scholarly journals Quantitative determination of the steady-state kinetics of multienzyme reactions using the algebraic rate equations for the component single-enzyme reactions

1993 ◽  
Vol 291 (2) ◽  
pp. 585-593 ◽  
Author(s):  
C D Stoner
Keyword(s):  
Steady State ◽  
Direct Calculation ◽  
Rate Equations ◽  
Maximum Efficiency ◽  
Control Analysis ◽  
Flux Control ◽  
Enzyme Reactions ◽  
Dependent Variables ◽  
The Individual ◽  
Single Enzyme

Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.

The regulatory design of an allosteric feedback loop: the effect of saturation by pathway substrate

2002 ◽  
Vol 30 (2) ◽  
pp. 19-25 ◽  
Author(s):  
S. Hofmeyr Jan-Hendrik ◽  
Brett G. Olivier
Keyword(s):  
Steady State ◽  
Metabolic Regulation ◽  
Supply And Demand ◽  
Graphical Analysis ◽  
Degree Of Saturation ◽  
Rate Equations ◽  
Distinct Advantage ◽  
Control Analysis ◽  
Hill Model ◽  
Wide Range

Aspects of metabolic regulation can be fruitfully studied with a combination of generic modelling, control analysis and graphical analysis using rate characteristics. This paper analyses a prototypical supply-demand system consisting of a biosynthetic subsystem subject to allosteric inhibition by its product and a demand process that consumes this product. The effect of changes in affinity of the committing supply enzyme for the pathway substrate on the regulatory properties of the supply subsystem is compared for the Monod-Wyman-Changeux and the reversible Hill allosteric enzyme models. We found that the Hill model has a distinct advantage in that the steady-state concentration at which it maintains the product is set by the half-saturating product concentration and is independent of changes in the degree of saturation for substrate. In contrast, with the Monod-Wyman-Changeux model this set point varies with affinity for substrate. Explicitly incorporating reversibility in all rate equations made it possible to distinguish between kinetic and thermodynamic aspects of regulation. Combining the supply and demand rate characteristics allows us to explore both the control distribution at steady state and the regulatory performance of the system over a wide range of demand activities.

Quantification of the control of carbohydrate catabolism in the tapeworm Hymenolepis diminuta

1993 ◽  
Vol 71 (7-8) ◽  
pp. 315-323 ◽  
Author(s):  
Wendy Y. Precious ◽  
John Barrett
Keyword(s):  
Phosphoenolpyruvate Carboxykinase ◽  
Glycogen Synthase ◽  
Hymenolepis Diminuta ◽  
Rate Equations ◽  
Control Analysis ◽  
Control Coefficient ◽  
Flux Control ◽  
Flux Control Coefficients ◽  
Carbohydrate Catabolism ◽  
Control Coefficients

The elasticities for the different steps of carbohydrate catabolism in the tapeworm Hymenolepis diminuta were estimated from perturbation experiments. These data were then used to calculate flux and metabolite control coefficients. Enzyme elasticities were also calculated from the rate equations and an independent estimate of the flux control coefficients for phosphoenolpyruvate carboxykinase was made by inhibitor titration. The values obtained for the flux control coefficients for carbohydrate breakdown in H. diminuta are consistent with how the pathway is thought to be controlled in vivo. A sensitivity analysis of the flux control coefficients of the important regulatory enzymes in the pathway shows that for hexokinase, phosphofructokinase, pyruvate kinase, and phosphoenolpyruvate carboxykinase there are three or four key elasticities which have a significant effect on the coefficient. For glycogen synthase, the major factor in determining the magnitude of the flux control coefficient is the relative flux through the branch.Key words: Hymenolepis diminuta, metabolic control analysis, control coefficient, enzyme elasticity.

scholarly journals The computerized derivation of rate equations for enzyme reactions on the basis of the pseudo-steady-state assumption and the rapid-equilibrium assumption

1988 ◽  
Vol 251 (1) ◽  
pp. 175-181 ◽  
Author(s):  
H Ishikawa ◽  
T Maeda ◽  
H Hikita ◽  
K Miyatake
Keyword(s):  
Steady State ◽  
Rate Equation ◽  
Rate Equations ◽  
British Library ◽  
Enzyme Reactions ◽  
Input Method ◽  
Steady State Assumption ◽  
Rapid Equilibrium Assumption ◽  
Rapid Equilibrium ◽  
State Assumption

