Modeling cellular metabolism and energetics in skeletal muscle: large-scale parameter estimation and sensitivity analysis

MITODYN: An Open Source Software for Quantitative Modeling of Mitochondrial and Cellular Energy Metabolic Flux Dynamics in Health and Disease

Mitochondrial respiratory chain (RC) transforms the reductive power of NADH or FADH2 oxidation into a proton gradient between the matrix and cytosolic sides of the inner mitochondrial membrane, that ATP synthase uses to generate ATP. This process constitutes a bridge between carbohydrates' central metabolism and ATP-consuming cellular functions. Moreover, the RC is responsible for a large part of reactive oxygen species (ROS) generation that play signaling and oxidizing roles in cells. Mathematical methods and computational analysis are required to understand and predict the possible behavior of this metabolic system. Here we propose a software tool that helps to analyze individual steps of respiratory electron transport in their dynamics, thus deepening understanding of the mechanism of energy transformation and ROS generation in the RC. This software's core is a kinetic model of the RC represented by a system of ordinary differential equations (ODEs). This model enables the analysis of complex dynamic behavior of the RC, including multistationarity and oscillations. The proposed RC modeling method can be applied to study respiration and ROS generation in various organisms and naturally extended to explore carbohydrates' metabolism and linked metabolic processes.

Detailed evaluation of pyruvate dehydrogenase complex inhibition in simulated exercise conditions

The mammalian pyruvate dehydrogenase complex (PDC) is a mitochondrial multienzyme complex that connects glycolysis to the tricarboxylic acid cycle by catalyzing pyruvate oxidation to produce acetyl-CoA, NADH, and CO₂. This reaction is required to aerobically utilize glucose, a preferred metabolic fuel, and is composed of three core enzymes: pyruvate dehydrogenase (E1), dihydrolipoyl transacetylase (E2), and dihydrolipoyl dehydrogenase (E3). The pyruvate-dehydrogenase-specific kinase (PDK) and pyruvate-dehydrogenase-specific phosphatase (PDP) are considered the main control mechanism of mammalian PDC activity. However, PDK and PDP activity are allosterically regulated by several effectors fully overlapping PDC substrates and products. This collection of positive and negative feedback mechanisms confounds simple predictions of relative PDC flux, especially when all effectors are dynamically modulated during metabolic states that exist in physiologically realistic conditions, such as exercise. Here, we provide, to our knowledge, the first globally fitted, pH-dependent kinetic model of the PDC accounting for the PDC core reaction because it is regulated by PDK, PDP, metal binding equilibria, and numerous allosteric effectors. The model was used to compute PDH regulatory complex flux as a function of previously determined metabolic conditions used to simulate exercise and demonstrates increased flux with exercise. Our model reveals that PDC flux in physiological conditions is primarily inhibited by product inhibition (∼60%), mostly NADH inhibition (∼30-50%), rather than phosphorylation cycle inhibition (∼40%), but the degree to which depends on the metabolic state and PDC tissue source.

Cardiopulmonary responses to maximal aerobic exercise in patients with cystic fibrosis

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients’ data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient’s treatment therapies.

Integrated computational model of the bioenergetics of isolated lung mitochondria

Integrated computational modeling provides a mechanistic and quantitative framework for describing lung mitochondrial bioenergetics. Thus, the objective of this study was to develop and validate a thermodynamically-constrained integrated computational model of the bioenergetics of isolated lung mitochondria. The model incorporates the major biochemical reactions and transport processes in lung mitochondria. A general framework was developed to model those biochemical reactions and transport processes. Intrinsic model parameters such as binding constants were estimated using previously published isolated enzymes and transporters kinetic data. Extrinsic model parameters such as maximal reaction and transport velocities were estimated by fitting the integrated bioenergetics model to published and new tricarboxylic acid cycle and respirometry data measured in isolated rat lung mitochondria. The integrated model was then validated by assessing its ability to predict experimental data not used for the estimation of the extrinsic model parameters. For example, the model was able to predict reasonably well the substrate and temperature dependency of mitochondrial oxygen consumption, kinetics of NADH redox status, and the kinetics of mitochondrial accumulation of the cationic dye rhodamine 123, driven by mitochondrial membrane potential, under different respiratory states. The latter required the coupling of the integrated bioenergetics model to a pharmacokinetic model for the mitochondrial uptake of rhodamine 123 from buffer. The integrated bioenergetics model provides a mechanistic and quantitative framework for 1) integrating experimental data from isolated lung mitochondria under diverse experimental conditions, and 2) assessing the impact of a change in one or more mitochondrial processes on overall lung mitochondrial bioenergetics. In addition, the model provides important insights into the bioenergetics and respiration of lung mitochondria and how they differ from those of mitochondria from other organs. To the best of our knowledge, this model is the first for the bioenergetics of isolated lung mitochondria.

