A computational model for glycogenolysis in skeletal muscle

The paradox of fatty-acid β-oxidation in muscle insulin resistance: Metabolic control and muscle heterogeneity

The skeletal muscle is a metabolically heterogeneous tissue that plays a key role in maintaining whole-body glucose homeostasis. It is well known that muscle insulin resistance (IR) precedes the development of type 2 diabetes. There is a consensus that the accumulation of specific lipid species in the tissue can drive IR. However, the role of the mitochondrial fatty-acid β-oxidation in IR and, consequently, in the control of glucose uptake remains paradoxical: interventions that either inhibit or activate fatty-acid β-oxidation have been shown to prevent IR. We here discuss the current theories and evidence for the interplay between β-oxidation and glucose uptake in IR. To address the underlying intricacies, we (1) dive into the control of glucose uptake fluxes into muscle tissues using the framework of Metabolic Control Analysis, and (2) disentangle concepts of flux and catalytic capacities taking into account skeletal muscle heterogeneity. Finally, we speculate about hitherto unexplored mechanisms that could bring contrasting evidence together. Elucidating how β-oxidation is connected to muscle IR and the underlying role of muscle heterogeneity enhances disease understanding and paves the way for new treatments for type 2 diabetes.

CytoCopasi: a chemical systems biology target and drug discovery visual data analytics platform

MOTIVATION

Target discovery and drug evaluation for diseases with complex mechanisms call for a streamlined chemical systems analysis platform. Currently available tools lack the emphasis on reaction kinetics, access to relevant databases, and algorithms to visualize perturbations on a chemical scale providing quantitative details as well streamlined visual data analytics functionality.

RESULTS

CytoCopasi, a Maven-based application for Cytoscape that combines the chemical systems analysis features of COPASI with the visualization and database access tools of Cytoscape and its plugin applications has been developed. The diverse functionality of CytoCopasi through ab initio model construction, model construction via pathway and parameter databases KEGG and BRENDA is presented. The comparative systems biology visualization analysis toolset is illustrated through a drug competence study on the cancerous RAF/MEK/ERK pathway.

AVAILABILITY AND IMPLEMENTATION

The COPASI files, simulation data, native libraries, and the manual are available on https://github.com/scientificomputing/CytoCopasi.

The mutual interaction of glycolytic enzymes and RNA in post-transcriptional regulation

About three decades ago, researchers suggested that metabolic enzymes participate in cellular processes that are unrelated to their catalytic activity, and the term "moonlighting functions" was proposed. Recently developed advanced technologies in the field of RNA interactome capture now unveil the unexpected RNA binding activity of many metabolic enzymes, as exemplified here for the enzymes of glycolysis. Although for most of these proteins a precise binding mechanism, binding conditions, and physiological relevance of the binding events still await in-depth clarification, several well explored examples demonstrate that metabolic enzymes hold crucial functions in post-transcriptional regulation of protein synthesis. This widely conserved RNA-binding function of glycolytic enzymes plays major roles in controlling cell activities. The best explored examples are glyceraldehyde 3-phosphate dehydrogenase, enolase, phosphoglycerate kinase, and pyruvate kinase. This review summarizes current knowledge about the RNA-binding activity of the ten core enzymes of glycolysis in plant, yeast, and animal cells, its regulation and physiological relevance. Apparently, a tight bidirectional regulation connects core metabolism and RNA biology, forcing us to rethink long established functional singularities.

Full humanization of the glycolytic pathway in Saccharomyces cerevisiae

Although transplantation of single genes in yeast plays a key role in elucidating gene functionality in metazoans, technical challenges hamper humanization of full pathways and processes. Empowered by advances in synthetic biology, this study demonstrates the feasibility and implementation of full humanization of glycolysis in yeast. Single gene and full pathway transplantation revealed the remarkable conservation of glycolytic and moonlighting functions and, combined with evolutionary strategies, brought to light context-dependent responses. Human hexokinase 1 and 2, but not 4, required mutations in their catalytic or allosteric sites for functionality in yeast, whereas hexokinase 3 was unable to complement its yeast ortholog. Comparison with human tissues cultures showed preservation of turnover numbers of human glycolytic enzymes in yeast and human cell cultures. This demonstration of transplantation of an entire essential pathway paves the way for establishment of species-, tissue-, and disease-specific metazoan models.

Lactate-Dependent Cross-Talk Between Astrocyte and GnRH-I Neurons in Hypothalamus of Aged Brain: Decreased GnRH-I Transcription

GnRH-I produced by hypothalamic neurosecretory cells is considered a master regulator of mammalian reproduction. Although GnRH-I transcription is well studied, the effect of ageing on transcriptional regulation of GnRH-I has not yet been explored. Here, we elucidate the effects of ageing on the metabolic environment like lactate level and TNF-α and how these affect GnRH-I transcription. Using pathway analysis of transcriptomic data, we found that lactate is upregulated in ageing astrocytes due to the downregulation of cellular respiration pathways possibly resulting in greater pyruvate concentration for lactate production. This lactate could then be shuttled into neurons where it would affect GnRH-I transcription. We showed that supra-physiological level of lactate in young mouse brain can mimic metabolic disturbances in the old brain and cause downregulation in GnRH-I transcription at a young age. In particular, we found upregulation of GnRH-I repressors in the young brain treated with high levels of lactate similar to old brain. Hence, this confirmed that aged metabolic environment can affect GnRH-I transcription even in the young brain. Further downstream analysis using the TRUST database showed NF-Kb signalling which lies downstream of both lactate and TNF-α as being capable of upregulating GnRH-I repressors. Since NF-Kb signalling has been shown in our study as well as others to be induced by TNF-α during ageing, it is likely that GnRH-I transcriptional regulation is mediated through these pathways. Thus, we formed a model for explaining the downregulation of GnRH-I transcription during ageing through differential expression of its TFs in an aged metabolic environment.

