Genetic-algorithm selection of a regulatory structure that directs flux in a simple metabolic model.

A genetic algorithm (GA) is used to optimize parameters for allosteric regulation of enzymes in a model of a metabolic futile cycle, in which two metabolites are interconverted by a pair of irreversible enzymatic reactions. The cycle is regulated by end products of the surrounding pathway. The optimization criterion for the GA is the proper direction of chemical flux in the regulated cycle toward one or the other end product in response to a simple, time-dependent model of biochemical "need" based on externally imposed variation of the end product concentrations. An energetic cost, to be held to a minimum, is also imposed on the operation of the cycle. The best-performing individuals selected by the GA are found to switch rapidly the direction of net flux according to need. In different "environments" (specific time courses of end product concentrations), the GA produces better- or poorer-performing individuals. In some cases "generalists" and "specialists" are produced. The present approach provides, purely as a consequence of formally specifying the task of flux direction, the new result of numerical confirmation, in a simple model, of the intuition that negative feedback and reciprocal regulation are important for good flux direction in arbitrary environments, and gives rise to a diversity of structures, suggestive of the results of biological evolution.     

Metabolic futile cycles and their functions: a systems analysis of energy and control

It has long been hypothesised that futile cycles in cellular metabolism are involved in the regulation of biochemical pathways. Following the work of Newsholme and Crabtree, a quantitative theory was developed for this idea based on open-system thermodynamics and metabolic control analysis. It is shown that the stoichiometric sensitivity of an intermediary metabolite concentration with respect to changes in steady-state flux is governed by the effective equilibrium constant of the intermediate formation, and the equilibrium can be regulated by a futile cycle. The direction of the shift in the effective equilibrium constant depends on the direction of operation of the futile cycle. High stoichiometric sensitivity corresponds to ultrasensitivity of an intermediate concentration to net flow through a pathway; low stoichiometric sensitivity corresponds to super-robustness of concentration with respect to changes in flux. Both cases potentially play important roles in metabolic regulation. Futile cycles actively shift the effective equilibrium by expending energy; the magnitude of changes in effective equilibria and sensitivities is a function of the amount of energy used by a futile cycle. This proposed mechanism for control by futile cycles works remarkably similar to kinetic proofreading in biosynthesis. The sensitivity of the system is also intimately related to the rate of concentration fluctuations of intermediate metabolites. The possibility of different roles for the two major mechanisms within cellular biochemical regulation, namely reversible chemical modifications via futile cycles and shifting equilibrium by macromolecular binding, are discussed.     

Application of the metabolic control theory to the study of the dynamics of substrate cycles

Substrate cycles are ubiquitous structures of the cellular metabolism (e.g. Krebs cycle, fatty acids -oxydation cycles, etc... ). Moiety-conserved cycles (e.g. adenine nucleotides and NADH/NAD, etc...) are also important.The role played by such cycles in the metabolism and its regulation is not clearly understood so far. However, it was shown that these cycles can generate multistationarity (bistability), irreversible transitions, enhancement of sensitivity, temporal oscillations and chaotic motions (Hervagault & Canu, 1987; Hervagault & Cimino, 1989; Reich & Sel'kov, 1981; Ricard & Soulié, 1982). Fig. 1: Scheme of the open binary substrate cycle under study. The substrate S is converted into P with a net rate v₂. Substrate P is converted in turn into S with a net rate v₃. Step v₂ is inhibited by excess of the substrate, S. In addition, the cycle operates under open conditions, that is zero-order input of S at rates \ga₀(v₁) and first order outputs of S and P at rates \gaS and \gaP(v₄), respectively.The metabolic control theory (see also Fell, 1990), which shows how a metabolic network reacts to small perturbations in the vicinity of a steady state, and is formulated with the so-called control coefficients, was applied to such a cycle in order to get a better knowledge on the importance of each step at the regulatory point of view.The behaviour of a binary substrate cycle (fig. 1) in which one of the enzymes may be subjected to inhibition by excess of its substrate (v₂) was studied theoretically. The flux and concentration control coefficients were calculated for various steady states of the system. The evolution of the different control coefficients is compared to the evolution of the steady states. We mainly focused our study on situations for which the steady states are stable.     

