Transition time control analysis of a glycolytic system under different glucose concentrations. Control of transition time versus control of flux

Control and Response Coefficients of transition time have been determined in a rat liver glycolytic system under different glucose concentrations. Results have been compared with the Flux Control and Flux Response Coefficients measured in the same conditions, showing that transition time and flux are different responses of the system, subject to different regulation and control. Control Coefficients of flux and transition time show a very different profile in each condition of glucose concentration assayed. Ratio of Flux Control coefficients of glucokinase over phosphofructokinase at 5 and 20 mM glucose concentration changes from 3.2 to 0.5, while the same ratio in the case of Transition Time Control Coefficients moves from 0.6 to 0.93. Moreover, the absolute values of Transition Time Control Coefficients in glycolytic conditions are one order of magnitude bigger than in gluconeogenic conditions. Values of Response Coefficients also show that the transition time has a bigger sensitivity to changes in glucose concentration than the flux in all conditions assayed, but particularly in glycolytic ones.     

Study of the flux and transition time control coefficient profiles in a metabolic system in vitro and the effect of an external stimulator.

Control of flux and transition time was investigated with a reconstructed rabbit muscle glycolytic system in vitro as an experimental model. The results show agreement with the summation property for the Flux Control Coefficients [Kacser & Burns (1973) Symp. Soc. Exp. Biol. 27, 65-104; Heinrich & Rapoport (1974) Eur. J. Biochem. 42, 89-95]. Control of flux is almost exclusively located at the hexokinase- and phosphofructokinase-catalysed steps, whereas control of transition time is distributed more evenly between the enzymes of the system. The summation value of the Transition Time Control Coefficients is near to -1, suggesting the existence of another Summation Theorem besides that already stated for Flux Control Coefficients. Finally, we study the effect of an external stimulator of the system (fructose 2,6-bisphosphate) on the Control Coefficient profiles. The effect appears to be greater on the Transition Time Control Coefficient distribution than on the Flux Control Coefficients.     

Control of glycolysis in rat liver by glucokinase and phosphofructokinase: influence of glucose concentration

Summary Control of glucose metabolism in rat liver under different glucose concentrations was studied. Flux Control Coefficients of glucokinase, glucose 6-phosphate isomerase and phosphofructokinase were determined by the shortening and enzyme titration method. Results obtained show that glucose concentration in liver can play an important role in control of liver glycolysis by enhancing the Flux Control Coefficient of phosphofructokinase. Possible physiological significance of this fact is discussed.     

Kinetics of metabolic pathways. A system in vitro to study the control of flux.

A method for determining Control Coefficients is proposed for systems studied in vitro and applied to a model pathway. Rat liver extract, which converts glucose into glycerol 3-phosphate, was used with the addition to the incubation mixture of fructose-bisphosphate aldolase, triose-phosphate isomerase and glycerol-3-phosphate dehydrogenase as 'auxiliary' enzymes, which leaves all the control on the first three enzymes. The flux of the metabolic pathway was recorded by assaying NADH decay. Flux Control Coefficients (CJE) of hexokinase, glucose-6-phosphate isomerase and phosphofructokinase were calculated by titration of the system with increasing quantities of extraneous enzymes. It is shown that the summation property is fulfilled. The applicability of this procedure to study the control in any metabolic pathway is discussed. Possible relevance of the method to conditions in vivo and its limitations are considered.     

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.     

Application of electrical analogues for control analysis of simple metabolic pathways.

I have used electrical analogues for calculating the Flux Control Coefficients of metabolic pathways. An analogue circuit consists of resistances that are connected in series (or parallel) with a voltage (or current) source. In constructing the analogues, each of the enzymes in the pathway is associated with a resistance whose magnitude depends on the Elasticity Coefficients of the enzymes. These circuits can be designed in a heuristic fashion directly from the configuration of the pathway, without the necessity of writing down the governing equations with the use of Summation and Connectivity Theorems. The Flux Control Coefficients of the enzymes are represented by voltages across (or currents through) the resistances and are determined by an application of Ohm's Law. Results are given for (a) a simple linear pathway without feedback or feedforward regulation, and (b) a linear pathway with feedback inhibition. The analogue circuits are also convenient for assessing the relative importance of the various enzymes in flux control, and for simplifying the structure of a given pathway.     

