acid (TCA) cycle, the TCA cycle, and oxidative phosphorylation. Each of these processes has multiple control points and exerts control over the other stages. This review discusses the basic stages of energy metabolism, mechanisms of control, and the mathematical and computational models that have been used to study these mechanisms.

Toward modeling the human physionome

The physionome is the description of the physiological dynamics of the normal intact organism. The march of science brings us now into the era where integration of the various facets of the knowledge of biology and medicine has become a major issue. Modeling is a vehicle for the combining of information from molecular biology, biophysics, and medical biology, but must be combined with strategies for databasing the raw data with greater efficiency than is currently possible. The lessons from the genome project can be applied to the next level major projects, the morphonome and the physionome, the objective being to put integrated forms of the data into the hands of physicians and medical scientists.

Identification of regulatory properties of metabolic networks by graph theoretical modeling

An earlier graph theoretical model of metabolic and gene-expression networks has been modified and extended to include the effect of electrical potentials on binding constants, representation of uncatalyzed processes, and treatment of parallel reactions catalyzed by a single enzyme. Formal operations on the graph, which are facilitated by a set of standardized guidelines, identify the feedback signals in the network and rank them according to their influence. The technique was applied to a model of glycolysis in ascites tumor cells in the absence and presence of 12.5 mM exogenous glucose. Feedback regulation was widely distributed and mostly due to binding of adenine nucleotide cofactors to the enzymes of the network. The major changes in feedback regulation on adding glucose is the relief of inhibition of hexokinase and phosphofructokinase and the activation of pyruvate kinase. We conclude that regulation of tumor cell glycolysis is not restricted to hexokinase or to (Na+,K+)-ATPase as was previously suggested by others.

A model for fluid secretion in the exocrine pancreas

Fluid secretion by the isolated rabbit pancreas is strongly dependent on the presence of Na+ in the bathing medium. Substitution of Na+ by another cation such as Li+ or K+ causes an inhibition of fluid secretion rate and a change in the composition of the secreted fluid which is dependent on the nature of the substituent cation. Stimulation of the pancreas by CCK-8 or carbachol increases paracellular ion permeability and, in some cases, also fluid secretion rate. We present a simple, quantitative model for ion and water secretion which accounts for the effects observed upon Na+ substitution and stimulation. The main features are active, Na+-dependent transcellular HCO3- transport and passive, paracellular cation and anion permeation. The activity of the HCO3- pump is dependent on the energy status of the cell and on the Na+ concentration in the bathing medium, and is competitively inhibited by K+. The paracellular ion permeabilities can be modulated by stimulatory agonists. We examine the extent to which, according to the model, fluid secretion is controlled by the various system parameters such as ion permeabilities and ion pump activity, and by external parameters such as the ion concentrations in the bathing medium. In addition, calculation of the effects of changes in these parameters are carried out in order to gain more insight in the mechanisms of secretion.

Computer simulation of metabolism in palmitate-perfused rat heart. III. Sensitivity analysis

The behavior of a computer model of metabolism in glucose- and palmitate-perfused rat hearts was interpreted by sensitivity analysis to explain why the heart preferentially utilizes fatty acids as fuel even in the presence of substantial exogenous glucose. The sensitivity functions identified those metabolites and enzymes which were most important in regulating the metabolic rate and determined which enzymes set the levels of the critical metabolites. Control of the mitochondrial redox potential and the distribution of coenzyme A thioesters regulated the rate of fatty acid utilization while strong inhibition of citrate synthetase resulted in accumulation of acetyl CoA and suppression of pyruvate oxidation. Glycolysis was limited by the cytosolic ATP/ADP ratio set largely by the creatine shuttle. Metabolic control appears to be widely distributed rather than localized at "key" enzymes. Metabolite levels are usually set by enzymes controlled by modifiers whereas metabolic flux is regulated by the enzymes that produce ligands for the modifier-controlled enzymes.