Modulation of functional and optimal (Na+-K+)ATPase activity during the cell cycle of neuroblastoma cells

Functional and optimal activities of the (Na+-K+)ATPase, as determined by ouabain-sensitive K+ influx in intact cells and ATP hydrolysis in cell homogenates respectively, have been measured during the cell cycle of neuroblastoma (clone Neuro-2A) cells. The cells were synchronized by selective detachment of mitotic cells. The ouabain-sensitive K+ influx decreased more than fourfold from 1.62 +/- 0.11 nmoles/min/10(6) cells to 0.36 +/- 0.25 nmoles/min/10(6) cells on passing from mitosis to early G1 phase. On entry into S phase a transient sixfold increase to 2.07 +/- 0.30 nmoles/min/10(6) cells was observed, followed by a rapid decline, after which the active K+ influx rose again steadily from 1.03 +/- 0.25 nmoles/min/10(6) cells in early S phase to 2.10 +/- 0.92 nmoles/min/10(6) cells just prior to the next mitosis. The ouabain-insensitive component rose linearly through the cycle in the same manner as the protein content/cell. Combining total K+ influx values with efflux data obtained previously showed that net loss of K+ occurred with transition from mitosis to G1 phase while net accumulation occurred with entry into S. Throughout mid-S phase net K+ flux was virtually zero, but a large net influx occurred again just before the next mitosis. The (Na+-K+)ATPase activity measured in cell homogenates decreased rapidly from mitosis to G1 phase and increased steadily throughout S phase, but the transient activation on entry into S phase was not observed. Complete inhibition of the (Na+-K+)ATPase mediated K+ influx by ouabain (5 mM) prevents the cells from entering S phase, while partial inhibition by lower concentrations of ouabain (0.2 and 0.5 mM; km = 0.17 mM) causes partial blockage in G1 and, to a lesser extent, a reduced rate of progression through the rest of the cell cycle. We conclude that the transient increase in (Na+-K+)ATPase mediated K+ influx at the G1/S transition is a prerequisite for entry into S phase, while maintenance of adequate levels of K+ influx is necessary for normal rate of progression through the rest of the cell cycle.     

Anaerobic metabolism in aerobic mammalian cells: information from the ratio of calorimetric heat flux and respirometric oxygen flux

Calorimetric and respirometric studies of cultured cells show that both neoplastic and non-neoplastic cell types maintain an anaerobic contribution to their total heat flux. In many mammalian cells this can be explained quantitatively by lactate production observed under fully aerobic conditions. Uncoupling and enhanced futile substrate cycling increase the ratio of heat flux to oxygen flux, the calorimetric-respirometric (CR) ratio. The interpretation of calorimetric and respirometric measurements requires an energy balance approach in which experimentally measured CR ratios are compared with thermochemically derived oxycaloric equivalents. The oxycaloric equivalent is the enthalpy change per mole of oxygen consumed, and equals -470 kJ/mol O2 in the aerobic catabolism of glucose, assuming that catabolism is 100% dissipative (the net efficiency of metabolic heat transformation is zero). CR ratios more negative than -470 kJ/mol O2 have been reported in well-oxygenated cell cultures and are discussed in terms of integrated aerobic and anaerobic metabolism.     

The metabolic architecture of plant cells. Stability of central metabolism and flexibility of anabolic pathways during the growth cycle of tomato cells

The changes in the intermediary metabolism of plant cells were quantified according to growth conditions at three different stages of the growth cycle of tomato cell suspension. Eighteen fluxes of central metabolism were calculated from (13)C enrichments after near steady-state labeling by a metabolic model similar to that described in Dieuaide-Noubhani et al. (Dieuaide-Noubhani, M., Raffard, G., Canioni, P., Pradet, A., and Raymond, P. (1995) J. Biol. Chem. 270, 13147-13159), and 10 net fluxes were obtained directly from end-product accumulation rates. The absolute flux values of central metabolic pathways gradually slowed down with the decrease of glucose influx into the cells. However, the relative fluxes of glycolysis, the pentose-P pathway, and the tricarboxylic acid cycle remained unchanged during the culture cycle at 70, 28, and 40% of glucose influx, respectively, and the futile cycle of sucrose remained high at about 6-fold the glucose influx, independently from carbon nutritional conditions. This natural resistance to flux alterations is referred to as metabolic stability. The numerous anabolic pathways, including starch synthesis, hexose accumulation, biosynthesis of wall polysaccharides, and amino and organic acid biosynthesis were comparatively low and variable. The phosphoenolpyruvate carboxylase flux decreased 5-fold in absolute terms and 2-fold in relation to the glucose influx rate during the culture cycle. We conclude that anabolic fluxes constitute the flexible part of plant cell metabolism that can fluctuate in relation to cell demands for growth.     