A computer program is developed for the derivation of the rate equation for enzyme reactions on the basis of the pseudo-steady-state assumption and the combination of the pseudo-steady-state and the rapid-equilibrium assumptions. The program not only has an easy input method, but also can obtain a complete rate equation in itself on only one run. The usefulness of the program is demonstrated by deriving the rate equations for some typical enzyme reactions. Details of the program have been deposited as Supplementary Publication SUP 50141 (42 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7QB, U.K., from whom copies may be obtained as indicated in Biochem. J. (1988), 249, 5.

scholarly journals Delving deeper: Relating the behaviour of a metabolic system to the properties of its components using symbolic metabolic control analysis

2018 ◽  
Author(s):  
Carl D. Christensen ◽  
Jan-Hendrik S. Hofmeyr ◽  
Johann M. Rohwer
Keyword(s):  
Reaction Rates ◽  
Mass Action ◽  
Control Analysis ◽  
Metabolic System ◽  
Flux Control ◽  
Symbolic Control ◽  
Mechanistic Understanding ◽  
The Individual ◽  
High Level ◽  
Molecular Components

AbstractHigh-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system’s components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions.Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic fluxor steady-state concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism inLactococcus lactisin order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control.These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.Author summaryMetabolic networks are complex systems consisting of numerous individual molecular components. The properties of these components, together with their non-linear interactions, give rise to high-level observed behaviour of the system in which they reside. Therefore, in order to fully understand the behaviour of a metabolic system, one has to consider the properties of all of its components. The analysis of computer models that capture and represent these systems and their components simplifies this task by allowing for an easy way to isolate the effects of each individual component. In this paper we use the framework of symbolic control analysis to investigate the sensitivity of the rate of flow of matter through one of the branches in a particular metabolic pathway towards changes in the rates of individual reactions. Here we are able to quantify how certain chains of reactions, individual reactions, and even thermodynamic and kinetic aspects of individual reactions contribute to the overall sensitivity of the rate of matter-flow. Thus, we are able to trace the behaviour of the system as a whole in a mechanistic way to the properties of the individual molecular components.

scholarly journals A steady-state approach for inhibition of heterogeneous enzyme reactions

2020 ◽  
Vol 477 (10) ◽  
pp. 1971-1982
Author(s):  
Jeppe Kari ◽  
Corinna Schiano-di-Cola ◽  
Stine Fredslund Hansen ◽  
Silke Flindt Badino ◽  
Trine Holst Sørensen ◽  
...  
Keyword(s):  
Steady State ◽  
Competitive Inhibition ◽  
Industrial Applications ◽  
Rate Equations ◽  
Inhibition Mechanism ◽  
Enzyme Reactions ◽  
Steady State Kinetic ◽  
Solid Liquid Interface ◽  
Solid Liquid

The kinetic theory of enzymes that modify insoluble substrates is still underdeveloped, despite the prevalence of this type of reaction both in vivo and industrial applications. Here, we present a steady-state kinetic approach to investigate inhibition occurring at the solid–liquid interface. We propose to conduct experiments under enzyme excess (E0 ≫ S0), i.e. the opposite limit compared with the conventional Michaelis–Menten framework. This inverse condition is practical for insoluble substrates and elucidates how the inhibitor reduces enzyme activity through binding to the substrate. We claim that this type of inhibition is common for interfacial enzyme reactions because substrate accessibility is low, and we show that it can be analyzed by experiments and rate equations that are analogous to the conventional approach, except that the roles of enzyme and substrate have been swapped. To illustrate the approach, we investigated the major cellulases from Trichoderma reesei (Cel6A and Cel7A) acting on insoluble cellulose. As model inhibitors, we used catalytically inactive variants of Cel6A and Cel7A. We made so-called inverse Michaelis–Menten curves at different concentrations of inhibitors and found that a new rate equation accounted well for the data. In most cases, we found a mixed type of surface-site inhibition mechanism, and this probably reflected that the inhibitor both competed with the enzyme for the productive binding-sites (competitive inhibition) and hampered the processive movement on the surface (uncompetitive inhibition). These results give new insights into the complex interplay of Cel7A and Cel6A on cellulose and the approach may be applicable to other heterogeneous enzyme reactions.