Carbon-Flux Distribution within Streptomyces coelicolor Metabolism: A Comparison between the Actinorhodin-Producing Strain M145 and Its Non-Producing Derivative M1146

Metabolic Flux Analysis is now viewed as essential to elucidate the metabolic pattern of cells and to design appropriate genetic engineering strategies to improve strain performance and production processes. Here, we investigated carbon flux distribution in two Streptomyces coelicolor A3 (2) strains: the wild type M145 and its derivative mutant M1146, in which gene clusters encoding the four main antibiotic biosynthetic pathways were deleted. Metabolic Flux Analysis and ¹³C-labeling allowed us to reconstruct a flux map under steady-state conditions for both strains. The mutant strain M1146 showed a higher growth rate, a higher flux through the pentose phosphate pathway and a higher flux through the anaplerotic phosphoenolpyruvate carboxylase. In that strain, glucose uptake and the flux through the Krebs cycle were lower than in M145. The enhanced flux through the pentose phosphate pathway in M1146 is thought to generate NADPH enough to face higher needs for biomass biosynthesis and other processes. In both strains, the production of NADPH was higher than NADPH needs, suggesting a key role for nicotinamide nucleotide transhydrogenase for redox homeostasis. ATP production is also likely to exceed metabolic ATP needs, indicating that ATP consumption for maintenance is substantial.Our results further suggest a possible competition between actinorhodin and triacylglycerol biosynthetic pathways for their common precursor, acetyl-CoA. These findings may be instrumental in developing new strategies exploiting S. coelicolor as a platform for the production of bio-based products of industrial interest.     

Control analysis of transition times in metabolic systems.

The transition time, tau, of a metabolic system is defined as the ratio of the metabolite concentrations in the system, sigma, to the steady-state flux, J. Its value reflects a temporal characteristic of the system as it relaxes towards the steady state. Like other systemic properties, the value of tau will be a function of the enzyme activities in the system. The influence of a particular enzyme activity on tau can be quantified by a Control Coefficient, C tau ei. We show that it is possible to derive a Summation Theorem sigma ni = 1 C tau ei = -1 and a Connectivity Theorem sigma ni = 1 C tau ei.epsilon viSk = -Sk/sigma. We establish a 'sign rule' that predicts the order of positive and negative Control Coefficients in a sequence.     

Antagonistic regulation of the glucose/glucose 6-phosphate cycle by insulin and glucagon in cultured hepatocytes.

Flux through the glucose/glucose 6-phosphate cycle in cultured hepatocytes was measured with radiochemical techniques. Utilization of [2-3H]glucose was taken as a measure of glucokinase flux. Liberation of [14C]glucose from [U-14C]glycogen and from [U-14C]lactate, as well as the difference between the utilization of [2-3H]glucose and of [U-14C]glucose, were taken as measures of glucose-6-phosphatase flux. At constant 5 mM-glucose and 2 mM-lactate concentrations insulin increased glucokinase flux by 35%; it decreased glucose-6-phosphatase flux from glycogen by 50%, from lactate by 15% and reverse flux from external glucose by 65%, i.e. overall by 40%. Glucagon had essentially no effect on glucokinase flux; it enhanced glucose-6-phosphatase flux from glycogen by 700%, from lactate by 45% and reverse flux from external glucose by 20%, i.e. overall by 110%. At constant glucose concentrations cellular glucose 6-phosphate concentrations were essentially not altered by insulin, but were increased by glucagon by 230%. In conclusion, under basic conditions without added hormones the glucose/glucose 6-phosphate cycle showed only a minor net glucose uptake, of 0.03 mumol/min per g of hepatocytes; this flux was increased by insulin to a net glucose uptake of 0.21 mumol/min per g and reversed by glucagon to a net glucose release of 0.22 mumol/min per g. Since the glucose 6-phosphate concentrations after hormone treatment did not correlate with the glucose-6-phosphatase flux, it is suggested that the hormones influenced the enzyme activity directly.     

Quantification of the importance of individual steps in the control of aromatic amino acid metabolism.

The quantitative importance of the individual steps of aromatic amino acid metabolism in rat liver was determined by calculation of the respective Control Coefficients (Strengths). The Control Coefficient of tryptophan 2,3-dioxygenase for tryptophan degradation was determined in a variety of physiological conditions and with a range of activities of tryptophan 2,3-dioxygenase. The Control Coefficient varied from 0.75 with basal enzyme activity to 0.25 after maximal induction of the enzyme by dexamethasone. The remainder of the control for tryptophan degradation was associated with the transport of the amino acid across the plasma membrane, with only very small contributions from kynureninase and kynurenine hydroxylase. The Control Coefficients of tyrosine aminotransferase for tyrosine degradation were approx. 0.70 and 0.20 with basal and dexamethasone-induced tyrosine aminotransferase activities respectively; the Control Coefficients of the transport of the amino acid into the cell were 0.22 and 0.58 respectively. Phenylalanine hydroxylase was found to have a Control Coefficient for the degradation of phenylalanine of approx. 0.50 under conditions of basal enzyme activity; after maximal activation by glucagon, the Control Coefficient decreased to 0.12. The transport of phenylalanine was responsible for the remaining control in the pathway. These results have important implications, directly for the regulation of aromatic amino acid metabolism in the liver, and indirectly for the regulation of neuroamine synthesis in the brain.     

The role of the regulatory protein of glucokinase in the glucose sensory mechanism of the hepatocyte

Glucokinase has a very high flux control coefficient (greater than unity) on glycogen synthesis from glucose in hepatocytes (Agius et al., J. Biol. Chem. 271, 30479-30486, 1996). Hepatic glucokinase is inhibited by a 68-kDa glucokinase regulatory protein (GKRP) that is expressed in molar excess. To establish the relative control exerted by glucokinase and GKRP, we applied metabolic control analysis to determine the flux control coefficient of GKRP on glucose metabolism in hepatocytes. Adenovirus-mediated overexpression of GKRP (by up to 2-fold above endogenous levels) increased glucokinase binding and inhibited glucose phosphorylation, glycolysis, and glycogen synthesis over a wide range of concentrations of glucose and sorbitol. It decreased the affinity of glucokinase translocation for glucose and increased the control coefficient of glucokinase on glycogen synthesis. GKRP had a negative control coefficient of glycogen synthesis that is slightly greater than unity (-1.2) and a control coefficient on glycolysis of -0.5. The control coefficient of GKRP on glycogen synthesis decreased with increasing glucokinase overexpression (4-fold) at elevated glucose concentration (35 mM), which favors dissociation of glucokinase from GKRP, but not at 7.5 mM glucose. Under the latter conditions, glucokinase and GKRP have large and inverse control coefficients on glycogen synthesis, suggesting that a large component of the positive control coefficient of glucokinase is counterbalanced by the negative coefficient of GKRP. It is concluded that glucokinase and GKRP exert reciprocal control; therefore, mutations in GKRP affecting the expression or function of the protein may impact the phenotype even in the heterozygote state, similar to glucokinase mutations in maturity onset diabetes of the young type 2. Our results show that the mechanism comprising glucokinase and GKRP confers a markedly extended responsiveness and sensitivity to changes in glucose concentration on the hepatocyte.     

Integration of temporal analysis and control analysis of metabolic systems.

A theory is developed that integrates approaches to the analysis of pathway transient response and metabolic control analysis. A Temporal Control Coefficient is defined that is a measure of the system's transient response to modulation of enzyme activity or concentration. The approach allows for the analysis of the establishment of a steady state from rest, of the system's 'agility' of response to minor perturbations of a pre-existing steady state and of the macroscopic transition between steady states. In the last-mentioned case it is shown that, like the transient time itself, the control of transient response retains the property of independence from the mechanism of the transition. In consequence, the Temporal Control Coefficient can be defined in terms of the control properties of the initial and final states alone without reference to the mechanism of transition. A summation property is shown to apply to the Temporal Control Coefficients in each case. Connectivity relationships between elasticities and Temporal Control Coefficients are also established.     