On the analysis of futile cycles in metabolism

So-called futile cycles in cellular metabolism consist of paired opposing reactions that, if simultaneously operant, act only to degrade free energy of ATP to heat. Previous considerations of the behavior of such substrate cycles have indicated their possible usefulness in regulating flux along metabolic pathways, but such analyses have treated the cycles in isolation, i.e. without taking into account the effects of enzymatic inputs to and outputs from the cycle. We here develop models of three typical substrate cycles that include enzymatic inputs to and outputs from the cycle and allow the enzymes of the cycles per se to be subject to a variety of allosteric modulations. The non-linear equations which describe these models were solved by an iterative procedure for sets of parameter values of metabolic interest. The results, when analyzed using appropriate definitions of regulatory sensitivity and energetic futility, demonstrate that the effects of the enzymes leading into and out of the cycle may cause profound changes in the operation of the substrate cycle and therefore may not be ignored. We find that the structural differences among the three cycles considered here result in corresponding functional differences. Our results suggest that (1) the fructose-6-P/fructose-1,6-di-P cycle acts effectively to gate bidirectional flux, but doesn't appreciably enhance regulation of unidirectional flux, (2) the glucose/glucose-6-P cycle is well suited to perform a homeostatic function and to adjust the set points for these two metabolites, and (3) the cycle at the pyruvate crossroads functions largely as a complex switch box that directs metabolic flow towards gluconeogenesis or glycolysis not only in response to inputs of or requirements for oxaloacetate, pyruvate, and phosphoenolpyruvate, but also in response to the combined action of allosteric modulators on the individual enzymes of this substrate cycle.     

Substrate cycles in the central metabolism of maize root tips under hypoxia

Substrate cycles, also called "futile" cycles, are ubiquitous and lead to a net consumption of ATP which, in the normoxic maize root, have been estimated at about 50% of the total ATP produced [Alonso, A.P., Vigeolas, H., Raymond, P., Rolin, D., Dieuaide-Noubhani, M., 2005. A new substrate cycle in plants. Evidence for a high glucose-phosphate-to-glucose turnover from in vivo steady-state and pulse-labeling experiments with [(13)C] glucose and [(14)C] glucose. Plant Physiol. 138, 2220-2232]. To evaluate their role we studied the substrate cycles of maize root tips under an oxygen limitation of respiration (3% O(2)). Short-time labeling experiments with [U-(14)C]-Glc were performed to quantify the fluxes through sucrose and starch cycles of synthesis and degradation. Steady-state labeling with [1-(13)C]-Glc followed by (1)H NMR and (13)C NMR analysis of sugars and free alanine was used to quantify fluxes in the central metabolic pathways, including the Glc-P/Glc cycle and the fructose-P/triose-P cycle of glycolysis. Comparison with results previously obtained in normoxia [Alonso et al., as mentioned above] showed that 3% O(2) induced fermentation and reduced respiration, which led to a lesser amount of ATP produced. The rates of Glc consumption, glycolytic flux and all substrate cycles were lower, but the proportion of ATP consumed in the substrate cycles remained unchanged. These findings suggest that substrate cycles are not a luxury but an integral part of the organization of the plant central metabolism.     

Retinoblastoma cancer suppressor gene product is a substrate of the cell cycle regulator cdc2 kinase.