Enhanced Oxygen Utilization Efficiency With Concomitant Activation of AMPK-TBC1D1 Signaling Nexus in Cyclophilin-D Conditional Knockout Mice

We have previously reported in HEK 293 T cells and in constitutive cyclophilin-D (Cyp-D) knockout (KO) mice that Cyp-D ablation downregulates oxygen consumption (VO₂) and triggers an adaptive response that manifest in higher exercise endurance with less VO₂. This adaptive response involves a metabolic switch toward preferential utilization of glucose via AMPK-TBC1D1 signaling nexus. We now investigated whether a similar response could be triggered in mice after acute ablation of Cyp-D using tamoxifen-induced ROSA26-Cre-mediated (i.e., conditional KO, CKO) by subjecting them to treadmill exercise involving five running sessions. At their first treadmill running session, CKO mice and controls had comparable VO₂ (208.4 ± 17.9 vs. 209.1 ± 16.8 ml/kg min⁻¹), VCO₂ (183.6 ± 17.2 vs. 184.8 ± 16.9 ml/kg min⁻¹), and RER (0.88 ± 0.043 vs. 0.88 ± 0.042). With subsequent sessions, CKO mice displayed more prominent reduction in VO₂ (genotype & session interaction p = 0.000) with less prominent reduction in VCO₂ resulting in significantly increased RER (genotype and session interaction p = 0.013). The increase in RER was consistent with preferential utilization of glucose as respiratory substrate (4.6 ± 0.8 vs. 4.0 ± 0.9 mg/min, p = 0.003). CKO mice also performed a significantly higher treadmill work for given VO₂ expressed as a power/VO₂ ratio (7.4 ± 0.2 × 10⁻³ vs. 6.7 ± 0.2 10⁻³ ratio, p = 0.025). Analysis of CKO skeletal muscle tissue after completion of five treadmill running sessions showed enhanced AMPK activation (0.669 ± 0.06 vs. 0.409 ± 0.11 pAMPK/β-tubulin ratio, p = 0.005) and TBC1D1 inactivation (0.877 ± 0.16 vs. 0.565 ± 0.09 pTBC1D1/β-tubulin ratio, p < 0.05) accompanied by increased glucose transporter-4 levels consistent with activation of the AMPK-TBC1D1 signaling nexus enabling increased glucose utilization. Taken together, our study demonstrates that like constitutive Cyp-D ablation, acute Cyp-D ablation also induces a state of increased O₂ utilization efficiency, paving the way for exploring the use of pharmacological approach to elicit the same response, which could be beneficial under O₂ limiting conditions.

Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Age-related susceptibility to insulin resistance arises from a combination of CPT1B decline and lipid overload

BACKGROUND

The skeletal muscle plays a central role in glucose homeostasis through the uptake of glucose from the extracellular medium in response to insulin. A number of factors are known to disrupt the normal response to insulin leading to the emergence of insulin resistance (IR). Advanced age and a high-fat diet are factors that increase the susceptibility to IR, with lipid accumulation in the skeletal muscle being a key driver of this phenomenon. It is debated, however, whether lipid accumulation arises due to dietary lipid overload or from a decline of mitochondrial function. To gain insights into the interplay of diet and age in the flexibility of muscle lipid and glucose handling, we combined lipidomics, proteomics, mitochondrial function analysis and computational modelling to investigate young and aged mice on a low- or high-fat diet (HFD).

RESULTS

As expected, aged mice were more susceptible to IR when given a HFD than young mice. The HFD induced intramuscular lipid accumulation specifically in aged mice, including C18:0-containing ceramides and diacylglycerols. This was reflected by the mitochondrial β-oxidation capacity, which was upregulated by the HFD in young, but not in old mice. Conspicuously, most β-oxidation proteins were upregulated by the HFD in both groups, but carnitine palmitoyltransferase 1B (CPT1B) declined in aged animals. Computational modelling traced the flux control mostly to CPT1B, suggesting a CPT1B-driven loss of flexibility to the HFD with age. Finally, in old animals, glycolytic protein levels were reduced and less flexible to the diet.

CONCLUSION

We conclude that intramuscular lipid accumulation and decreased insulin sensitivity are not due to age-related mitochondrial dysfunction or nutritional overload alone, but rather to their combined effects. Moreover, we identify CPT1B as a potential target to counteract age-dependent intramuscular lipid accumulation and thereby IR.

ADP is the dominant controller of AMP-activated protein kinase activity dynamics in skeletal muscle during exercise

Exercise training elicits profound metabolic adaptations in skeletal muscle cells. A key molecule in coordinating these adaptations is AMP-activated protein kinase (AMPK), whose activity increases in response to cellular energy demand. AMPK activity dynamics are primarily controlled by the adenine nucleotides ADP and AMP, but how each contributes to its control in skeletal muscle during exercise is unclear. We developed and validated a mathematical model of AMPK signaling dynamics, and then applied global parameter sensitivity analyses with data-informed constraints to predict that AMPK activity dynamics are determined principally by ADP and not AMP. We then used the model to predict the effects of two additional direct-binding activators of AMPK, ZMP and Compound 991, further validating the model and demonstrating its applicability to understanding AMPK pharmacology. The relative effects of direct-binding activators can be understood in terms of four properties, namely their concentrations, binding affinities for AMPK, abilities to enhance AMPK phosphorylation, and the magnitudes of their allosteric activation of AMPK. Despite AMP's favorable values in three of these four properties, ADP is the dominant controller of AMPK activity dynamics in skeletal muscle during exercise by virtue of its higher concentration compared to that of AMP.

Lactate: the ugly duckling of energy metabolism

Lactate, perhaps the best-known metabolic waste product, was first isolated from sour milk, in which it is produced by lactobacilli. Whereas microbes also generate other fermentation products, such as ethanol or acetone, lactate dominates in mammals. Lactate production increases when the demand for ATP and oxygen exceeds supply, as occurs during intense exercise and ischaemia. The build-up of lactate in stressed muscle and ischaemic tissues has established lactate's reputation as a deleterious waste product. In this Perspective, we summarize emerging evidence that, in mammals, lactate also serves as a major circulating carbohydrate fuel. By providing mammalian cells with both a convenient source and sink for three-carbon compounds, circulating lactate enables the uncoupling of carbohydrate-driven mitochondrial energy generation from glycolysis. Lactate and pyruvate together serve as a circulating redox buffer that equilibrates the NADH/NAD ratio across cells and tissues. This reconceptualization of lactate as a fuel-analogous to how Hans Christian Andersen's ugly duckling is actually a beautiful swan-has the potential to reshape the field of energy metabolism.

31 P magnetic resonance spectroscopy in skeletal muscle: Experts' consensus recommendations

Skeletal muscle phosphorus-31 31 P MRS is the oldest MRS methodology to be applied to in vivo metabolic research. The technical requirements of 31 P MRS in skeletal muscle depend on the research question, and to assess those questions requires understanding both the relevant muscle physiology, and how 31 P MRS methods can probe it. Here we consider basic signal-acquisition parameters related to radio frequency excitation, TR, TE, spectral resolution, shim and localisation. We make specific recommendations for studies of resting and exercising muscle, including magnetisation transfer, and for data processing. We summarise the metabolic information that can be quantitatively assessed with 31 P MRS, either measured directly or derived by calculations that depend on particular metabolic models, and we give advice on potential problems of interpretation. We give expected values and tolerable ranges for some measured quantities, and minimum requirements for reporting acquisition parameters and experimental results in publications. Reliable examination depends on a reproducible setup, standardised preconditioning of the subject, and careful control of potential difficulties, and we summarise some important considerations and potential confounders. Our recommendations include the quantification and standardisation of contraction intensity, and how best to account for heterogeneous muscle recruitment. We highlight some pitfalls in the assessment of mitochondrial function by analysis of phosphocreatine (PCr) recovery kinetics. Finally, we outline how complementary techniques (near-infrared spectroscopy, arterial spin labelling, BOLD and various other MRI and 1 H MRS measurements) can help in the physiological/metabolic interpretation of 31 P MRS studies by providing information about blood flow and oxygen delivery/utilisation. Our recommendations will assist in achieving the fullest possible reliable picture of muscle physiology and pathophysiology.

