Phase-plane geometries in enzyme kinetics

1994 ◽  
Vol 72 (3) ◽  
pp. 800-812 ◽  
Author(s):  
Simon J. Fraser ◽  
Marc R. Roussel
Keyword(s):  
Steady State ◽  
Phase Plane ◽  
Competitive Inhibition ◽  
Three Dimensional ◽  
Product Inhibition ◽  
Slow Manifold ◽  
Dimensional System ◽  
Planar System ◽  
State Behaviour ◽  
Kinetics Of

The transient and steady-state behaviour of the reversible Michaelis–Menten mechanism [R] and Competitive Inhibition (CI) mechanism is studied by analysis in the phase plane. Usually, the kinetics of both mechanisms is simplified to give a modified Michaelis–Menten velocity expression; this applies to the CI mechanism with excess inhibitor and to mechanism [R] in the product inhibition limit. In this paper, [R] is treated exactly as a plane autonomous system of differential equations and its true (dynamical) steady state is described by a line-like slow manifold M. Initial velocity experiments for [R] no longer strictly correspond to the hyperbolic law (as in the irreversible Michaelis–Menten mechanism) and this leads to corrections to the standard integrated rate law. Using a new analysis, the slow dynamics of the CI mechanism is reduced from a three-dimensional system to a planar system. In this mechanism transient decay collapses the trajectory flow onto a two-dimensional "slow" surface Σ; motion on Σ can be treated exactly as projected dynamics in the plane. This projected flow may differ in important ways from that of two-step mechanisms, e.g., it may lack a proper steady state. The relevance of these more accurate dynamical descriptions is discussed in relation to experimental design and metabolic function.

scholarly journals Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Piotr Hachuła ◽  
Magdalena Nockowska-Rosiak ◽  
Ewa Schmeidel
Keyword(s):  
Equilibrium Points ◽  
Three Dimensional ◽  
Inventory Model ◽  
Phase Portraits ◽  
Dimensional System ◽  
Planar System ◽  
Stock Level ◽  
Lyapunov Coefficient ◽  
Analysis Of Dynamics ◽  
Dependent Demand

An analysis of dynamics of demand-inventory model with stock-level-dependent demand formulated as a three-dimensional system of difference equations with four parameters is considered. By reducing the model to the planar system with five parameters, an analysis of one-parameter bifurcation of equilibrium points is presented. By the analytical method, we prove that nondegeneracy conditions for the existence of Neimark-Sacker bifurcation for the planar system are fulfilled. To check the sign of the first Lyapunov coefficient of Neimark-Sacker bifurcation, we use numerical simulations. We give phase portraits of the planar system to confirm the previous analytical results and show new interesting complex dynamical behaviours emerging in it. Finally, the economical interpretation of the system is given.

scholarly journals Kinetic mechanism of Escherichia coli isocitrate dehydrogenase and its inhibition by glyoxylate and oxaloacetate

1986 ◽  
Vol 234 (2) ◽  
pp. 317-323 ◽  
Author(s):  
H G Nimmo
Keyword(s):  
Escherichia Coli ◽  
Steady State ◽  
Isocitrate Dehydrogenase ◽  
Initial Rate ◽  
Potent Inhibitor ◽  
Competitive Inhibition ◽  
Kinetic Mechanism ◽  
Product Inhibition ◽  
Coenzyme Binding ◽  
Inhibition Studies

The inhibition of Escherichia coli isocitrate dehydrogenase by glyoxylate and oxaloacetate was examined. The shapes of the progress curves in the presence of the inhibitors depended on the order of addition of the assay components. When isocitrate dehydrogenase or NADP+ was added last, the rate slowly decreased until a new, inhibited, steady state was obtained. When isocitrate was added last, the initial rate was almost zero, but the rate increased slowly until the same steady-state value was obtained. Glyoxylate and oxaloacetate gave competitive inhibition against isocitrate and uncompetitive inhibition against NADP+. Product-inhibition studies showed that isocitrate dehydrogenase obeys a compulsory-order mechanism, with coenzyme binding first. Glyoxylate and oxaloacetate bind to and dissociate from isocitrate dehydrogenase slowly. These observations can account for the shapes of the progress curves observed in the presence of the inhibitors. Condensation of glyoxylate and oxaloacetate produced an extremely potent inhibitor of isocitrate dehydrogenase. Analysis of the reaction by h.p.l.c. showed that this correlated with the formation of oxalomalate. This compound decomposed spontaneously in assay mixtures, giving 4-hydroxy-2-oxoglutarate, which was a much less potent inhibitor of the enzyme. Oxalomalate inhibited isocitrate dehydrogenase competitively with respect to isocitrate and was a very poor substrate for the enzyme. The data suggest that the inhibition of isocitrate dehydrogenase by glyoxylate and oxaloacetate is not physiologically significant.

scholarly journals Interspecific density-dependent model of predator–prey relationship in the chemostat

2020 ◽  
pp. 2050086
Author(s):  
Tahani Mtar ◽  
Radhouane Fekih-Salem ◽  
Tewfik Sari
Keyword(s):  
Three Dimensional ◽  
Steady States ◽  
Dimensional System ◽  
Planar System ◽  
Predator Species ◽  
Predator Prey ◽  
Density Dependent ◽  
Existence And Stability ◽  
Dependent Growth ◽  
Transcritical Bifurcations

The objective of this study is to analyze a model of competition for one resource in the chemostat with general interspecific density-dependent growth rates, taking into account the predator–prey relationship. This relationship is characterized by the fact that the prey species promotes the growth of the predator species which in turn inhibits the growth of the first species. The model is a three-dimensional system of ordinary differential equations. With the same dilution rates, the model can be reduced to a planar system where the two models have the same local and even global behavior. The existence and stability conditions of all steady states of the reduced model in the plane are determined according to the operating parameters. Using the nullcline method, we present a geometric characterization of the existence and stability of all equilibria showing the multiplicity of coexistence steady states. The bifurcation diagrams illustrate that the steady states can appear or disappear only through saddle-node or transcritical bifurcations. Moreover, the operating diagrams describe the asymptotic behavior of this system by varying the control parameters and show the effect of the inhibition of predation on the emergence of the bistability region and the reduction until the disappearance of the coexistence region by increasing this inhibition parameter.

scholarly journals Purification and kinetics of phenylpropanoid O-methyltransferase activities from Brassica oleracea

1989 ◽  
Vol 67 (11-12) ◽  
pp. 763-769 ◽  
Author(s):  
Emidio De Carolis ◽  
Ragai K. Ibrahim
Keyword(s):  
Competitive Inhibition ◽  
Divalent Cations ◽  
Product Inhibition ◽  
Affinity Column ◽  
Ph Optimum ◽  
Substrate Interaction ◽  
Interaction Kinetics ◽  
Molecular Masses ◽  
Inhibition Studies ◽  
Kinetics Of

Two phenylpropanoid O-methyltransferase isoforms were purified to homogeneity from young cabbage leaves. They catalyzed the meta-O-methylation of caffeic and 5-hydroxyferulic acids to ferulic and sinapic acids, respectively. Both isoforms I and II exhibited different elution patterns from a Mono Q column, distinct apparent pIs on chromatofocusing, different product ratios, and stability on adenosine–agarose affinity column. On the other hand, both isoforms had similar apparent molecular masses (42 kilodaltons) and a pH optimum of 7.6. They exhibited no requirement for divalent cations and were both irreversibly inhibited by iodoacetate. Substrate interaction kinetics of the more stable isoform I, using the 5-hydroxyferulic acid and S-adenosyl-L-methionine, gave converging lines. Product inhibition studies showed competitive inhibition between S-adenosyl-L-methionine and S-adenosyl-L-homocysteine and non-competitive inhibition between the phenylpropanoid substrate and its methylated product. The kinetic patterns are consistent with an ordered bi bi mechanism, where S-adenosyl-L-methionine is the first substrate to bind and S-adenosyl-L-homocysteine is the last product released.Key words: phenylpropanoid O-methyltransferase, purification, isoforms, adenosine–agarose affinity chromatography, kinectic mechanism.

scholarly journals Bell-shaped dose response for a system with no IFFLs

2020 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
T Cell Activation ◽  
Dose Response ◽  
Cell Activation ◽  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Converse Implication ◽  
Feedforward Loop ◽  
Three Dimensional System

AbstractIt is well known that the presence of an incoherent feedforward loop (IFFL) in a network may give rise to a steady state non-monotonic dose response. This note shows that the converse implication does not hold. It gives an example of a three-dimensional system that has no IFFLs, yet its dose response is bell-shaped. It also studies under what conditions the result is true for two-dimensional systems, in the process recovering, in far more generality, a result given in the T-cell activation literature.

RELAP5-3D Analysis of OECD-NEA/NRC BFBT Benchmark

2008 ◽  
Author(s):  
Andriy Kovtonyuk ◽  
Alessandro Petruzzi ◽  
Carlo Parisi ◽  
Francesco D’Auria
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Fuel Assembly ◽  
Void Fraction ◽  
Critical Power ◽  
Three Dimensional ◽  
Dimensional System ◽  
3D Analysis ◽  
Thermal Hydraulics ◽  
Fuel Bundle

OECD-NEA and the NRC organized and sponsored the BWR Fuel Bundle Test (BFBT) Benchmark with the main purpose of assessing sub-channel and Computational Fluid Dynamic codes capabilities in estimating relevant thermal-hydraulics parameters like void fraction and critical power for a BWR boiling channel. The assessment activity is performed comparing the code calculation results with the experimental data at steady state and transient conditions available through the Japanese Nuclear Power Engineering Corporation (NUPEC). In this framework, the San Piero a Grado Nuclear Research Group (GRNSPG) of the University of Pisa (UNIPI) developed a RELAP5-3D© thermal-hydraulic nodalization of the experimental bundle. The main purpose of this activity was the assessment of the capability of the well-known three-dimensional system thermal-hydraulic code RELAP5-3D© for the prediction of relevant parameters at the fuel assembly scale. In order to exploit the large amount of experimental data available, a three dimensional thermal-hydraulic nodalization was developed, simulating all sub-channels with MULTI-D component. The overall activities resulted in challenges for the code and the code users because of the necessary large number of nodes and heat structures used and because of the different solutions that had to be found for performing a typical sub-channel analysis with a system thermal-hydraulic code. Several calculations simulating steady state conditions were performed for different fuel assembly configurations. For each of them the void fraction distributions in all fuel assembly sub-channels and pressure drops along different part of an assembly were compared with the available experimental data. In the next exercises, BWR transients were executed (turbine trip and recirculation pump trip, respectively), calculating again the void distributions and critical power conditions. The results of the activity demonstrated the capability of the RELAP5-3D© code to perform calculations using a sub-channel approach. The code was able to calculate several thermal-hydraulics parameters with high accuracy at “fuel bundle” level of resolution; the results of “sub-channel” level are instead affected by a higher error (e.g. deviation of around 20% in the prediction of void distribution). Sub-channel results showed a better agreement when considering high quality tests compared to the lower quality ones.

Kinetic Aspects of the Interaction of Blood Clotting Enzymes

1968 ◽  
Vol 19 (03/04) ◽  
pp. 364-367 ◽  
Author(s):  
H. C Hemker ◽  
P. W Hemker
Keyword(s):  
Enzyme Kinetics ◽  
Blood Clotting ◽  
Competitive Inhibition ◽  
Competitive Inhibitor ◽  
Kinetics Of

SummaryThe enzyme kinetics of competitive inhibition under conditions prevailing in clotting tests are developed and a method is given to measure relative amounts of a competitive inhibitor by means of the t — D plot.

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