A Linear Steady‐State Treatment of Enzymatic Chains
TL;DR: A theoretical analysis of linear enzymatic chains is presented and three cardinal terms are proposed for the quantitative description of enzyme systems, including the effector strength, which defines the dependence of the velocity of an enzyme on the concentration of an effector.
Abstract: A theoretical analysis of linear enzymatic chains is presented By linear approximation simple analytical solutions can be obtained for the metabolite concentrations and the flux through the chain for steady-state conditions The equations are greatly simplified if the common kinetic constants are expressed as functions of two parameters, ie the thermodynamic equilibrium constant and the “characteristic time” Three cardinal terms are proposed for the quantitative description of enzyme systems The first two are the control strength and the control matrix; these indicate the dependence of the flux and the metabolite concentrations, respectively, on the kinetic properties of a given enzyme The third is the effector strength, which defines the dependence of the velocity of an enzyme on the concentration of an effector; it expresses the importance of an effector By linear approximation simple analytical expressions were derived for the control strength, the control matrix and the mass-action ratios The effector strength was calculated for two cases: for a competitive inhibitor and for allosteric effectors according to the Monod (1965) model The influence of an effector on the concentrations of the metabolites was considered
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TL;DR: In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined.
Abstract: Metabolites are the end products of cellular regulatory processes, and their levels can be regarded as the ultimate response of biological systems to genetic or environmental changes. In parallel to the terms ‘transcriptome’ and ‘proteome’, the set of metabolites synthesized by a biological system constitute its ‘metabolome’. Yet, unlike other functional genomics approaches, the unbiased simultaneous identification and quantification of plant metabolomes has been largely neglected. Until recently, most analyses were restricted to profiling selected classes of compounds, or to fingerprinting metabolic changes without sufficient analytical resolution to determine metabolite levels and identities individually. As a prerequisite for metabolomic analysis, careful consideration of the methods employed for tissue extraction, sample preparation, data acquisition, and data mining must be taken. In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined. Current approaches are examined, and potential applications are summarized with a special emphasis on data mining and mathematical modelling of metabolism.
3,547 citations
Cites background from "A Linear Steady‐State Treatment of ..."
...The theory of MCA was introduced by Kacser and Burns (1973, reprinted with additional comments in 1995) and Heinrich and Rapoport (1974)....
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TL;DR: The IIAGlc protein, part of the glucose-specific PTS, is a central regulatory protein which in its nonphosphorylated form can bind to and inhibit several non-PTS uptake systems and thus prevent entry of inducers.
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TL;DR: The computational OptKnock framework is introduced for suggesting gene deletion strategies leading to the overproduction of chemicals or biochemicals in E. coli, and hints at a growth selection/adaptation system for indirectly evolving overproducing mutants.
Abstract: The advent of genome-scale models of metabo- lism has laid the foundation for the development of computational procedures for suggesting genetic manipu- lations that lead to overproduction. In this work, the computational OptKnock framework is introduced for suggesting gene deletion strategies leading to the over- production of chemicals or biochemicals in E. coli. This is accomplished by ensuring that a drain towards growth resources (i.e., carbon, redox potential, and energy) must be accompanied, due to stoichiometry, by the production of a desired product. Computational results for gene de- letions for succinate, lactate, and 1,3-propanediol (PDO) production are in good agreement with mutant strains published in the literature. While some of the suggested deletion strategies are straightforward and involve elimi- nating competing reaction pathways, many others suggest complex and nonintuitive mechanisms of compensating for the removed functionalities. Finally, the OptKnock procedure, by coupling biomass formation with chemical production, hints at a growth selection/adaptation sys- tem for indirectly evolving overproducing mutants. B 2003 Wiley Periodicals. Biotechnol Bioeng 85: 000-000, 2003.
1,261 citations
Cites background from "A Linear Steady‐State Treatment of ..."
...…cybernetic (Kompala et al., 1984; Ramakrishna et al., 1996; Varner and Ramakrishna, 1999), metabolic control analysis (Kacser and Burns, 1973; Heinrich and Rapoport, 1974; Hatzimanikatis et al., 1998)), if available, could also be incorporated within the OptKnock framework to more accurately…...
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TL;DR: The genome sequence of the yeast Saccharomyces cerevisiae has provided the first complete inventory of the working parts of a eukaryotic cell, and systematic and comprehensive approaches to the elucidation of yeast gene function are discussed.
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TL;DR: It is now established that the rate of C02 assimilation in the leaves is depressed at moderate water deficits, mostly as a consequence of stomatal closure, and carbon assimilation may diminish to values close to zero without any significant decline in mesophyll photosynthetic capacity.
Abstract: This review focuses on the effects of water deficits on photosynthesis and partitioning of assimilates at the leaf level. It is now established that the rate of C02 assimilation in the leaves is depressed at moderate water deficits, mostly as a consequence of stomatal closure. In fact, depending on the species and on the nature of dehydration, carbon assimilation may diminish to values close to zero without any significant decline in mesophyll photosynthetic capacity. This remarkable resistance of the photosynthetic apparatus to water deficits became apparent after the measurement of photosynthesis at saturating C02 concentrations was made possible. Whenever light or heat stress are superimposed a decline in mesophyll photosynthesis may occur as a result of a 'down-regulation' process, which seems to vary among genotypes. A major secondary effect of dehydration on photosynthetic carbon metabolism is the change in partitioning of recently fixed carbon towards sucrose, which occurs in a number of species in parallel to the increase in starch breakdown. This increase in compounds of low molecular weight may contribute to an osmotic adjustment. Controlling mechanisms involved in this process deserve further investigation.