Identifying Biomarkers of Wharton's Jelly Mesenchymal Stromal Cells Using a Dynamic Metabolic Model: The Cell Passage Effect

Because of their unique ability to modulate the immune system, mesenchymal stromal cells (MSCs) are widely studied to develop cell therapies for detrimental immune and inflammatory disorders. However, controlling the final cell phenotype and determining immunosuppressive function following cell amplification in vitro often requires prolonged cell culture assays, all of which contribute to major bottlenecks, limiting the clinical emergence of cell therapies. For instance, the multipotent Wharton's Jelly mesenchymal stem/stromal cells (WJMSC), extracted from human umbilical cord, exhibit immunosuppressive traits under pro-inflammatory conditions, in the presence of interferon-γ (IFNγ), and tumor necrosis factor-α (TNFα). However, WJMSCs require co-culture bioassays with immune cells, which can take days, to confirm their immunomodulatory function. Therefore, the establishment of robust cell therapies would benefit from fast and reliable characterization assays. To this end, we have explored the metabolic behaviour of WJMSCs in in vitro culture, to identify biomarkers that are specific to the cell passage effect and the loss of their immunosuppressive phenotype. We clearly show distinct metabolic behaviours comparing WJMSCs at the fourth (P4) and the late ninth (P9) passages, although both P4 and P9 cells do not exhibit significant differences in their low immunosuppressive capacity. Metabolomics data were analysed using an in silico modelling platform specifically adapted to WJMSCs. Of interest, P4 cells exhibit a glycolytic metabolism compared to late passage (P9) cells, which show a phosphorylation oxidative metabolism, while P4 cells show a doubling time of 29 h representing almost half of that for P9 cells (46 h). We also clearly show that fourth passage WJMSCs still express known immunosuppressive biomarkers, although, this behaviour shows overlapping with a senescence phenotype.

Influence of plasma macronutrient levels on hepatic metabolism: role of regulatory networks in homeostasis and disease states

Multilevel regulations by metabolic, signaling and transcription pathways form a complex network that works to provide robust metabolic regulation in the liver. This analysis indicates that dietary perturbations in these networks can lead to insulin resistance.

A Single Dynamic Metabolic Model Can Describe mAb Producing CHO Cell Batch and Fed-Batch Cultures on Different Culture Media

CHO cell culture high productivity relies on optimized culture medium management under fed-batch or perfused chemostat strategies enabling high cell densities. In this work, a dynamic metabolic model for CHO cells was further developed, calibrated and challenged using datasets obtained under four different culture conditions, including two batch and two fed-batch cultures comparing two different culture media. The recombinant CHO-DXB11 cell line producing the EG2-hFc monoclonal antibody was studied. Quantification of extracellular substrates and metabolites concentration, viable cell density, monoclonal antibody concentration and intracellular concentration of metabolite intermediates of glycolysis, pentose-phosphate and TCA cycle, as well as of energetic nucleotides, were obtained for model calibration. Results suggest that a single model structure with a single set of kinetic parameter values is efficient at simulating viable cell behavior in all cases under study, estimating the time course of measured and non-measured intracellular and extracellular metabolites. Model simulations also allowed performing dynamic metabolic flux analysis, showing that the culture media and the fed-batch strategies tested had little impact on flux distribution. This work thus paves the way to an in silico platform allowing to assess the performance of different culture media and fed-batch strategies.

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.