The retinoblastoma gene product (RB) is a nuclear protein which has been shown to function as a tumor suppressor. It is phosphorylated from S to M phase of the cell cycle and dephosphorylated in G1. This suggests that the function of RB is regulated by its phosphorylation in the cell cycle. Ten phosphotryptic peptides are found in human RB proteins. The pattern of RB phosphorylation does not change from S to M phases of the cell cycle. Hypophosphorylated RB prepared from insect cells infected with an RB-recombinant baculovirus is used as a substrate for in vitro phosphorylation reactions. Of several protein kinases tested, only cdc2 kinase phosphorylates RB efficiently and all 10 peptides can be phosphorylated by cdc2 in vitro. Removal of cdc2 from mitotic cell extracts by immunoprecipitation causes a concomitant depletion of RB kinase activity. These results indicate that cdc2 or a kinase with similar substrate specificity is involved in the cell cycle-dependent phosphorylation of the RB protein.     

Pentachlorophenol hydroxylase, a poorly functioning enzyme required for degradation of pentachlorophenol by Sphingobium chlorophenolicum

Several strains of Sphingobium chlorophenolicum have been isolated from soil that was heavily contaminated with pentachlorophenol (PCP), a toxic pesticide introduced in the 1930s. S. chlorophenolicum appears to have assembled a poorly functioning pathway for degradation of PCP by patching enzymes recruited via two independent horizontal gene transfer events into an existing metabolic pathway. Flux through the pathway is limited by PCP hydroxylase. PCP hydroxylase is a dimeric protein that belongs to the family of flavin-dependent phenol hydroxylases. In the presence of NADPH, PCP hydroxylase converts PCP to tetrachlorobenzoquinone (TCBQ). The k(cat) for PCP (0.024 s(-1)) is very low, suggesting that the enzyme is not well evolved for turnover of this substrate. Structure-activity studies reveal that substrate binding and activity are enhanced by a low pK(a) for the phenolic proton, increased hydrophobicity, and the presence of a substituent ortho to the hydroxyl group of the phenol. PCP hydroxylase exhibits substantial uncoupling; the C4a-hydroxyflavin intermediate, instead of hydroxylating the substrate, can decompose to produce H(2)O(2) in a futile cycle that consumes NADPH. The extent of uncoupling varies from 0 to 100% with different substrates. The extent of uncoupling is increased by the presence of bulky substituents at position 3, 4, or 5 and decreased by the presence of a chlorine in the ortho position. The effectiveness of PCP hydroxylase is additionally hindered by its promiscuous activity with tetrachlorohydroquinone (TCHQ), a downstream metabolite in the degradation pathway. The conversion of TCHQ to TCBQ reverses flux through the pathway. Substantial uncoupling also occurs during the reaction with TCHQ.     

Futile substrate cycles in the glycolytic pathway of boar and rat spermatozoa and the effect of alpha-chlorohydrin

In boar spermatozoa incubated with 0.1 mM-glucose about 20 nmol glucose were converted to lactate and CO2 and the rate of futile substrate cycling between glucose and glucose 6-phosphate was about 6 nmol/10(8) spermatozoa/30 min. Futile cycling was increased in the presence of 0.05 or 1 mM-alpha-chlorohydrin but not to an extent sufficient to account for the rapid decline in ATP concentration observed under these conditions. These estimates include a substantial rate of fructose formation from fructose phosphates. The addition of 10 mM-L-lactate plus 1 mM-pyruvate protected the spermatozoa against the effect of alpha-chlorohydrin and glucose on the ATP concentration but increased futile substrate cycling. Substrate cycling between fructose 6-phosphate and fructose 1,6-bisphosphate could not be measured in boar spermatozoa but in rat spermatozoa its rate (nmol/10(8) spermatozoa/30 min) was about 10 under control condition and about 25 in the presence of 1 mM-alpha-chlorohydrin. This increase was insufficient to account for the decline in ATP concentration. In both species futile substrate cycling consumed a significant proportion of the ATP synthesis during lactate production but only about 5% of that produced in the oxidation of glucose to acetyl carnitine and CO2.     