1,093 citations
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TL;DR: "It is certain that all bodies whatsoever, though they have no sense, yet they have perception, and whether the body be alterant or alterec, evermore a perception precedeth operation; for else all bodies would be like one to another."
8,157 citations
TL;DR: A comparison between the model and the phosphofructokinase reaction shows a close resemblance between their dynamical properties, which makes it possible to explain qualitatively most experimental data on single-frequency oscillations in glycolysis.
Abstract: The paper describes a simple kinetic model of an open monosubstrate enzyme reaction with substrate inhibition and product activation. A comparison between the model and the phosphofructokinase reaction shows a close resemblance between their dynamical properties. This makes it possible to explain qualitatively most experimental data on single-frequency oscillations in glycolysis. A mathematical analysis of the model has shown the following.
1In the model, at a definite relationship between the parameters, self-oscillations arise.
2The condition of self-excitation is satisfied more readily with a lower source rate, larger product sink rate constants, lower product-enzyme affinity and higher enzyme activity.
3Self-oscillations exist only in a certain range of values of the parameter determining the degree of substrate inhibition. This range increases with decreasing source rate. Too strong or, conversely, too weak substrate inhibition leads to damped oscillations.
4The period of self-oscillations depends on the degree of substrate inhibition, the source rate, the sink rate constant, the enzyme activity, the affinity of the substrate and the product for the enzyme; it decreases with an increase in these values.
5With an increase in the relative sink rate constant the steady state amplitude of self-oscillations initially increases until a definite maximum is reached and then drops to zero.
6A self-oscillatory state in the phosphofructokinase reaction exists only when the maximum rate of this reaction is essentially higher than the source rate, and lower than the maximum rate of the reactions controlling the sink of the products.
7An experimental investigation of self-oscillations in the phosphofructokinase reaction may be considerably simplified by using a reconstituted system consisting of a small number of reactions with an irreversible sink of the products and artificial substrate supply. In this case the above relationship (section 6) should hold.
675 citations
TL;DR: Phosphofructokinase has been partially purified from Escherichia coli, and its kinetic properties investigated, finding co-operative interactions with respect to one of its substrates, fructose-6-phosphate, but not towards the second, namely ATP.
400 citations
TL;DR: The study of oscillations reveals the dynamics of a pathway over a large range of states and an implicit function of their feedback structure, which involves cross-coupling and self-Coupling with opposite sign in a two variable structure and might produce kinetic instability involving more than one singularity of the trajectories in a phase plane.
324 citations
TL;DR: It is concluded that for real systems the identification of the interaction sites of an effector with an enzymatic chain cannot be achieved by the simple crossover theorem, and even the Identification of “rate controlling” or “regulatory important” enzymes by means of c crossover must be done with great caution.
Abstract: A theoretical analysis of the crossover theorem is presented based on a linear approximation. Cases are considered in which the simple crossover theorem may lead to erroneus conclusions. Among them are the following : more than one interaction site of an effector with the enzymatic chain; influx and efflux of metabolites regulated by outer metabolic processes ; existence of inner effectors ; conservation equations for metabolite concentrations ; and changes of the state of complexes with the metabolites. It is shown that the action of an effector does not always produce a crossover at the affected enzyme. On the other hand, examples are given where “pseudo-crossovers’’ occur at unaffected enzymes. It is concluded that for real systems the identification of the interaction sites of an effector with an enzymatic chain cannot be achieved by the simple crossover theorem. Furthermore, even the identification of “rate controlling” or “regulatory important” enzymes by means of crossovers must be done with great caution. A simple and general procedure for the identification of interaction sites of an outer effector with an enzymatic chain is proposed. It requires the determination of the flux through the chain, the concentrations of the substrates and products of the enzymatic step under consideration and the rate law by which an inner effector, if present, influences the reaction rate of this step. The crossover theorem was first formulated by Chance et al. [l-41. It deals with the influence of outer effectors on the levels of the metabolites in an enzymatic chain. In its simplest form, the “classical” crossover theorem can be stated in the following way: the variations of the concentrations of the metabolites before and beyond an enzyme which is influenced by an effector have different signs. It has been widely used to identify the interaction sites of effectors within the chain. Chance et al. [l--51 have applied the crossover theorem for the investigation of the changes in the steady-state oxidation-reduction levels of the components of the respiratory chain. With the help of this theorem they were able to identify the sites of phosphorylation. An inspection of the literature on metabolic regulation shows that subsequently the crossover theorem has been applied to a variety of systems including very complicated ones. It was tacitly assumed that in all these cases the crossover theorem is valid in its simple form (e.g. [6-8)). Only few theoretical considerations of the crossover theorem have been published so far. Chance et al. [7] have studied the crossover behaviour of the respiratory chain by means of analogue computers. In a more general manner, Holmes [9] considered several types of sequences of chemical reactions and proved the theorem for some simple cases. For the characterization of a crossover he used pairs of neighbouring metabolites where the signs (-, +) and (+, -) indicate the direction of the variation of the concentrations produced by the effector. For the condition that the effector increases the flux the pairs were called “forward)’ and “backward” crossovers, respectively, by Williamson [lo]. The present paper deals with the limitations of the simple crossover theorem in its application to real systema. We shall consider five situations where the crossover theorem is not valid. It will be shown that the uncritical application of the crossover theorem may lead to serious misinterpretations. On the other hand, the procedure proposed in this paper for the identification of the interaction sites of an effector with an enzymatic chain will give correct results if the linear approximation holds. Parts of the results have been presented at the FEBS Advanced Course on “Mathematical Models of Metabolic Regulation”, Oberhof, November 1972.
223 citations