Analyzing clonal variation of monoclonal antibody-producing CHO cell lines using an in silico metabolomic platform

Monoclonal antibody producing Chinese hamster ovary (CHO) cells have been shown to undergo metabolic changes when engineered to produce high titers of recombinant proteins. In this work, we have studied the distinct metabolism of CHO cell clones harboring an efficient inducible expression system, based on the cumate gene switch, and displaying different expression levels, high and low productivities, compared to that of the parental cells from which they were derived. A kinetic model for CHO cell metabolism was further developed to include metabolic regulation. Model calibration was performed using intracellular and extracellular metabolite profiles obtained from shake flask batch cultures. Model simulations of intracellular fluxes and ratios known as biomarkers revealed significant changes correlated with clonal variation but not to the recombinant protein expression level. Metabolic flux distribution mostly differs in the reactions involving pyruvate metabolism, with an increased net flux of pyruvate into the tricarboxylic acid (TCA) cycle in the high-producer clone, either being induced or non-induced with cumate. More specifically, CHO cell metabolism in this clone was characterized by an efficient utilization of glucose and a high pyruvate dehydrogenase flux. Moreover, the high-producer clone shows a high rate of anaplerosis from pyruvate to oxaloacetate, through pyruvate carboxylase and from glutamate to α-ketoglutarate, through glutamate dehydrogenase, and a reduced rate of cataplerosis from malate to pyruvate, through malic enzyme. Indeed, the increase of flux through pyruvate carboxylase was not driven by an increased anabolic demand. It is in fact linked to an increase of the TCA cycle global flux, which allows better regulation of higher redox and more efficient metabolic states. To the best of our knowledge, this is the first time a dynamic in silico platform is proposed to analyze and compare the metabolomic behavior of different CHO clones.

Computational approaches for understanding energy metabolism

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

Exercise: Kinetic considerations for gas exchange

The activities of daily living typically occur at metabolic rates below the maximum rate of aerobic energy production. Such activity is characteristic of the nonsteady state, where energy demands, and consequential physiological responses, are in constant flux. The dynamics of the integrated physiological processes during these activities determine the degree to which exercise can be supported through rates of O₂ utilization and CO₂ clearance appropriate for their demands and, as such, provide a physiological framework for the notion of exercise intensity. The rate at which O₂ exchange responds to meet the changing energy demands of exercise--its kinetics--is dependent on the ability of the pulmonary, circulatory, and muscle bioenergetic systems to respond appropriately. Slow response kinetics in pulmonary O₂ uptake predispose toward a greater necessity for substrate-level energy supply, processes that are limited in their capacity, challenge system homeostasis and hence contribute to exercise intolerance. This review provides a physiological systems perspective of pulmonary gas exchange kinetics: from an integrative view on the control of muscle oxygen consumption kinetics to the dissociation of cellular respiration from its pulmonary expression by the circulatory dynamics and the gas capacitance of the lungs, blood, and tissues. The intensity dependence of gas exchange kinetics is discussed in relation to constant, intermittent, and ramped work rate changes. The influence of heterogeneity in the kinetic matching of O₂ delivery to utilization is presented in reference to exercise tolerance in endurance-trained athletes, the elderly, and patients with chronic heart or lung disease.

Rationale and resources for teaching the mathematical modeling of athletic training and performance

A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call "performance modeling," is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relationship between work rates and the durations for which an individual can sustain them during constant-work-rate or intermittent exercise. The IR model describes the dynamics by which an individual's performance capacity changes over time as a function of training. Both models elegantly abstract the underlying physiology, and both can accurately fit performance data, such that educating exercise practitioners in the science of performance modeling offers both pedagogical and practical benefits. In addition, performance modeling offers an avenue for introducing mathematical modeling skills to exercise physiology researchers. A principal limitation to the adoption of performance modeling is a lack of education. The goal of this report is therefore to encourage educators of exercise physiology practitioners and researchers to incorporate the science of performance modeling in their curricula and to serve as a resource to support this effort. The resources include a comprehensive review of the concepts associated with the development and use of the models, software to enable hands-on computer exercises, and strategies for teaching the models to different audiences.