The propagation of errors in long-term measurements of land-atmosphere fluxes of carbon and water

For surface fluxes of carbon dioxide, the net daily flux is the sum of daytime and nighttime fluxes of approximately the same magnitude and opposite direction. The net flux is therefore significantly smaller than the individual flux measurements and error assessment is critical in determining whether a surface is a net source or sink of carbon dioxide. For carbon dioxide flux measurements, it is an occasional misconception that the net flux is measured as the difference between the net upward and downward fluxes (i.e. a small difference between large terms). This is not the case. The net flux is the sum of individual (half-hourly or hourly) flux measurements, each with an associated error term. The question of errors and uncertainties in long-term flux measurements of carbon and water is addressed by first considering the potential for errors in flux measuring systems in general and thus errors which are relevant to a wide range of timescales of measurement. We also focus exclusively on flux measurements made by the micrometeorological method of eddy covariance. Errors can loosely be divided into random errors and systematic errors, although in reality any particular error may be a combination of both types. Systematic errors can be fully systematic errors (errors that apply on all of the daily cycle) or selectively systematic errors (errors that apply to only part of the daily cycle), which have very different effects. Random errors may also be full or selective, but these do not differ substantially in their properties. We describe an error analysis in which these three different types of error are applied to a long-term dataset to discover how errors may propagate through long-term data and which can be used to estimate the range of uncertainty in the reported sink strength of the particular ecosystem studied.     

Detecting and investigating substrate cycles in a genome-scale human metabolic network

Substrate cycles, also known as futile cycles, are cyclic metabolic routes that dissipate energy by hydrolysing cofactors such as ATP. They were first described to occur in the muscles of bumblebees and brown adipose tissue in the 1970s. A popular example is the conversion of fructose?6-phosphate to fructose?1,6-bisphosphate and back. In the present study, we analyze a large number of substrate cycles in human metabolism that consume ATP and discuss their statistics. For this purpose, we use two recently published methods (i.e. EFMEvolver and the K-shortest EFM method) to calculate samples of 100?000 and 15?000 substrate cycles, respectively. We find an unexpectedly high number of substrate cycles in human metabolism, with up to 100 reactions per cycle, utilizing reactions from up to six different compartments. An analysis of tissue-specific models of liver and brain metabolism shows that there is selective pressure that acts against the uncontrolled dissipation of energy by avoiding the coexpression of enzymes belonging to the same substrate cycle. This selective force is particularly strong against futile cycles that have a high flux as a result of thermodynamic principles.     

Toxoplasma-induced autophagy: A window into nutritional futile cycles in mammalian cells?

The regulation and function of autophagy in response to metabolic signals is not yet well understood. A recent study from our laboratory indicates than an intracellular parasite, Toxoplasma gondii, derives nutritive benefit from the upregulation of host cell autophagy. We discuss these and related findings suggesting that autophagy in infected cells functions as part of a metabolic futile cycle. The hypothesis is presented that endogenous autophagy-based futile cycles may operate in normal mammalian cells, providing a substrate for manipulation by pathogens.     

Effects of hormones and of ethanol on the fructose 6-P-fructose 1,6-P2 futile cycle during gluconeogenesis in the liver

Carbon-14 was incorporated into C-6 of glucose from [1-¹⁴C]galactose during gluconeogenesis from dihydroxyacetone in liver cells from fasted rats, proving the existence of a futile cycle between fructose-6-P and fructose-1,6-P₂ under the conditions used. Using a steady-state model and assumed values for the rates of aldolase and glucose-6-P isomerase, the rates of phosphofructokinase were estimated, ranging from about 15% to nearly 40% of the net rate of gluconeogenesis. Glucagon depressed the rate of phosphofructokinase by as much as 85% and increased the rate of gluconeogenesis by up to 45%. l-epinephrine in the range from 10 to 100 μm also depressed phosphofructokinase, being nearly as effective as glucagon only at high concentrations. The effect of epinephrine was only partially reversed by 10 μm dl-propranolol. Ethanol (10 mm) depressed phosphofructokinase flux nearly as well as glucagon, but had no significant effect on the rate of gluconeogenesis from dihydroxyacetone.     

A minimal model of liver glycogen metabolism; feasibility for predicting flux rates

A minimal model of glycogen metabolism can allow the estimation of the flux rates in the glycogen pathway from the time course of the intermediates in the pathway, measured during substrate administration and hormonal stimulation. The comprehensive model of El-Refai & Bergman (Am. J. Physiol. 231, 1608, 1976) consisting of six compartments and 26 non-estimable parameters has successfully accounted for the responses of hepatic glycogenic intermediates in response to a glucose load in hepatocytes (Katz et al., J. biol. Chem. 253, 4530, 1978), in perfused liver (Nordlie et al., J. biol. Chem. 255, 1834, 1980) and during refeeding in vivo (Van DeWerve & Jeanrenaud, Am. J. Physiol. 247, E271, 1984). The comprehensive model is here reduced to a minimal model, consisting of five compartments representing extracellular and intracellular glucose, glucose-phosphate, uridine diphosphate glucose (UDPG), glycogen, and five parameters estimated from the hepatic response to a given stimulus. Estimation of these parameters requires the measurement of the net hepatic glucose balance, the net gluconeogenic flux, and the time course of glycogenic intermediates responding to a hormone or substrate stimulus. The hepatic glycogenolytic response predicted by the comprehensive model in response to an increase in glucagon is closely fitted by the minimal model. When Gaussian distributed random error was added, 0-5% SD in the glucose and glycogen compartments and 0-10% SD in the glucose-phosphate and UDPG compartments, the hepatic response predicted by the minimal model was virtually free of the added error, and the model parameters were found to be within 30% of their true values. When the minimal model was used to interpret the experimental response to an increase in glucose concentration it predicted that: (1) glucokinase can phosphorylate glucose at rates similar to maximal rates of net glycogen synthesis; (2) futile cycling at the glycogen/glucose-1-phosphate level can limit glycogen synthesis; and (3) glucose-6-phosphatase inhibition by glucose has a significant role in net glycogen synthesis.     

On the analysis of substrate cycles in large metabolic systems

The simultaneous operation of paired, opposing reactions (substrate cycles) or parallel reactions (dual pathways) with seeming wastage of ATP is widespread in cellular metabolism. Analysis of such “futile” pathways has hitherto been limited to loci with only two or three interconnecting fluxes. We introduce here a method that allows straightforward analysis of more complex systems. The method involves the linear superposition of “fundamental” modes, one or more of which may be energetically wasteful. Decomposition of a flux pattern into such modes allows computation of the amount of free energy “wasted” at any locus. Appropriate normalizations of energy wastage yield a number of indices useful for assessing the energetic impact of futile pathways on the cell and for comparing the degree of regulation of substrate cycles or dual pathways under different metabolic conditions. This approach is applied to steady-state flux data obtained in the protozoanTetrahymena pyriformis and in isolated rat hepatocytes under a variety of conditions.     

重组巴氏毕赤酵母恒化培养动力学及代谢迁移特性研究

通过对甲醇营养型毕赤酵母基因工程菌以碳源甘油为限制性基质进行恒化培养动力学试验 ,结果认为 :(1 )细胞光密度与其干、湿重呈线性关系 ,当细胞光密度 (OD60 0 )为 1 0 0时细胞湿重 (WCW)为 1 2 8 3g L ,细胞干重 (WDW)则为 2 2 9g L ;(2 )基因工程菌P .pastoris的生长与限制性基质甘油残留浓度的关系符合Monod关系式 ,通过 1 μ对 1 S进行线性回归得 μmax=0 .366h- 1,Ks=0 .1 82 3g L ,经参数推导甘油最大菌体得率系数YG =0 .54g g ,菌体维持生长消耗底物系数m =0 .0 0 69g (g·h) ;氧最大菌体系数YX O2 =30 .96g moL ,菌体维持生长时消耗氧系数mO2 =0 .0 0 0 8mol (g·h) ,最适理论稀释速率Dm =0 .341h- 1;(3)从氨水的消耗速率和呼吸商 (RQ)的变化认为随着比生长速率 (μ)的增大 ,甘油代谢流从糖原异生和磷酸戊糖途径线性地向糖酵解和三羧酸循环途径进行代谢迁移 ,即糖酵解和三羧酸循环途径的代谢流量在线性地增大