Effects of modifiers on the kinetics of two-substrate enzyme reactions

1968 ◽  
Vol 46 (11) ◽  
pp. 1381-1396 ◽  
Author(s):  
J. Frank Henderson
Keyword(s):  
Steady State ◽  
Binding Sites ◽  
Rate Equations ◽  
Enzyme Reactions ◽  
Ping Pong ◽  
Steady State Rate ◽  
State Rate ◽  
Kinetics Of

Steady state rate equations have been derived for ordered bi bi and ping pong bi bi reactions in which there are (a) one or two nonsubstrate modifiers, (b) two different binding sites for a single nonsubstrate modifier, (c) one or two substrates acting as modifiers, and (d) both nonsubstrate modifiers and substrates acting as modifiers. The deviation of these equations from the Michaelis–Menten equation is shown and methods are suggested by which many of these mechanisms can be distinguished experimentally.

scholarly journals Metabolic Control Analysis of Exponential Growth and Product Formation

2018 ◽  
Author(s):  
David Andrew Fell
Keyword(s):  
Steady State ◽  
Metabolic Control ◽  
Product Yield ◽  
Product Formation ◽  
Metabolic Control Analysis ◽  
Control Analysis ◽  
Control Coefficient ◽  
Flux Control ◽  
Flux Control Coefficient ◽  
Metabolic Fluxes

Metabolic Control Analysis defines the relationships between the change in activity of an enzyme and the resulting impacts on metabolic fluxes and metabolite concentrations at steady state. In many biotechnological applications of metabolic engineering, however, the goal is to alter the product yield. In this case, although metabolism may be at a pseudo-steady state, the amount of biomass catalysing the metabolism can be growing exponentially. Here, expressions are derived that relate the change in activity of an enzyme and its flux control coefficient to the change in yield from an exponentially growing system. Conversely, the expressions allow estimation of an enzyme's flux control coefficient over the pathway generating the product from measurements of the changes in enzyme activity and yield.

scholarly journals A steady-state kinetic model of butyrylcholinesterase from horse plasma

1974 ◽  
Vol 141 (3) ◽  
pp. 825-834 ◽  
Author(s):  
Klas-Bertil Augustinsson ◽  
Tamas Bartfai ◽  
Bengt Mannervik
Keyword(s):  
Steady State ◽  
Molecular Model ◽  
Rate Equations ◽  
Phenyl Acetate ◽  
Thiol Ester ◽  
Regression Methods ◽  
Steady State Kinetics ◽  
Steady State Kinetic ◽  
Hydrolysis Of ◽  
Single Enzyme

The steady-state kinetics of the butyrylcholinesterase-catalysed hydrolysis of butyrylthiocholine and thiophenyl acetate were shown to deviate from Michaelis–Menten kinetics. The ‘best’ empirical rate law was selected by fitting different rate equations to the experimental data by non-linear regression methods. The results were analysed in view of two alternative interpretations: (1) the reaction is catalysed by a mixture of enzymes, or (2) the activity is due to a single enzyme displaying deviations from Michaelis–Menten kinetics. It was concluded that the second alternative applies, and this conclusion was further supported by experiments involving simultaneous hydrolysis of alternative thiol ester substrates (butyrylthiocholine/thiophenyl acetate) as well as alternative thiol ester and oxygen ester substrates (butyrylthiocholine/phenyl acetate; thiophenyl acetate/butyrylcholine; acetylthiocholine/phenyl acetate). On the basis of the conclusion that a single enzyme is responsible for the activity, a molecular model is proposed. This model involves an acylated enzyme, and implies binding to the enzyme of one acyl group and one ester molecule, but not two ester molecules at the same time. Thus butyrylcholinesterase, which is structurally a tetramer, behaves functionally as a co-operative dimer, an interpretation in accordance with available data from active-site titrations.

A kinetic analysis of coupled sequential enzyme reactions

2018 ◽  
Author(s):  
Justin Eilertsen ◽  
Santiago Schnell
Keyword(s):  
Enzyme Assay ◽  
Sequential Reaction ◽  
Enzyme Reactions ◽  
Indicator Reaction ◽  
Single Substrate ◽  
Complex Sequences ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Single Enzyme

<div>As a case study, we consider a coupled enzyme assay of sequential enzyme reactions obeying the Michaelis--Menten reaction mechanism. The sequential reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction becomes the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the sequential reaction is described by a pair of interacting Michaelis--Menten equations. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis--Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

A kinetic analysis of coupled sequential enzyme reactions

2018 ◽  
Author(s):  
Justin Eilertsen ◽  
Santiago Schnell
Keyword(s):  
Enzyme Assay ◽  
Sequential Reaction ◽  
Enzyme Reactions ◽  
Indicator Reaction ◽  
Single Substrate ◽  
Complex Sequences ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Single Enzyme

<div>As a case study, we consider a coupled enzyme assay of sequential enzyme reactions obeying the Michaelis-Menten reaction mechanism. The sequential reaction consists of a single-substrate, single enzyme non-observable reaction followed by another single-substrate, single enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction becomes the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the sequential reaction is described by a pair of interacting Michaelis-Menten equations. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis-Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

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