Functional classification of skeletal muscle networks. I. Normal physiology

Extensive measurements of the parts list of human skeletal muscle through transcriptomics and other phenotypic assays offer the opportunity to reconstruct detailed functional models. Through integration of vast amounts of data present in databases and extant knowledge of muscle function combined with robust analyses that include a clustering approach, we present both a protein parts list and network models for skeletal muscle function. The model comprises the four key functional family networks that coexist within a functional space; namely, excitation-activation family (forward pathways that transmit a motoneuronal command signal into the spatial volume of the cell and then use Ca(2+) fluxes to bind Ca(2+) to troponin C sites on F-actin filaments, plus transmembrane pumps that maintain transmission capacity); mechanical transmission family (a sophisticated three-dimensional mechanical apparatus that bidirectionally couples the millions of actin-myosin nanomotors with external axial tensile forces at insertion sites); metabolic and bioenergetics family (pathways that supply energy for the skeletal muscle function under widely varying demands and provide for other cellular processes); and signaling-production family (which represents various sensing, signal transduction, and nuclear infrastructure that controls the turn over and structural integrity and regulates the maintenance, regeneration, and remodeling of the muscle). Within each family, we identify subfamilies that function as a unit through analysis of large-scale transcription profiles of muscle and other tissues. This comprehensive network model provides a framework for exploring functional mechanisms of the skeletal muscle in normal and pathophysiology, as well as for quantitative modeling.

The metabolism of neurons and astrocytes through mathematical models

Mathematical modeling of the energy metabolism of brain cells plays a central role in understanding data collected with different imaging modalities, and in making predictions based on them. During the last decade, several sophisticated brain metabolism models have appeared. Unfortunately, the picture of the metabolic details that emerges from them is far from coherent: while each model has its justification and is in agreement with some experimental data, some of the predictions of different models can diverge from each other significantly. In this article, we review some of the recent published models, emphasizing similarities and differences between them to understand where the differences in predictions stem from. In that context we present a probabilistic approach, which rather than assigning fixed values to the model parameters, regard them as random variables whose distributions are inferred on in the light of stoichiometric information and different observations. The probabilistic approach reveals how much intrinsic variability a metabolic system may contain, which in turn may be a valid explanation of the different findings.

Model analysis of the relationship between intracellular PO2 and energy demand in skeletal muscle

On the basis of experimental studies, the intracellular O(2) (iPo(2))-work rate (WR) relationship in skeletal muscle is not unique. One study found that iPo(2) reached a plateau at 60% of maximal WR, while another found that iPo(2) decreased linearly at higher WR, inferring capillary permeability-surface area (PS) and blood-tissue O(2) gradient, respectively, as alternative dominant factors for determining O(2) diffusion changes during exercise. This relationship is affected by several factors, including O(2) delivery and oxidative and glycolytic capacities of the muscle. In this study, these factors are examined using a mechanistic, mathematical model to analyze experimental data from contracting skeletal muscle and predict the effects of muscle contraction on O(2) transport, glycogenolysis, and iPo(2). The model describes convection, O(2) diffusion, and cellular metabolism, including anaerobic glycogenolysis. Consequently, the model simulates iPo(2) in response to muscle contraction under a variety of experimental conditions. The model was validated by comparison of simulations of O(2) uptake with corresponding experimental responses of electrically stimulated canine muscle under different O(2) content, blood flow, and contraction intensities. The model allows hypothetical variation of PS, glycogenolytic capacity, and blood flow and predictions of the distinctive effects of these factors on the iPo(2)-contraction intensity relationship in canine muscle. Although PS is the main factor regulating O(2) diffusion rate, model simulations indicate that PS and O(2) gradient have essential roles, depending on the specific conditions. Furthermore, the model predicts that different convection and diffusion patterns and metabolic factors may be responsible for different iPo(2)-WR relationships in humans.