Systems biology towards life in silico: mathematics of the control of living cells

Systems Biology is the science that aims to understand how biological function absent from macromolecules in isolation, arises when they are components of their system. Dedicated to the memory of Reinhart Heinrich, this paper discusses the origin and evolution of the new part of systems biology that relates to metabolic and signal-transduction pathways and extends mathematical biology so as to address postgenomic experimental reality. Various approaches to modeling the dynamics generated by metabolic and signal-transduction pathways are compared. The silicon cell approach aims to describe the intracellular network of interest precisely, by numerically integrating the precise rate equations that characterize the ways macromolecules’ interact with each other. The non-equilibrium thermodynamic or ‘lin–log’ approach approximates the enzyme rate equations in terms of linear functions of the logarithms of the concentrations. Biochemical Systems Analysis approximates in terms of power laws. Importantly all these approaches link system behavior to molecular interaction properties. The latter two do this less precisely but enable analytical solutions. By limiting the questions asked, to optimal flux patterns, or to control of fluxes and concentrations around the (patho)physiological state, Flux Balance Analysis and Metabolic/Hierarchical Control Analysis again enable analytical solutions. Both the silicon cell approach and Metabolic/Hierarchical Control Analysis are able to highlight where and how system function derives from molecular interactions. The latter approach has also discovered a set of fundamental principles underlying the control of biological systems. The new law that relates concentration control to control by time is illustrated for an important signal transduction pathway, i.e. nuclear hormone receptor signaling such as relevant to bone formation. It is envisaged that there is much more Mathematical Biology to be discovered in the area between molecules and Life.     

Glucose-induced dissociation of glucokinase from its regulatory protein in the nucleus of hepatocytes prior to nuclear export

The glucose phosphorylating enzyme glucokinase regulates glucose metabolism in the liver. Glucokinase activity is modulated by a liver-specific competitive inhibitor, the glucokinase regulatory protein (GRP), which mediates sequestration of glucokinase to the nucleus at low glucose concentrations. However, the mechanism of glucokinase nuclear export is not fully understood. In this study we investigated the dynamics of glucose-dependent interaction and translocation of glucokinase and GRP in primary hepatocytes using fluorescence resonance energy transfer, selective photoconversion and fluorescence recovery after photobleaching. The formation of the glucokinase:GRP complex in the nucleus of primary hepatocytes at 5 mmol/l glucose was significantly reduced after a 2 h incubation at 20 mmol/l glucose. The GRP was predominantly localized in the nucleus, but a mobile fraction moved between the nucleus and the cytoplasm. The glucose concentration only marginally affected GRP shuttling. In contrast, the nuclear export rate of glucokinase was significantly higher at 20 than at 5 mmol/l glucose. Thus, glucose was proven to be the driving-force for nuclear export of glucokinase in hepatocytes. Using the FLII12Pglu-700μ-δ6 glucose nanosensor it could be shown that in hepatocytes the kinetics of nuclear glucose influx, metabolism or efflux were significantly faster compared to insulin-secreting cells. The rapid equilibration kinetics of glucose flux into the nucleus facilitates dissociation of the glucokinase:GRP complex and also nuclear glucose metabolism by free glucokinase enzyme. In conclusion, we could show that a rise of glucose in the nucleus of hepatocytes releases active glucokinase from the glucokinase:GRP complex and promotes the subsequent nuclear export of glucokinase.     

Decreased-activity mutants of phosphoglucose isomerase in the cytosol and chloroplast of Clarkia xantiana. Impact on mass-action ratios and fluxes to sucrose and starch, and estimation of Flux Control Coefficients and Elasticity Coefficients.

1. Subcellular-compartment-specific decreased-activity mutants of phosphoglucose isomerase in Clarkia xantiana were used to analyse the control of sucrose and starch synthesis during photosynthesis. Mutants were available in which the plastid phosphoglucose isomerase complement is decreased to 75% or 50% of the wild-type level, and the cytosol complement to 64%, 36% or 18% of the wild-type level. 2. The effects on the [product]/[substrate] ratio and on fluxes to sucrose or starch and the rate of photosynthesis were studied with the use of saturating or limiting light intensity to impose a high or low flux through these pathways. 3. Removal of a small fraction of either phosphoglucose isomerase leads to a significant shift of the [product]/[substrate] ratio away, from equilibrium. We conclude that there is no 'excess' of enzyme over that needed to maintain its reactants reasonably close to equilibrium. 4. Decreased phosphoglucose isomerase activity can also alter the fluxes to starch or sucrose. However, the effect on flux does not correlate with the extent of disequilibrium, and also varies depending on the subcellular compartment and on the conditions. 5. The results were used to estimate Flux Control Coefficients for the chloroplast and cytosolic phosphoglucose isomerases. The chloroplast isoenzyme exerts control on the rate of starch synthesis and on photosynthesis in saturating light intensity and CO2, but not at low light intensity. The cytosolic enzyme only exerts significant control when its complement is decreased 3-5-fold, and differs from the plastid isoenzyme in exerting more control in low light intensity. It has a positive Control Coefficient for sucrose synthesis, and a negative Control Coefficient for starch synthesis. 6. The Elasticity Coefficients in vivo of the cytosolic phosphoglucose isomerase were estimated to lie between 5 and 8 in the wild-type. They decrease in mutants with a lowered complement of cytosolic phosphoglucose isomerase. 7. The implications of these results for regulation and for evolution are discussed.     