The dynamic side of the Warburg effect: glycolytic intermediate storage as buffer for fluctuating glucose and O 2 supply in tumor cells

Background: Tumor cells often show altered metabolism which supports uncontrolled proliferation. A classic example is the Warburg effect: high glucose uptake and lactate production despite sufficient oxygen supply. Remarkably, tumor cells can transiently take up glucose even an order of magnitude faster when glucose is reintroduced after depletion. Regulation and significance of this high glucose uptake are investigated here. Methods: A new computational model was developed which reproduces two types of experimental data on Ehrlich ascites tumor cells: measurements by Otto Warburg of the average aerobic glycolytic rate during one hour (Warburg effect), and fast metabolic responses measured by others during the first minutes after reintroducing glucose. The model is subsequently extended with equations for glucose and O 2 transport to predict the role of metabolism during fluctuations of blood flow in tumor tissue. Results: Model analysis reveals dynamic regulation of the head section of glycolysis where glucose uptake and phosphorylation occur. The head section is disinhibited slowly when concentrations of glycolytic intermediates fall, causing glucose uptake rate to considerably exceed that found by Warburg. The head section is partially inhibited in about a minute when sufficient glucose has been taken up. Simulations predict that tumors greedily take up glucose when blood flow resumes after periods of low flow. The cells then store glucose as fructose 1,6-bisphosphate and other glycolytic intermediates. During subsequent periods of low flow that cause O 2 and glucose depletion these stores are used for ATP production and biomass. Conclusions: The powerful glycolytic system in tumors not only synthesizes ATP at high steady rates, but can also store glycolytic intermediates to buffer temporary oxygen and nutrient shortages for up to 10 minutes. The head section of glycolysis in tumor cells, disinhibited during glucose shortages, becomes very efficient at stealing glucose from other cells, even at low glucose concentrations.

The dynamic side of the Warburg effect: glycolytic intermediates as buffer for fluctuating glucose and O 2 supply in tumor cells

Background: Tumor cells show the Warburg effect: high glucose uptake and lactate production despite sufficient oxygen supply. Otto Warburg found this effect in tissue slices and in suspensions of Ehrlich ascites tumor cells. Remarkably, these ascites tumor cells can transiently take up glucose an order of magnitude faster than the steady high rate measured by Warburg for hours. Methods: The purpose of the transiently very high glucose uptake is investigated here with a computational model of glycolysis, oxidative phosphorylation and ATP consumption which reproduces short kinetic experiments on the ascites tumor cells as well as the long-lasting Warburg, Crabtree and Pasteur effects. The model, extended with equations for glucose and O 2 transport in tissue, is subsequently used to predict metabolism in tumor cells during fluctuations of tissue blood flow resulting in cycling hypoxia. Results: The model analysis suggests that the head section of the glycolytic chain in the tumor cells is partially inhibited in about a minute when substantial amounts of glucose have been taken up intracellularly; this head section of the glycolytic chain is subsequently disinhibited slowly when concentrations of glycolytic intermediates are low. Based on these dynamic characteristics, simulations of tissue with fluctuating O 2 and glucose supply predict that tumor cells greedily take up glucose when this periodically becomes available, leaving very little for other cells. The glucose is stored as fructose 1,6-bisphosphate and other glycolytic intermediates, which are used for ATP production during   O 2 and glucose shortages. Conclusions: The head section of glycolysis which phosphorylates glucose may be dynamically regulated and takes up glucose at rates exceeding the Warburg effect if glucose levels have been low for some time. The hypothesis is put forward here that dynamic regulation of the powerful glycolytic enzyme system in tumors is used to buffer oxygen and nutrient fluctuations in tissue.

Lactate metabolism: historical context, prior misinterpretations, and current understanding

Lactate (La^-) has long been at the center of controversy in research, clinical, and athletic settings. Since its discovery in 1780, La^- has often been erroneously viewed as simply a hypoxic waste product with multiple deleterious effects. Not until the 1980s, with the introduction of the cell-to-cell lactate shuttle did a paradigm shift in our understanding of the role of La^- in metabolism begin. The evidence for La^- as a major player in the coordination of whole-body metabolism has since grown rapidly. La^- is a readily combusted fuel that is shuttled throughout the body, and it is a potent signal for angiogenesis irrespective of oxygen tension. Despite this, many fundamental discoveries about La^- are still working their way into mainstream research, clinical care, and practice. The purpose of this review is to synthesize current understanding of La^- metabolism via an appraisal of its robust experimental history, particularly in exercise physiology. That La^- production increases during dysoxia is beyond debate, but this condition is the exception rather than the rule. Fluctuations in blood [La^-] in health and disease are not typically due to low oxygen tension, a principle first demonstrated with exercise and now understood to varying degrees across disciplines. From its role in coordinating whole-body metabolism as a fuel to its role as a signaling molecule in tumors, the study of La^- metabolism continues to expand and holds potential for multiple clinical applications. This review highlights La^-'s central role in metabolism and amplifies our understanding of past research.

Developmental changes in the balance of glycolytic ATP production and oxidative phosphorylation in ventricular cells: A simulation study

The developmental program of the heart requires accurate regulation to ensure continuous circulation and simultaneous cardiac morphogenesis, because any functional abnormalities may progress to congenital heart malformation. Notably, energy metabolism in fetal ventricular cells is regulated in a manner that differs from adult ventricular cells: fetal cardiomyocytes generally have immature mitochondria and fetal ventricular cells show greater dependence on glycolytic ATP production. However, although various characteristics of energy metabolism in fetal ventricular cells have been reported, to our knowledge, a quantitative description of the contributions of these factors to fetal ventricular cell functions has not yet been established. Here, we constructed a mathematical model to integrate various characteristics of fetal ventricular cells and predicted the contribution of each characteristic to the maintenance of intracellular ATP concentration and sarcomere contraction under anoxic conditions. Our simulation results demonstrated that higher glycogen content, higher hexokinase activity, and lower creatine concentration helped prolong the time for which ventricular cell contraction was maintained under anoxic conditions. The integrated model also enabled us to quantitatively assess the contributions of factors related to energy metabolism in ventricular cells. Because fetal cardiomyocytes exhibit similar energy metabolic profiles to stem cell-derived cardiomyocytes and those in the failing heart, an improved understanding of these fetal ventricular cells will contribute to a better comprehension of the processes in stem cell-derived cardiomyocytes or under pathological conditions.

Coupling calcium dynamics and mitochondrial bioenergetic: an in silico study to simulate cardiomyocyte dysfunction

The coupling of intracellular Ca(2+) dynamics with mitochondrial bioenergetic is crucial for the functioning of cardiomyocytes both in healthy and disease conditions. The pathophysiological signature of the Cardiomyocyte Dysfunction (CD) is commonly related to decreased ATP production due to mitochondrial functional impairment and to an increased mitochondrial calcium content ([Ca(2+)]m). These features advanced the therapeutic approaches which aim to reduce [Ca(2+)]m. But whether [Ca(2+)]m overload is the pathological trigger for CD or a physiological consequence, remained controversial. We addressed this issue in silico and showed that [Ca(2+)]m might not directly cause CD. Through model parameter recalibration, we demonstrated how mitochondria cope up with functionally impaired processes and consequently accumulate calcium. A strong coupling of the [Ca(2+)]m oscillations with the ATP synthesis rate ensures robust calcium cycling and avoids CD. We suggested a cardioprotective role of the mitochondrial calcium uniporter and predicted that a mitochondrial sodium calcium exchanger could be a potential therapeutic target to restore the normal functioning of the cardiomyocyte.

A systemic approach to explore the flexibility of energy stores at the cellular scale: Examples from muscle cells

Variations in energy storage and expenditure are key elements for animals adaptation to rapidly changing environments. Because of the multiplicity of metabolic pathways, metabolic crossroads and interactions between anabolic and catabolic processes within and between different cells, the flexibility of energy stores in animal cells is difficult to describe by simple verbal, textual or graphic terms. We propose a mathematical model to study the influence of internal and external challenges on the dynamic behavior of energy stores and its consequence on cell energy status. The role of the flexibility of energy stores on the energy equilibrium at the cellular level is illustrated through three case studies: variation in eating frequency (i.e., glucose input), level of physical activity (i.e., ATP requirement), and changes in cell characteristics (i.e., maximum capacity of glycogen storage). Sensitivity analysis has been performed to highlight the most relevant parameters of the model; model simulations have then been performed to illustrate how variation in these key parameters affects cellular energy balance. According to this analysis, glycogen maximum accumulation capacity and homeostatic energy demand are among the most important parameters regulating muscle cell metabolism to ensure its energy equilibrium.

Flux Control in Glycolysis Varies Across the Tree of Life

Biochemical thought posits that rate-limiting steps (defined here as points of flux control) are strongly selected as points of pathway regulation and control and are thus expected to be evolutionarily conserved. Conversely, population genetic thought based upon the concepts of mutation-selection-drift balance at the pathway level might suggest variation in flux controlling steps over evolutionary time. Glycolysis, as one of the most conserved and best characterized pathways, was studied to evaluate its evolutionary conservation. The flux controlling step in glycolysis was found to vary over the tree of life. Further, phylogenetic analysis suggested at least 60 events of gene duplication and additional events of putative positive selection that might alter pathway kinetic properties. Together, these results suggest that even with presumed largely negative selection on pathway output on glycolysis, the co-evolutionary process under the hood is dynamic.

Hierarchical bond graph modelling of biochemical networks

The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open systems exchanging mass and energy via ports. A key feature of this approach is that the resultant models are robustly thermodynamically compliant: the thermodynamic compliance is not dependent on precise numerical values of parameters. Moreover, the models are reusable owing to the well-defined interface provided by the energy ports. To extract bond graph model parameters from parameters found in the literature, general and compact formulae are developed to relate free-energy constants and equilibrium constants. The existence and uniqueness of solutions is considered in terms of fundamental properties of stoichiometric matrices. The approach is illustrated by building a hierarchical bond graph model of glycogenolysis in skeletal muscle.

From metabolomics to fluxomics: a computational procedure to translate metabolite profiles into metabolic fluxes

We describe a believed-novel procedure for translating metabolite profiles (metabolome) into the set of metabolic fluxes (fluxome) from which they originated. Methodologically, computational modeling is integrated with an analytical platform comprising linear optimization, continuation and dynamic analyses, and metabolic control. The procedure was tested with metabolite profiles obtained from ex vivo mice Langendorff-heart preparations perfused with glucose. The metabolic profiles were analyzed using a detailed kinetic model of the glucose catabolic pathways including glycolysis, pentose phosphate (PP), glycogenolysis, and polyols to translate the glucose metabolome of the heart into the fluxome. After optimization, the ability of the model to simulate the initial metabolite profile was confirmed, and metabolic fluxes as well as the structure of control and regulation of the glucose catabolic network could be calculated. We show that the step catalyzed by phosphofructokinase together with ATP demand and glycogenolysis exert the highest control on the glycolytic flux. The negative flux control exerted by phosphofructokinase on the PP and polyol pathways revealed that the extent of glycolytic flux directly affects flux redirection through these pathways, i.e., the higher the glycolytic flux the lower the PP and polyols. This believed-novel methodological approach represents a step forward that may help in designing therapeutic strategies targeted to diagnose, prevent, and treat metabolic diseases.

Drug target identification through systems biology

To rationalise drug target selection, we should understand the role of putative targets in biological pathways quantitatively. We review here how experimental and computational network-based approaches can aid more rational drug target selection and illustrate this with results obtained for microbes and for cancer. Comparison of the drug response of biochemical networks in target cells and (healthy) host cells can reveal network-selective targets.

Lactate is always the end product of glycolysis

Through much of the history of metabolism, lactate (La⁻) has been considered merely a dead-end waste product during periods of dysoxia. Congruently, the end product of glycolysis has been viewed dichotomously: pyruvate in the presence of adequate oxygenation, La⁻ in the absence of adequate oxygenation. In contrast, given the near-equilibrium nature of the lactate dehydrogenase (LDH) reaction and that LDH has a much higher activity than the putative regulatory enzymes of the glycolytic and oxidative pathways, we contend that La⁻ is always the end product of glycolysis. Cellular La⁻ accumulation, as opposed to flux, is dependent on (1) the rate of glycolysis, (2) oxidative enzyme activity, (3) cellular O₂ level, and (4) the net rate of La⁻ transport into (influx) or out of (efflux) the cell. For intracellular metabolism, we reintroduce the Cytosol-to-Mitochondria Lactate Shuttle. Our proposition, analogous to the phosphocreatine shuttle, purports that pyruvate, NAD⁺, NADH, and La⁻ are held uniformly near equilibrium throughout the cell cytosol due to the high activity of LDH. La⁻ is always the end product of glycolysis and represents the primary diffusing species capable of spatially linking glycolysis to oxidative phosphorylation.

Diverse Data Sets Can Yield Reliable Information through Mechanistic Modeling: Salicylic Acid Clearance

This is a practical example of a powerful research strategy: putting together data from studies covering a diversity of conditions can yield a scientifically sound grasp of the phenomenon when the individual observations failed to provide definitive understanding. The rationale is that defining a realistic, quantitative, explanatory hypothesis for the whole set of studies, brings about a “consilience” of the often competing hypotheses considered for individual data sets. An internally consistent conjecture linking multiple data sets simultaneously provides stronger evidence on the characteristics of a system than does analysis of individual data sets limited to narrow ranges of conditions. Our example examines three very different data sets on the clearance of salicylic acid from humans: a high concentration set from aspirin overdoses; a set with medium concentrations from a research study on the influences of the route of administration and of sex on the clearance kinetics, and a set on low dose aspirin for cardiovascular health. Three models were tested: (1) a first order reaction, (2) a Michaelis-Menten (M-M) approach, and (3) an enzyme kinetic model with forward and backward reactions. The reaction rates found from model 1 were distinctly different for the three data sets, having no commonality. The M-M model 2 fitted each of the three data sets but gave a reliable estimates of the Michaelis constant only for the medium level data (K_m = 24±5.4 mg/L); analyzing the three data sets together with model 2 gave K_m = 18±2.6 mg/L. (Estimating parameters using larger numbers of data points in an optimization increases the degrees of freedom, constraining the range of the estimates). Using the enzyme kinetic model (3) increased the number of free parameters but nevertheless improved the goodness of fit to the combined data sets, giving tighter constraints, and a lower estimated K_m = 14.6±2.9 mg/L, demonstrating that fitting diverse data sets with a single model improves confidence in the results. This modeling effort is also an example of reproducible science available at html://www.physiome.org/jsim/models/webmodel/NSR/SalicylicAcidClearance

Glycolysis is governed by growth regime and simple enzyme regulation in adherent MDCK cells

Due to its vital importance in the supply of cellular pathways with energy and precursors, glycolysis has been studied for several decades regarding its capacity and regulation. For a systems-level understanding of the Madin-Darby canine kidney (MDCK) cell metabolism, we couple a segregated cell growth model published earlier with a structured model of glycolysis, which is based on relatively simple kinetics for enzymatic reactions of glycolysis, to explain the pathway dynamics under various cultivation conditions. The structured model takes into account in vitro enzyme activities, and links glycolysis with pentose phosphate pathway and glycogenesis. Using a single parameterization, metabolite pool dynamics during cell cultivation, glucose limitation and glucose pulse experiments can be consistently reproduced by considering the cultivation history of the cells. Growth phase-dependent glucose uptake together with cell-specific volume changes generate high intracellular metabolite pools and flux rates to satisfy the cellular demand during growth. Under glucose limitation, the coordinated control of glycolytic enzymes re-adjusts the glycolytic flux to prevent the depletion of glycolytic intermediates. Finally, the model's predictive power supports the design of more efficient bioprocesses.

Glycolysis generates biomass precursors and energy from sugars and is therefore a key element in the metabolism of mammalian cells. Changes in its activity greatly affect cellular function which is often recognized as metabolic disease but also as opportunity for the design of efficient bioprocesses. Metabolic research discovered that continuously growing mammalian cells often exhibit a high glycolytic activity but also delivered seemingly endless facets in the pathway operation. The latter call for a systems-level understanding regarding capacity and regulation for a broad range of cultivation conditions. In this work, we couple a cell growth model to a simple kinetic description of glycolysis to consistently explain intracellular metabolite pool dynamics of the Madin-Darby canine kidney cell line over a variety of experiments and time scales while considering the growth status and cultivation history of the cells. We argue that the many different dynamics in glycolysis result from an interplay between a growth-dependent sugar uptake together with simple intrinsic enzyme regulation.

A mathematical model of the human metabolic system and metabolic flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

Skeletal Muscle Fuel Selection Occurs at the Mitochondrial Level

Mammals exponentially increase the rate of carbohydrate oxidation as exercise intensity rises, while birds combust lipid almost exclusively while flying at high percentages of aerobic capacity. The fuel oxidized by contracting muscle depends on many factors: whole body fuel storage masses, mobilization, blood transport, cellular uptake, and substrate selection at the level of the mitochondrion. We examined the fuel preferences of mitochondria isolated from mammalian and avian locomotory muscles using two approaches. First, the influence of substrates on the kinetics of respiration (KMADP and Vmax) was evaluated. For all substrates and combinations, KMADP was generally two-fold higher in avian mitochondria. Second, fuel competition between pyruvate, glutamate, and/or palmitoyl-l-carnitine at three levels of ATP free energy was determined using the principle of mass balance and the measured rates of O2 consumption and metabolite accumulation/utilization. Avian mitochondria strongly spared pyruvate from oxidation when another substrate was available and fatty acid was the dominant substrate, regardless of energy state. Mammalian mitochondria exhibited some preference for fatty acid over pyruvate at lower flux (higher energy state), but exhibited much greater tendency to select pyruvate and glutamate when available. Studies in sonicated mitochondria revealed two-fold higher electron transport chain electron conductance in avian mitochondria. We conclude that substantial fuel selection occurs at the level of the mitochondrial matrix and that avian flight muscle mitochondria are particularly biased toward the selection of fatty acid, possibly by facilitating high β-oxidation flux by maintaining a more oxidized matrix.

Biochemical competition makes fatty-acid β-oxidation vulnerable to substrate overload

Fatty-acid metabolism plays a key role in acquired and inborn metabolic diseases. To obtain insight into the network dynamics of fatty-acid β-oxidation, we constructed a detailed computational model of the pathway and subjected it to a fat overload condition. The model contains reversible and saturable enzyme-kinetic equations and experimentally determined parameters for rat-liver enzymes. It was validated by adding palmitoyl CoA or palmitoyl carnitine to isolated rat-liver mitochondria: without refitting of measured parameters, the model correctly predicted the β-oxidation flux as well as the time profiles of most acyl-carnitine concentrations. Subsequently, we simulated the condition of obesity by increasing the palmitoyl-CoA concentration. At a high concentration of palmitoyl CoA the β-oxidation became overloaded: the flux dropped and metabolites accumulated. This behavior originated from the competition between acyl CoAs of different chain lengths for a set of acyl-CoA dehydrogenases with overlapping substrate specificity. This effectively induced competitive feedforward inhibition and thereby led to accumulation of CoA-ester intermediates and depletion of free CoA (CoASH). The mitochondrial [NAD⁺]/[NADH] ratio modulated the sensitivity to substrate overload, revealing a tight interplay between regulation of β-oxidation and mitochondrial respiration.

Lipid metabolism plays an important role in the development of metabolic syndrome, a major risk factor for cardiovascular disease and diabetes. Furthermore, inborn errors in lipid oxidation cause rare, but severe diseases in children. To obtain more insight into the response of lipid oxidation to dietary and medical interventions, we constructed a computational model. The model correctly simulated the rate of lipid oxidation and the time courses of most acyl carnitines. The latter are used as diagnostic markers in blood. Subsequently, we subjected the model to an increased supply of lipids, as often happens in obese people. We discovered that the lipid-oxidation machinery easily becomes overloaded, very much like a highway during rush hours: the more cars enter the road, the slower they proceed and the more they clog the road. Analogously, an overload of lipids slowed down the lipid oxidation and led to an accumulation of intermediate metabolites in the pathway. Potential protection mechanisms of cells consist of restricted entry of lipids into the oxidation pathway or efficient downstream processing of reaction products. In future research we will use the model to test dietary or medical interventions in silico and thereby guide the development of new treatment and prevention strategies.

Computational modeling of the metabolic States regulated by the kinase akt

Signal transduction and gene regulation determine a major reorganization of metabolic activities in order to support cell proliferation. Protein Kinase B (PKB), also known as Akt, participates in the PI3K/Akt/mTOR pathway, a master regulator of aerobic glycolysis and cellular biosynthesis, two activities shown by both normal and cancer proliferating cells. Not surprisingly considering its relevance for cellular metabolism, Akt/PKB is often found hyperactive in cancer cells. In the last decade, many efforts have been made to improve the understanding of the control of glucose metabolism and the identification of a therapeutic window between proliferating cancer cells and proliferating normal cells. In this context, we have modeled the link between the PI3K/Akt/mTOR pathway, glycolysis, lactic acid production, and nucleotide biosynthesis. We used a computational model to compare two metabolic states generated by two different levels of signaling through the PI3K/Akt/mTOR pathway: one of the two states represents the metabolism of a growing cancer cell characterized by aerobic glycolysis and cellular biosynthesis, while the other state represents the same metabolic network with a reduced glycolytic rate and a higher mitochondrial pyruvate metabolism. Biochemical reactions that link glycolysis and pentose phosphate pathway revealed their importance for controlling the dynamics of cancer glucose metabolism.

A kinetic-metabolic model based on cell energetic state: study of CHO cell behavior under Na-butyrate stimulation

A kinetic-metabolic model approach describing and simulating Chinese hamster ovary (CHO) cell behavior is presented. The model includes glycolysis, pentose phosphate pathway, TCA cycle, respiratory chain, redox state and energetic metabolism. Growth kinetic is defined as a function of the major precursors for the synthesis of cell building blocks. Michaelis-Menten type kinetic is used for metabolic intermediates as well as for regulatory functions from energy shuttles (ATP/ADP) and cofactors (NAD/H and NADP/H). Model structure and parameters were first calibrated using results from bioreactor cultures of CHO cells expressing recombinant t-PA. It is shown that the model can simulate experimental data for all available experimental data, such as extracellular glucose, glutamine, lactate and ammonium concentration time profiles, as well as cell energetic state. A sensitivity analysis allowed identifying the most sensitive parameters. The model was then shown to be readily adaptable for studying the effect of sodium butyrate on CHO cells metabolism, where it was applied to the cases with sodium butyrate addition either at mid-exponential growth phase (48 h) or at the early plateau phase (74 h). In both cases, a global optimization routine was used for the simultaneous estimation of the most sensitive parameters, while the insensitive parameters were considered as constants. Finally, confidence intervals for the estimated parameters were calculated. Results presented here further substantiate our previous findings that butyrate treatment at mid-exponential phase may cause a shift in cellular metabolism toward a sustained and increased efficiency of glucose utilization channeled through the TCA cycle.

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.

Computer-aided analysis of biochemical mechanisms that increase metabolite and proton stability in the heart during severe hypoxia and generate post-ischemic PCr overshoot

During severe hypoxia in the heart, impaired supply of ATP by oxidative phosphorylation could lead to a great drop in ATP turnover and heart work. Anaerobic glycolysis enables unchanged ATP turnover to be maintained, but leads to huge changes in metabolite (PCr, ATP, ADP, P (i)) concentrations and to cytosol acidification. A computer model of heart energetics developed previously is used to analyze semi-quantitatively the effect of different processes/mechanisms that can partly counteract these effects. Down-regulation of ATP usage compromises cardiac output, but reduces changes in cytosolic pH and metabolite concentrations. AMP decomposition delays cytosol acidification but reduces metabolite homeostasis (concentration stability). An increase in the parallel activation of oxidative phosphorylation (OXPHOS) (a hypothetical mechanism involving direct activation of all OXPHOS complexes by a cytosolic factor, postulated to take place also during work increase) reduces cytosol acidification and elevates metabolite homeostasis. All these mechanisms can generate the post-ischemic PCr overshoot.

Systems biology of the metabolic network regulated by the Akt pathway

Cancer has been proposed as an example of systems biology disease or network disease. Accordingly, tumor cells differ from their normal counterparts more in terms of intracellular network dynamics than single markers. Here we shall focus on a recently recognized hallmark of cancer, the deregulation of cellular energetics. The constitutive activation of the phosphatidylinositol 3-kinase (PI3K)/Akt pathway has been confirmed as an essential step toward cell transformation. We will consider how the effects of Akt activation are connected with cell metabolism; more precisely, we will review existing metabolic models and discuss the current knowledge available to construct a kinetic model of the most relevant metabolic processes regulated by the PI3K/Akt pathway. The model will enable a systems biology approach to predict the metabolic targets that may inhibit cell growth under hyper activation of Akt.

Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle

Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction-diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction-diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle.

Systems biology from micro-organisms to human metabolic diseases: the role of detailed kinetic models

Human metabolic diseases are typically network diseases. This holds not only for multifactorial diseases, such as metabolic syndrome or Type 2 diabetes, but even when a single gene defect is the primary cause, where the adaptive response of the entire network determines the severity of disease. The latter may differ between individuals carrying the same mutation. Understanding the adaptive responses of human metabolism naturally requires a systems biology approach. Modelling of metabolic pathways in micro-organisms and some mammalian tissues has yielded many insights, qualitative as well as quantitative, into their control and regulation. Yet, even for a well-known pathway such as glycolysis, precise predictions of metabolite dynamics from experimentally determined enzyme kinetics have been only moderately successful. In the present review, we compare kinetic models of glycolysis in three cell types (African trypanosomes, yeast and skeletal muscle), evaluate their predictive power and identify limitations in our understanding. Although each of these models has its own merits and shortcomings, they also share common features. For example, in each case independently measured enzyme kinetic parameters were used as input. Based on these 'lessons from glycolysis', we will discuss how to make best use of kinetic computer models to advance our understanding of human metabolic diseases.

Glycogenolysis in astrocytes supports blood-borne glucose channeling not glycogen-derived lactate shuttling to neurons: evidence from mathematical modeling

In this article, we examined theoretically the role of human cerebral glycogen in buffering the metabolic requirement of a 360-second brain stimulation, expanding our previous modeling study of neurometabolic coupling. We found that glycogen synthesis and degradation affects the relative amount of glucose taken up by neurons versus astrocytes. Under conditions of 175:115 mmol/L (∼1.5:1) neuronal versus astrocytic activation-induced Na(+) influx ratio, ∼12% of astrocytic glycogen is mobilized. This results in the rapid increase of intracellular glucose-6-phosphate level on stimulation and nearly 40% mean decrease of glucose flow through hexokinase (HK) in astrocytes via product inhibition. The suppression of astrocytic glucose phosphorylation, in turn, favors the channeling of glucose from interstitium to nearby activated neurons, without a critical effect on the concurrent intercellular lactate trafficking. Under conditions of increased neuronal versus astrocytic activation-induced Na(+) influx ratio to 190:65 mmol/L (∼3:1), glycogen is not significantly degraded and blood glucose is primarily taken up by neurons. These results support a role for astrocytic glycogen in preserving extracellular glucose for neuronal utilization, rather than providing lactate to neurons as is commonly accepted by the current 'thinking paradigm'. This might be critical in subcellular domains during functional conditions associated with fast energetic demands.

Streamlining the construction of large-scale dynamic models using generic kinetic equations

MOTIVATION

Studying biological systems, not just at an individual component level but at a system-wide level, gives us great potential to understand fundamental functions and essential biological properties. Despite considerable advances in the topological analysis of metabolic networks, inadequate knowledge of the enzyme kinetic rate laws and their associated parameter values still hampers large-scale kinetic modelling. Furthermore, the integration of gene expression and protein levels into kinetic models is not straightforward.

RESULTS

The focus of our research is on streamlining the construction of large-scale kinetic models. A novel software tool was developed, which enables the generation of generic rate equations for all reactions in a model. It encompasses an algorithm for estimating the concentration of proteins for a reaction to reach a particular steady state when kinetic parameters are unknown, and two robust methods for parameter estimation. It also allows for the seamless integration of gene expression or protein levels into a reaction and can generate equations for both transcription and translation. We applied this methodology to model the yeast glycolysis pathway; our results show that the behaviour of the system can be accurately described using generic kinetic equations.

AVAILABILITY AND IMPLEMENTATION

The software tool, together with its source code in Java, is available from our project web site at http://www.bioinf.manchester.ac.uk/schwartz/grape

CONTACT

jean-marc.schwartz@manchester.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Common phenotype of resting mouse extensor digitorum longus and soleus muscles: equal ATPase and glycolytic flux during transient anoxia

Rates of ATPase and glycolysis are several times faster in actively contracting mouse extensor digitorum longus muscle (EDL) than soleus (SOL), but we find these rates are not distinguishable at rest. We used a transient anoxic perturbation of steady state energy balance to decrease phosphocreatine (PCr) reversibly and to measure the rates of ATPase and of lactate production without muscle activation or contraction. The rate of glycolytic ATP synthesis is less than the ATPase rate, accounting for the continual PCr decrease during anoxia in both muscles. We fitted a mathematical model validated with properties of enzymes and solutes measured in vitro and appropriate for the transient perturbation of these muscles to experimental data to test whether the model accounts for the results. Simulations showed equal rates of ATPase and lactate production in both muscles. ATPase controls glycolytic flux by feedback from its products. Adenylate kinase function is critical because a rise in [AMP] is necessary to activate glycogen phosphorylase. ATPase is the primary source of H+ production. The sum of contributions of the 13 reactions of the glycogenolytic and glycolytic network to total proton load is negligible. The stoichiometry of lactate and H+ production is near unity. These results identify a default state of energy metabolism for resting muscle in which there is no difference in the metabolic phenotype of EDL and SOL. Therefore, additional control mechanisms, involving higher ATPase flux and [Ca2+], must exist to explain the well-known difference in glycolytic rates in fast-twitch and slow-twitch muscles in actively contracting muscle.

Cellular signaling identifiability analysis: a case study

Two primary purposes for mathematical modeling in cell biology are (1) simulation for making predictions of experimental outcomes and (2) parameter estimation for drawing inferences from experimental data about unobserved aspects of biological systems. While the former purpose has become common in the biological sciences, the latter is less common, particularly when studying cellular and subcellular phenomena such as signaling-the focus of the current study. Data are difficult to obtain at this level. Therefore, even models of only modest complexity can contain parameters for which the available data are insufficient for estimation. In the present study, we use a set of published cellular signaling models to address issues related to global parameter identifiability. That is, we address the following question: assuming known time courses for some model variables, which parameters is it theoretically impossible to estimate, even with continuous, noise-free data? Following an introduction to this problem and its relevance, we perform a full identifiability analysis on a set of cellular signaling models using DAISY (Differential Algebra for the Identifiability of SYstems). We use our analysis to bring to light important issues related to parameter identifiability in ordinary differential equation (ODE) models. We contend that this is, as of yet, an under-appreciated issue in biological modeling and, more particularly, cell biology.

Lactic acidosis in vivo: testing the link between lactate generation and H+ accumulation in ischemic mouse muscle

The link between lactate generation and cellular acidosis has been questioned based on the possibility of H+ generation, independent of lactate production during glycolysis under physiological conditions. Here we test whether glycolytic H+ generation matches lactate production over a physiological pH and lactate range using ischemia applied to the hindlimb of a mouse. We measured the H+ generation and ATP level in vivo using 31P-magnetic resonance spectroscopy and chemically determined intracellular lactate level in the hindlimb muscles. No significant change was found in ATP content by chemical analysis (P>0.1), in agreement with the stoichiometric decline in phosphocreatine (20.2+/-1.2 mM) vs. rise in Pi (18.7+/-2.0 mM), as measured by 31P-magnetic resonance spectroscopy. A substantial drop in pH from 7.0 to 6.7 and lactate accumulation to 25 mM were found during 25 min of ischemia. The rise in H+ generation closely agreed with the accumulation of lactate, as shown by a close correlation with a slope near identity (0.98; r2=0.86). This agreement between glycolytic H+ production and elevation of lactate is confirmed by an analysis of the underlying reactions involved in glycolysis in vivo and supports the concept of lactic acidosis under conditions that substantially elevate lactate and drop pH. However, this link is expected to fail with conditions that deplete phosphocreatine, leading to net ATP hydrolysis and nonglycolytic H+ generation. Thus both direct measurements and an analysis of the stoichiometry of glycolysis in vivo support lactate acidosis as a robust concept for physiological conditions of the muscle cell.

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.

Numerical analysis of ischemia- and compression-induced injury in tissue-engineered skeletal muscle constructs

Pressure-related deep tissue injury may develop in skeletal muscle tissue which is subjected to prolonged compression. For early detection, it is important to understand the underlying damage processes. Gawlitta et al. [Gawlitta, D., C. W. J. Oomens, D. L. Bader, F. P. T. Baaijens, and C. V. C. Bouten. Temporal differences in the influence of ischemic factors and deformation on the metabolism of engineered skeletal muscle. J. Appl. Physiol. 103(2):464–473, 2007b] subjected tissue-engineered muscle constructs to ischemia and deformation to study their effects on viability. Contrary to previous findings, no decrease in viability was found due to compression. However, the nature of their measurement method complicated interpretation of the results, particulary when deformation was involved. Changes in the constructs were assessed by measurements in the surrounding medium. The theoretical model developed in the present study describes metabolism, diffusion, and cell death in the experiments, and accounts for reduced diffusion due to compression. It was demonstrated that the lack of effect of compression on tissue viability, as measured in the experiments, could be explained by the compression-induced decrease in diffusivity. Compression did lead to considerable cell death but this could not be measured by Gawlitta et al. [Gawlitta, D., C. W. J. Oomens, D. L. Bader, F. P. T. Baaijens, and C. V. C. Bouten. Temporal differences in the influence of ischemic factors and deformation on the metabolism of engineered skeletal muscle. J. Appl. Physiol. 103(2):464–473, 2007b] because diffusion of the cell death marker to the medium was limited. This study shows that a proper description of transport processes is essential for a correct interpretation of experiments in which indirect measurement methods are used.

The control systems structures of energy metabolism

The biochemical regulation of energy metabolism (EM) allows cells to modulate their energetic output depending on available substrates and requirements. To this end, numerous biomolecular mechanisms exist that allow the sensing of the energetic state and corresponding adjustment of enzymatic reaction rates. This regulation is known to induce dynamic systems properties such as oscillations or perfect adaptation. Although the various mechanisms of energy regulation have been studied in detail from many angles at the experimental and theoretical levels, no framework is available for the systematic analysis of EM from a control systems perspective. In this study, we have used principles well known in control to clarify the basic system features that govern EM. The major result is a subdivision of the biomolecular mechanisms of energy regulation in terms of widely used engineering control mechanisms: proportional, integral, derivative control, and structures: feedback, cascade and feed-forward control. Evidence for each mechanism and structure is demonstrated and the implications for systems properties are shown through simulations. As the equivalence between biological systems and control components presented here is generic, it is also hypothesized that our work could eventually have an applicability that is much wider than the focus of the current study.

Silencing of glycolysis in muscle: experimental observation and numerical analysis

The longstanding problem of rapid inactivation of the glycolytic pathway in skeletal muscle after contraction was investigated using (31)P NMR spectroscopy and computational modelling. Accumulation of phosphorylated glycolytic intermediates (hexose monophosphates) during cyclic contraction and subsequent turnover during metabolic recovery was measured in vivo in human quadriceps muscle using dynamic (31)P NMR spectroscopy. The concentration of hexose monophosphates in muscle peaked 40 s into metabolic recovery from maximal contractile work at 6.9 +/- 1.3 mm (mean +/- s.d.; n = 8) and subsequently declined at a rate of 0.009 +/- 0.001 mm s(1). It was next tested whether the current knowledge of the kinetic controls in the glycolytic pathway in muscle integrated in the Lambeth and Kushmerick computational model of skeletal muscle glycolysis explained the experimental data. It was found that the model underestimated the magnitude of deactivation of the glycolytic pathway in resting muscle, resulting in depletion of glycolytic intermediates and substrate for oxidative ATP synthesis. Numerical analysis of the model identified phosphofructokinase and pyruvate kinase as the kinetic control sites involved in deactivation of the glycolytic pathway. Ancillary 100-fold inhibition of both phosphofructokinase and pyruvate kinase was found necessary to predict glycolytic intermediate and ADP concentrations correctly in resting human muscle. Incorporation of this information into the model resulted in highly improved agreement between predicted and measured in vivo dynamics of hexose monophosphates in muscle following contraction. We concluded that silencing of the glycolytic pathway in muscle following contraction is most likely to be mediated by phosphofructokinase and pyruvate kinase inactivation on a time scale of seconds and minutes, respectively, and is necessary to prevent depletion of vital cellular substrates.

Mitochondria in cardiomyocyte Ca2+ signaling

Ca(2+) signaling is of vital importance to cardiac cell function and plays an important role in heart failure. It is based on sarcolemmal, sarcoplasmic reticulum and mitochondrial Ca(2+) cycling. While the first two are well characterized, the latter remains unclear, controversial and technically challenging. In mammalian cardiac myocytes, Ca(2+) influx through L-type calcium channels in the sarcolemmal membrane triggers Ca(2+) release from the nearby junctional sarcoplasmic reticulum to produce Ca(2+) sparks. When this triggering is synchronized by the cardiac action potential, a global [Ca(2+)](i) transient arises from coordinated Ca(2+) release events. The ends of intermyofibrillar mitochondria are located within 20 nm of the junctional sarcoplasmic reticulum and thereby experience a high local [Ca(2+)] during the Ca(2+) release process. Both local and global Ca(2+) signals may thus influence calcium signaling in mitochondria and, reciprocally, mitochondria may contribute to the local control of calcium signaling. In addition to the intermyofibrillar mitochondria, morphologically distinct mitochondria are also located in the perinuclear and subsarcolemmal regions of the cardiomyocyte and thus experience a different local [Ca(2+)]. Here we review the literature in regard to several issues of broad interest: (1) the ultrastructural basis for mitochondrion - sarcoplasmic reticulum cross-signaling; (2) mechanisms of sarcoplasmic reticulum signaling; (3) mitochondrial calcium signaling; and (4) the possible interplay of calcium signaling between the sarcoplasmic reticulum and adjacent mitochondria. Finally, this review discusses experimental findings and mathematical models of cardiac calcium signaling between the sarcoplasmic reticulum and mitochondria, identifies weaknesses in these models, and suggests strategies and approaches for future investigations.

Towards the engineering of in vitro systems

Synthetic biology aims at rationally implementing biological systems from scratch. Given the complexity of living systems and our current lack of understanding of many aspects of living cells, this is a major undertaking. The design of in vitro systems can be considerably easier, because they can consist of fewer constituents, are quasi time invariant, their parameter space can be better accessed and they can be much more easily perturbed and then analysed chemically and mathematically. However, even for simplified in vitro systems, following a comprehensively rational design procedure is still difficult. When looking at a comparatively simple system, such as a medium-sized enzymatic reaction network as it is represented by glycolysis, major issues such as a lack of comprehensive enzyme kinetics and of suitable knowledge on crucial design parameters remain. Nevertheless, in vitro systems are very suitable to overcome these obstacles and therefore well placed to act as a stepping stone to engineering living systems.

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.