Regulation of whole body energy homeostasis with growth hormone replacement therapy and endurance exercise

We hypothesized that network analysis is useful to expose coordination between whole body and myocellular levels of energy metabolism and can identify entities that underlie skeletal muscle's contribution to growth hormone-stimulated lipid handling and metabolic fitness. We assessed 112 metabolic parameters characterizing metabolic rate and substrate handling in tibialis anterior muscle and vascular compartment at rest, after a meal and exercise with growth hormone replacement therapy (GH-RT) of hypopituitary patients (n = 11). The topology of linear relationships (| r | ≥ 0.7, P ≤ 0.01) and mutual dependencies exposed the organization of metabolic relationships in three entities reflecting basal and exercise-induced metabolic rate, triglyceride handling, and substrate utilization in the pre- and postprandial state, respectively. GH-RT improved aerobic performance (+5%), lean-to-fat mass (+19%), and muscle area of tibialis anterior (+2%) but did not alter its mitochondrial and capillary content. Concomitantly, connectivity was established between myocellular parameters of mitochondrial lipid metabolism and meal-induced triglyceride handling in serum. This was mediated via the recruitment of transcripts of muscle lipid mobilization (LIPE, FABP3, and FABP4) and fatty acid-sensitive transcription factors (PPARA, PPARG) to the metabolic network. The interdependence of gene regulatory elements of muscle lipid metabolism reflected the norm in healthy subjects (n = 12) and distinguished the regulation of the mitochondrial respiration factor COX1 by GH and endurance exercise. Our observations validate the use of network analysis for systems medicine and highlight the notion that an improved stochiometry between muscle and whole body lipid metabolism, rather than alterations of single bottlenecks, contributes to GH-driven elevations in metabolic fitness.

Dynamic activation model for a glutamatergic neurovascular unit

This article considers a dynamic spatially lumped model for brain energy metabolism and proposes to use the results of a Markov chain Monte Carlo (MCMC) based flux balance analysis to estimate the kinetic model parameters. By treating steady state reaction fluxes and transport rates as random variables we are able to propagate the uncertainty in the steady state configurations to the predictions of the dynamic model, whose responses are no longer individual but ensembles of time courses. The kinetic model consists of five compartments and is governed by kinetic mass balance equations with Michaelis-Menten type expressions for reaction rates and transports between the compartments. The neuronal activation is implemented in terms of the effect of neuronal activity on parameters controlling the blood flow and neurotransmitter transport, and a feedback mechanism coupling the glutamate concentration in the synaptic cleft and the ATP hydrolysis, thus accounting for the energetic cost of the membrane potential restoration in the postsynaptic neurons. The changes in capillary volume follow the balloon model developed for BOLD MRI. The model follows the time course of the saturation levels of the blood hemoglobin, which link metabolism and BOLD FMRI signal. Analysis of the model predictions suggest that stoichiometry alone is not enough to determine glucose partitioning between neuron and astrocyte. Lactate exchange between neuron and astrocyte is supported by the model predictions, but the uncertainty on the direction and rate is rather elevated. By and large, the model suggests that astrocyte produces and effluxes lactate, while neuron may switch from using to producing lactate. The level of ATP hydrolysis in astrocyte is substantially higher than strictly required for neurotransmitter cycling, in agreement with the literature.

Glucose sensing in the pancreatic beta cell: a computational systems analysis

Background

Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of K_ATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach.

Methods

We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F₁F₀ ATPase. Redox shuttles and mitochondrial Ca²⁺ handling were also modeled.

Results

The model correctly predicts changes in the ATP/ADP ratio, Ca²⁺ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca²⁺ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca²⁺ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential.

Conclusion

This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic β-cells.

Metabolica: a statistical research tool for analyzing metabolic networks

Steady state flux balance analysis (FBA) for cellular metabolism is used, e.g., to seek information on the activity of the different pathways under equilibrium conditions, or as a basis for kinetic models. In metabolic models, the stoichiometry of the system, commonly completed with bounds on some of the variables, is used as the constraint in the search of a meaningful solution. As model complexity and number of constraints increase, deterministic approach to FBA is no longer viable: a multitude of very different solutions may exist, or the constraints may be in conflict, implying that no precise solution can be found. Moreover, the solution may become overly sensitive to parameter values defining the constraints. Bayesian FBA treats the unknowns as random variables and provides estimates of their probability density functions. This stochastic setting naturally represents the variability which can be expected to occur over a population and helps to circumvent the drawbacks of the classical approach, but its implementation can be quite tedious for users without background in statistical computations. This article presents a software package called Metabolica for performing Bayesian FBA for complex multi-compartment models and visualization of the results.