Role of hexokinase in controlling the glucose metabolism flux: a study of its flux control coefficient in different tissues

Flux control coefficients of hexokinase for glucose metabolism in different rat tissues have been determined, showing that the hepatocyte cytosolic hexokinase is the only one which plays an important role in the control of the glucose-input flux studied among the different tissues. Explanation of these results are given in terms of the kinetics features of hexokinase and the metabolic role of glucose in these tissues.     

Constraint-based metabolic control analysis for rational strain engineering

The advancements in genome editing techniques over the past years have rekindled interest in rational metabolic engineering strategies. While Metabolic Control Analysis (MCA) is a well-established method for quantifying the effects of metabolic engineering interventions on flows in metabolic networks and metabolite concentrations, it does not consider the physiological limitations of the cellular environment and metabolic engineering design constraints. We report here a constraint-based framework, Network Response Analysis (NRA), for rational genetic strain design. NRA is cast as a Mixed-Integer Linear Programming problem that integrates MCA, Thermodynamically-based Flux Analysis (TFA), biologically relevant constraints, as well as genome editing restrictions into a comprehensive platform for identifying metabolic engineering targets. We show that the NRA formulation and its core constraints are equivalent to the ones of Flux Balance Analysis (FBA) and TFA, which allows it to be used for a wide range of optimization criteria and with various physiological constraints. We also show how the parametrization and introduction of biological constraints enhance the NRA formulation compared to the classical MCA approach, and we demonstrate its features and its ability to generate multiple alternative optimal strategies given several user-defined boundaries and objectives. In summary, NRA is a sophisticated alternative to classical MCA for rational metabolic engineering that accommodates the incorporation of physiological data at metabolic flux, metabolite concentration, and enzyme expression levels.     

应用最大熵原理通过酶控制通量预测突变体的通量分布

在代谢工程和系统生物学领域, 计算机模拟比以往更为有效的应用于生物过程的分析和优化。胞内代谢通量可以用代谢通量分析和基元模式分析来估算。由于测定数据的不足和误差, 以及基元途径的冗余, 经常很难得到准确的代谢通量分布数据。本研究提出一种基于最大熵原理的算法来计算基元模式系数。欠定和不确定条件下, 通过胞外代谢通量数据估算胞内代谢通量分布。为了检验算法的可行性, 对杂交瘤细胞、枯草芽孢杆菌和大肠杆菌的胞内代谢通量分布做了估算。本研究提出的基于最大熵原理的优化算法避免了对细胞状态的生理学假设。与其他目标函数相比, 可以更为可靠和可行的估算胞内代谢通量分布。     

Functional studies of yeast glucokinase.

Glucose phosphorylation capacity is known to be in excess of glucose flux in Saccharomyces cerevisiae wild type but not in a mutant strain lacking the two hexokinases but still having glucokinase. Nonetheless, we show here that in the latter strain, as in the wild type, the internal concentration of glucose is apparently low during growth on glucose and that additional glucokinase activity does not increase glucose flux. The glucokinase-dependent strain accumulates substantial amounts of glucose internally in batch culture after exhaustion of glucose, as well as from maltose. In both of these situations, low concentrations of radioactive glucose provided to the medium are used with incomplete, if any, mixing with the internal pool. Furthermore, in contrast to activity of hexokinase and other enzymes, little glucokinase activity is revealed by toluene treatment of cells. These results may point to a connection between glucose entry and its phosphorylation by glucokinase, but separate explanations for the various findings are also possible.