Control theory of metabolic channelling

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control.This chapter develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy form the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives methods functionally to diagnose the extent to which channelling and metabolite sequestration occur.     

Control, regulation and thermodynamics of free-energy transduction

The quantitative formalism called Metabolic Control Theory makes it possible to be precise in discussions of metabolic control. To illustrate this, I will mention 2 experimental systems where free energy is converted from one form to another, i.e., bacteriorhodopsin liposomes and mitochondrial oxidative phosphorylation. More specifically I shall discuss how the distribution of the control of fluxes, concentrations and potentials, among the various enzymes (catalysts) in these systems has been measured and how this distribution can be understood in terms of the enzyme properties. From the outset, Metabolic Control Theory was valid for branched metabolic pathways with non-linear kinetics. Yet, it seemed to be limited to metabolic pathways without enzyme-enzyme interactions and to steady states. It is now clear that these limitations were apparent only and recent extensions to Metabolic Control Theory deal explicitly with enzyme-enzyme interaction and with transient-time analysis. Other limitations are inherent. For instance, Metabolic Control Theory pays for its clarity and exactness by being limited to small modulations. Mosaic Non Equilibrium Thermodynamics and Biochemical System Analysis are formalisms that deal with larger changes, at the cost of accuracy and exactness.     

Metabolic control over the oxygen consumption flux in intact skeletal muscle: in silico studies

It has been postulated previously that a direct activation of all oxidative phosphorylation complexes in parallel with the activation of ATP usage and substrate dehydrogenation (the so-called each-step activation) is the main mechanism responsible for adjusting the rate of ATP production by mitochondria to the current energy demand during rest-to-work transition in intact skeletal muscle in vivo. The present in silico study, using a computer model of oxidative phosphorylation developed previously, analyzes the impact of the each-step-activation mechanism on the distribution of control (defined within Metabolic Control Analysis) over the oxygen consumption flux among the components of the bioenergetic system in intact oxidative skeletal muscle at different energy demands. It is demonstrated that in the absence of each-step activation, the oxidative phosphorylation complexes take over from ATP usage most of the control over the respiration rate and oxidative ATP production at higher (but still physiological) energy demands. This leads to a saturation of oxidative phosphorylation, impossibility of a further acceleration of oxidative ATP synthesis, and dramatic drop in the phosphorylation potential. On the other hand, the each-step-activation mechanism allows maintenance of a high degree of the control exerted by ATP usage over the ATP turnover and oxygen consumption flux even at high energy demands and thus enables a potentially very large increase in ATP turnover. It is also shown that low oxygen concentration shifts the metabolic control from ATP usage to cytochrome oxidase and thus limits the oxidative ATP production. respiration rate; parallel activation; oxidative phosphorylation; metabolic control analysis; flux control coefficient; muscle contraction     

Control and Regulation of Mitochondrial Energetics in an Integrated Model of Cardiomyocyte Function

Understanding the regulation and control of complex networks of reactions requires analytical tools that take into account the interactions between individual network components controlling global network function. Here, we apply a generalized matrix method of control analysis to calculate flux and concentration control coefficients, as well as response coefficients, in an integrated model of excitation-contraction (EC) coupling and mitochondrial energetics (ECME model) in the cardiac ventricular myocyte. Control and regulation of oxygen consumption (V_O2) was first assessed in a mitochondrion model, and then in the integrated cardiac myocyte model under resting and working conditions. The results demonstrate that in the ECME model, control of respiration is distributed among cytoplasmic ATPases and mitochondrial processes. The magnitude of control by cytoplasmic ATPases increases under working conditions. The model prediction that the respiratory chain exerts strong positive control on V_O2 (control coefficient 0.89) was corroborated experimentally in cardiac trabeculae utilizing the inhibitor titration method. In the model, mitochondrial respiration displayed the highest response coefficients with respect to the concentration of cytoplasmic ATP. This was due to the high elasticity of ANT flux toward ATP in the cytoplasm. The analysis reveals the complex interdependence of sarcolemmal, cytoplasmic, and mitochondrial processes that contribute to the control of energy supply and demand in the heart. Moreover, by visualizing the structure of control of the metabolic network of the myocyte, we provide support for the emerging concept of control by diffuse loops, in which action on the network (e.g., by a pharmacological agent) may bring about changes in processes without obvious direct mechanistic links between them.     

Regulation and control of compartmentalized glycolysis in bloodstream formTrypanosoma brucei

Unlike other eukaryotic cells, trypanosomes possess a compartmentalized glycolytic pathway. The conversion of glucose into 3-phosphoglycerate takes place in specialized peroxisomes, called glycosomes. Further conversion of this intermediate into pyruvate occurs in the cytosol. Due to this compartmentation, many regulatory mechanisms operating in other cell types cannot work in trypanosomes. This is reflected by the insensitivity of the glycosomal enzymes to compounds that act as activity regulators in other cell types. Several speculations have been raised about the function of compartmentation of glycolysis in trypanosomes. We calculate that even in a noncompartmentalized trypanosome the flux through glycolysis should not be limited by diffusion. Therefore, the sequestration of glycolytic enzymes in an organelle may not serve to overcome a diffusion limitation. We also search the available data for a possible relation between compartmentation and the distribution of control of the glycolytic flux among the glycolytic enzymes. Under physiological conditions, the rate of glycolytic ATP production in the bloodstream form of the parasite is possibly controlled by the oxygen tension, but not by the glucose concentration. Within the framework of Metabolic Control Analysis, we discuss evidence that glucose transport, although it does not qualify as the sole rate-limiting step, does have a high flux control coefficient. This, however, does not distinguish trypanosomes from other eukaryotic cell types without glycosomes.     

Histidine and histamine metabolism in rat enterocytes

We have shown that the Metabolic Control Analysis (MCA) can explain the threshold effect observed in the expression of mitochondrial diseases [8]. As a matter of fact, the effect of a specific inhibitor on the flux of O2 consumption mimics a defect in a step of oxidative phosphorylation. The observed threshold is correlated to the value of the control coefficient of the inhibited step.For this reason, we have studied the repartition of the control coefficients of different steps in oxidative phosphorylation on various tissues (liver, kidney, brain, skeletal muscle and heart). We discuss the results in terms of metabolic control theory and provide a possible explanation for the heterogeneous phenotype of those pathologies. We present the double threshold hypothesis of both a threshold in the energy demand of a tissue and in the energy supply by oxidative phosphorylation. (Mol Cell Biochem 174: 143–148, 1997)     

31P-NMR observation of free ADP during fatiguing, repetitive contractions of murine skeletal muscle lacking AK1

Metabolic control within skeletal muscle is designed to limit ADP accumulation even during conditions where ATP demand is out of balance with ATP synthesis. This is accomplished by the reactions of adenylate kinase (AK; ADP+ADP AMP+ATP) and AMP deaminase (AMP+H₂O NH₃+IMP), which limit ADP accumulation under these conditions. The purpose of this study was to determine whether AK deficiency (AK^–/–) would result in sufficient ADP accumulation to be visible using ³¹P-NMRS during the high energy demands of frequent in situ tetanic contractions. To do this we examined the high-energy phosphates of the gastrocnemius muscle in the knockout mouse with AK1^–/– and wild-type (WT) control muscle over the course of 64 rapid (2/s) isometric tetanic contractions. Near-complete depletion of phosphocreatine was apparent after 16 contractions in both groups. By 40 contractions, ADP was clearly visible in AK1^–/– muscle. This transient concentration of the NMR visible free ADP was estimated to be 1.7 mM, and represents the first time free ADP has been directly measured in contracting skeletal muscle. Such an increase in free ADP is severalfold greater than previously thought to occur. This large accumulation of free ADP also represents a significant reduction in energy available from ATP, and has implications on cellular processes that depend on a high yield of energy from ATP such as calcium sequestration. Remarkably, the AK1^–/– and WT muscles exhibited similar fatigue profiles. Our findings suggest that skeletal muscle is surprisingly tolerant to a large increase in ADP and by extension, a decline in energy from ATP. muscle energetics; muscle relaxation; magnetic resonance spectroscopy     

Acute and chronic effects of bupivacaine on muscle energetics during contraction in vivo: a modular metabolic control analysis

Bupivacaine is a widely used anaesthetic injected locally in clinical practice for short-term neurotransmission blockade. However, persistent side effects on mitochondrial integrity have been demonstrated in muscle parts surrounding the injection site. We use the precise language of metabolic control analysis in the present study to describe in vivo consequences of bupivacaine injection on muscle energetics during contraction. We define a model system of muscle energy metabolism in rats with a sciatic nerve catheter that consists of two modules of reactions, ATP/PCr (phosphocreatine) supply and ATP/PCr demand, linked by the common intermediate PCr detected in vivo by (31)P-MRS (magnetic resonance spectroscopy). Measured system variables were [PCr] (intermediate) and contraction (flux). We first applied regulation analysis to quantify acute effects of bupivacaine. After bupivacaine injection, contraction decreased by 15.7% and, concomitantly, [PCr] increased by 11.2%. The regulation analysis quantified that demand was in fact directly inhibited by bupivacaine (-21.3%), causing an increase in PCr. This increase in PCr indirectly reduced mitochondrial activity (-22.4%). Globally, the decrease in contractions was almost fully explained by inhibition of demand (-17.0%) without significant effect through energy supply. Finally we applied elasticity analysis to quantify chronic effects of bupivacaine iterative injections. The absence of a difference in elasticities obtained in treated rats when compared with healthy control rats clearly shows the absence of dysfunction in energetic control of muscle contraction energetics. The present study constitutes the first and direct evidence that bupivacaine myotoxicity is compromised by other factors during contraction in vivo, and illustrates the interest of modular approaches to appreciate simple rules governing bioenergetic systems when affected by drugs.     

Metabolic control analysis of integrated energy metabolism in permeabilized cardiomyocytes - experimental study

The main focus of this research was to apply Metabolic Control Analysis to quantitative investigation of the regulation of respiration by components of the Mitochondrial Interactosome (MI, a supercomplex consisting of ATP Synthasome, mitochondrial creatine kinase (MtCK), voltage dependent anion channel (VDAC), and tubulin) in permeabilized cardiomyocytes. Flux control coefficients (FCC) were measured using two protocols: 1) with direct ADP activation, and 2) with MtCK activation by creatine (Cr) in the presence of ATP and pyruvate kinase-phosphoenolpyruvate system. The results show that the metabolic control is much stronger in the latter case: the sum of the measured FCC is 2.7 versus 0.74 (ADP activation). This is consistent with previous data showing recycling of ADP and ATP inside the MI due to the functional coupling between MtCK and ANT and limited permeability of VDAC for these compounds, PCr being the major energy carrier between the mitochondria and ATPases. In physiological conditions, when the MI is activated, the key sites of regulation of respiration in mitochondria are MtCK (FCC = 0.93), adenine nucleotide translocase ANT (FCC = 0.95) and CoQ cytochrome c oxidoreductase (FCC = 0.4). These results show clearly that under the physiological conditions the energy transfer from mitochondria to the cytoplasm is regulated by the MI supercomplex and is very sensitive to metabolic signals.     

Lack of dystrophin is associated with altered integration of the mitochondria and ATPases in slow-twitch muscle cells of MDX mice

The potential role of dystrophin-mediated control of systems integrating mitochondria with ATPases was assessed in muscle cells. Mitochondrial distribution and function in skinned cardiac and skeletal muscle fibers from dystrophin-deficient (MDX) and wild-type mice were compared. Laser confocal microscopy revealed disorganized mitochondrial arrays in m. gastrocnemius in MDX mice, whereas the other muscles appeared normal in this group. Irrespective of muscle type, the absence of dystrophin had no effect on the maximal capacity of oxidative phosphorylation, nor on coupling between oxidation and phosphorylation. However, in the myocardium and m. soleus, the coupling of mitochondrial creatine kinase to adenine nucleotide translocase was attenuated as evidenced by the decreased effect of creatine on the Km for ADP in the reactions of oxidative phosphorylation. In m. soleus, a low Km for ADP compared to the wild-type counterpart was found, which implies increased permeability for that nucleotide across the mitochondrial outer membrane. In normal cardiac fibers 35% of the ADP flux generated by ATPases was not accessible to the external pyruvate kinase-phosphoenolpyruvate system, which suggests the compartmentalized (direct) channeling of that fraction of ADP to mitochondria. Compared to control, the direct ADP transfer was increased in MDX ventricles. In conclusion, our data indicate that in slow-twitch muscle cells, the absence of dystrophin is associated with the rearrangement of the intracellular energy and feedback signal transfer systems between mitochondria and ATPases. As the mechanisms mediated by creatine kinases become ineffective, the role of diffusion of adenine nucleotides increases due to the higher permeability of the mitochondrial outer membrane for ADP and enhanced compartmentalization of ADP flux.     

Mitochondrial function in vivo: spectroscopy provides window on cellular energetics

Mitochondria integrate the key metabolic fluxes in the cell. This role places this organelle at the center of cellular energetics and, hence, mitochondrial dysfunction underlies a growing number of human disorders and age-related degenerative diseases. Here we present novel analytical and technical methods for evaluating mitochondrial metabolism and (dys)function in human muscle in vivo. Three innovations involving advances in optical spectroscopy (OS) and magnetic resonance spectroscopy (MRS) permit quantifying key compounds in energy metabolism to yield mitochondrial oxidation and phosphorylation fluxes. The first of these uses analytical methods applied to optical spectra to measure hemoglobin (Hb) and myoglobin (Mb) oxygenation states and relative contents ([Hb]/[Mb]) to determine mitochondrial respiration (O₂ uptake) in vivo. The second uses MRS methods to quantify key high-energy compounds (creatine phosphate, PCr, and adenosine triphosphate, ATP) to determine mitochondrial phosphorylation (ATP flux) in vivo. The third involves a functional test that combines these spectroscopic approaches to determine mitochondrial energy coupling (ATP/O₂), phosphorylation capacity (ATP_max) and oxidative capacity (O_2max) of muscle. These new developments in optical and MR tools allow us to determine the function and capacity of mitochondria noninvasively in order to identify specific defects in vivo that are associated with disease in human and animal muscle. The clinical implication of this unique diagnostic probe is the insight into the nature and extent of dysfunction in metabolic and degenerative disorders, as well as the ability to follow the impact of interventions designed to reverse these disorders.     

Distribution of the flux control in convergent metabolic pathways: theory and application to experimental and simulated systems

1. Metabolic systems involving branched convergent pathways are analyzed under Flux Control Theory, obtaining a relationship between the contribution of every convergent pathway to the total flux and its Flux Control Coefficient. 2. An experimental model system is carried out to demonstrate the physical application of some conclusions of theoretical treatment. 3. Two different types of branched pathways are simulated by computer. 4. In both cases results are in agreement with the theoretical conclusions, showing in addition some new aspects on metabolic control.     

Structural organization of the mitochondrial respiratory chain

Two models exist of the mitochondrial respiratory chain: the model of a random organization of the individual respiratory enzyme complexes and that of a super-complex assembly formed by stable association between the individual complexes. Recently Sch?gger, using digitonin solubilization and Blue Native PAGE produced new evidence of preferential associations, in particular a Complex I monomer with a Complex III dimer, and suggested a model of the respiratory chain (the respirasome) based on direct electron channelling between complexes. Discrimination between the two models is amenable to kinetic testing using flux control analysis. Experimental evidence obtained in beef heart SMP, according to the extension of the Metabolic Control Theory for pathways with metabolic channelling, showed that enzyme associations involving Complex I and Complex III take place in the respiratory chain while Complex IV seems to be randomly distributed, with cytochrome c behaving as a mobile component. Flux control analysis at anyone of the respiratory complexes involved in aerobic succinate oxidation indicated that Complex II and III are not functionally associated in a stable supercomplex. A critical appraisal of the solid-state model of the mitochondrial respiratory chain requires its reconciliation with previous biophysical and kinetic evidence that CoQ behaves as a homogeneous diffusible pool between all reducing enzyme and all oxidizing enzymes: the hypothesis can be advanced that both models (CoQ pool and supercomplexes) are true, by postulating that supercomplexes physiologically exist in equilibrium with isolated complexes depending on metabolic conditions of the cell.     

MITOCHONDRIA: Investigation of in vivo muscle mitochondrial function by 31P magnetic resonance spectroscopy

The most important function of mitochondria is the production of energy in the form of ATP. The socio-economic impact of human diseases that affect skeletal muscle mitochondrial function is growing, and improving their clinical management critically depends on the development of non-invasive assays to assess mitochondrial function and monitor the effects of interventions. ³¹P magnetic resonance spectroscopy provides two approaches that have been used to assess in vivo ATP synthesis in skeletal muscle: measuring P_i ⟶ ATP exchange flux using saturation transfer in resting muscle, and measuring phosphocreatine recovery kinetics after exercise. However, P_i ⟶ ATP exchange does not represent net mitochondrial ATP synthesis flux and has no simple relationship with mitochondrial function. Post-exercise phosphocreatine recovery kinetics, on the other hand, yield reliable measures of muscle mitochondrial capacity in vivo, whose ability to define the site of functional defects is enhanced by combination with other non-invasive techniques.     

Control of mitochondrial beta-oxidation flux

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

Cold exposure differently influences mitochondrial energy efficiency in rat liver and skeletal muscle

This study deals with mitochondrial energy efficiency in liver and skeletal muscle mitochondria in 15 days cold exposed rats. Cold exposure strongly increases the sensitivity to uncoupling by added palmitate of skeletal muscle but not liver mitochondria, while mitochondrial energy coupling in the absence of fatty acids is only slightly affected by cold in liver and skeletal muscle. In addition, uncoupling protein 3 content does not follow changes in skeletal muscle mitochondrial coupling. It is therefore concluded that skeletal muscle could play a direct thermogenic role based on fatty acid-induced mild uncoupling of mitochondrial oxidative phosphorylation.     

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.     

On the regulation of cellular energetics in health and disease

Very recent experimental data, obtained by using the permeabilized cell technique or tissue homogenates for investigation of the mechanisms of regulation of respiration in the cells in vivo, are shortly summarized. In these studies, surprisingly high values of apparent Km for ADP, exceeding that for isolated mitochondria in vitro by more than order of magnitude, were recorded for heart, slow twitch skeletal muscle, hepatocytes, brain tissue homogenates but not for fast twitch skeletal muscle. Mitochondrial swelling in the hypo-osmotic medium resulted in the sharp decrease of the value of Km for ADP in correlation with the degree of rupture of mitochondrial outer membrane, as determined by the cytochrome c test. Very similar effect was observed when trypsin was used for treatment of skinned fibers, permeabilized cells or homogenates. It is concluded that, in many but not all types of cells, the permeability of the mitochondrial outer membrane for ADP is controlled by some cytoplasmic protein factor(s). Since colchicine and taxol were not found to change high values of the apparent Km for ADP, the participation of microtubular system seems to be excluded in this kind of control of respiration but studies of the roles of other cytoskeletal structures seem to be of high interest.In acute ischemia we observed rapid increase of the permeability of the mitochondrial outer membrane for ADP due to mitochondrial swelling and concomitant loss of creatine control of respiration as a result of dissociation of creatine kinase from the inner mitochondrial membrane. The extent of these damages was decreased by use of proper procedures of myocardial protection showing that outer mitochondrial membrane permeability and creatine control of respiration are valuable indices of myocardial preservation. In contrast to acute ischemia, chronic hypoxia seems to improve the cardiac cell energetics as seen from better postischemic recovery of phosphocreatine, and phosphocreatine overshoot after inotropic stimulation.In general, adaptational possibilities and pathophysiological changes in the mitochondrial outer membrane system point to the central role such a system may play in regulation of cellular energetics in vivo.