Modelling muscle energy-metabolism in anaerobic muscle

A mathematical model of anaerobic muscle energy-metabolism was developed to predict pH and the concentrations of nine muscle metabolites over time. Phosphorous-31 Nuclear Magnetic Resonance was used to measure time-course data for some phosphate metabolites and pH in anoxic M. semitendinosus taken from three slaughtered sheep. Muscles were held at 35 degrees C during the experiment. Measurement commenced 25 min post mortem and concluded before rigor mortis. The model was fitted to these data within experimental error, by simultaneously varying model parameter values and initial substrate concentrations. The model was used to simulate the period from death until metabolic activity ceased, in order to predict the different stages of metabolic response to anoxia. The model suggested that alkalinisation would occur in all three muscles in the first few minutes after the onset of anoxia, followed by a steady decline in pH. For two of the muscles this decline continued until rigor, with final pH values of 5.60 and 6.07. For the other muscle, pH reached a low of 5.60 near rigor but then increased to a final value of 5.73. A rise in pH after rigor has been observed but not previously explained in the literature. The modelling results suggest it was caused by the alkalising effect of adenosine monophosphate deamination being greater at low pH than the acidifying effect of inosine monophosphate dephosphorylation.

Models of muscle contraction and energetics

How does skeletal muscle manage to regulate the pathways of ATP synthesis during large-scale changes in work rate while maintaining metabolic homeostasis remains unknown. The classic model of metabolic regulation during muscle contraction states that accelerating ATP utilization leads to increasing concentrations of ADP and Pi, which serve as substrates for oxidative phosphorylation and thus accelerate ATP synthesis. An alternative model states that both the ATP demand and ATP supply pathways are simultaneously activated. Here, we review experimental and computational models of muscle contraction and energetics at various organizational levels and compare them with respect to their pros and cons in facilitating understanding of the regulation of energy metabolism during exercise in the intact organism.

Role of NADH/NAD+ transport activity and glycogen store on skeletal muscle energy metabolism during exercise: in silico studies

Skeletal muscle can maintain ATP concentration constant during the transition from rest to exercise, whereas metabolic reaction rates may increase substantially. Among the key regulatory factors of skeletal muscle energy metabolism during exercise, the dynamics of cytosolic and mitochondrial NADH and NAD+ have not been characterized. To quantify these regulatory factors, we have developed a physiologically based computational model of skeletal muscle energy metabolism. This model integrates transport and reaction fluxes in distinct capillary, cytosolic, and mitochondrial domains and investigates the roles of mitochondrial NADH/NAD+ transport (shuttling) activity and muscle glycogen concentration (stores) during moderate intensity exercise (60% maximal O2 consumption). The underlying hypothesis is that the cytosolic redox state (NADH/NAD+) is much more sensitive to a metabolic disturbance in contracting skeletal muscle than the mitochondrial redox state. This hypothesis was tested by simulating the dynamic metabolic responses of skeletal muscle to exercise while altering the transport rate of reducing equivalents (NADH and NAD+) between cytosol and mitochondria and muscle glycogen stores. Simulations with optimal parameter estimates showed good agreement with the available experimental data from muscle biopsies in human subjects. Compared with these simulations, a 20% increase (or approximately 20% decrease) in mitochondrial NADH/NAD+ shuttling activity led to an approximately 70% decrease (or approximately 3-fold increase) in cytosolic redox state and an approximately 35% decrease (or approximately 25% increase) in muscle lactate level. Doubling (or halving) muscle glycogen concentration resulted in an approximately 50% increase (or approximately 35% decrease) in cytosolic redox state and an approximately 30% increase (or approximately 25% decrease) in muscle lactate concentration. In both cases, changes in mitochondrial redox state were minimal. In conclusion, the model simulations of exercise response are consistent with the hypothesis that mitochondrial NADH/NAD+ shuttling activity and muscle glycogen stores affect primarily the cytosolic redox state. Furthermore, muscle lactate production is regulated primarily by the cytosolic redox state.

Metabolic dynamics in skeletal muscle during acute reduction in blood flow and oxygen supply to mitochondria: in-silico studies using a multi-scale, top-down integrated model

Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD(+). The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise.