scholarly journals Non-steady state mass action dynamics without rate constants: dynamics of coupled reactions using chemical potentials

2017 ◽  
Vol 14 (5) ◽  
pp. 055003 ◽  
Author(s):  
William R Cannon ◽  
Scott E Baker
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Mass Action ◽  
Chemical Potentials ◽  
Action Dynamics ◽  
Coupled Reactions

scholarly journals Reaction mechanism of the magnesium ion-dependent adenosine triphosphatase of frog muscle myosin and subfragment 1

1978 ◽  
Vol 171 (1) ◽  
pp. 165-175 ◽  
Author(s):  
M A Ferenczi ◽  
E Homsher ◽  
R M Simmons ◽  
D R Trentham
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Myosin Atpase ◽  
Forward Rate ◽  
Magnesium Ion ◽  
Skeletal Muscle Myosin ◽  
General Terms ◽  
Predominant Component ◽  
Main Components ◽  
Muscle Myosin

The Mg2+-dependent ATPase (adenosine 5′-triphosphatase) mechanism of myosin and subfragment 1 prepared from frog leg muscle was investigated by transient kinetic technique. The results show that in general terms the mechanism is similar to that of the rabbit skeletal-muscle myosin ATPase. During subfragment-1 ATPase activity at 0-5 degrees C pH 7.0 and I0.15, the predominant component of the steady-state intermediate is a subfragment-1-products complex (E.ADP.Pi). Binary subfragment-1-ATP (E.ATP) and subfragment-1-ADP (E.ADP) complexes are the other main components of the steady-state intermediate, the relative concentrations of the three components E.ATP, E.ADP.Pi and E.ADP being 5.5:92.5:2.0 respectively. The frog myosin ATPase mechanism is distinguished from that of the rabbit at 0-5 degrees C by the low steady-state concentrations of E.ATP and E.ADP relative to that of E.ADP.Pi and can be described by: E + ATP k' + 1 in equilibrium k' − 1 E.ATP k' + 2 in equilibrium k' − 2 E.ADP.Pi k' + 3 in equilibrium k' − 3 E.ADP + Pi k' + 4 in equilibrium k' − 4 E + ADP. In the above conditions successive forward rate constants have values: k' + 1, 1.1 × 10(5)M-1.S-1; k' + 2 greater than 5s-1; k' + 3, 0.011 s-1; k' + 4, 0.5 s-1; k'-1 is probably less than 0.006s-1. The observed second-order rate constants of the association of actin to subfragment 1 and of ATP-induced dissociation of the actin-subfragment-1 complex are 5.5 × 10(4) M-1.S-1 and 7.4 × 10(5) M-1.S-1 respectively at 2-5 degrees C and pH 7.0. The physiological implications of these results are discussed.

scholarly journals Determination of the steady-state turnover rates of the metabolically active pools of phosphatidylinositol 4-phosphate and phosphatidylinositol 4,5-bisphosphate in human erythrocytes

1989 ◽  
Vol 259 (3) ◽  
pp. 893-896 ◽  
Author(s):  
C E King ◽  
P T Hawkins ◽  
L R Stephens ◽  
R H Michell
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Human Erythrocytes ◽  
Turnover Rates ◽  
Metabolic Fluxes ◽  
Metabolic Pool ◽  
Phosphatidylinositol 4 ◽  
Kinetics Of ◽  
Phosphate Groups

When intact human erythrocytes are incubated at metabolic steady state in a chloride-free medium containing [32P]Pi, there is rapid labelling of the gamma-phosphate of ATP, followed by a slower labelling of the monoester phosphate groups of phosphatidylinositol 4-phosphate (PtdIns4P) and phosphatidylinositol 4,5-bisphosphate [PtdIns(4,5)P2] [King, Stephens, Hawkins, Guy & Michell (1987) Biochem. J. 244, 209-217]. We have analysed the early kinetics of the labelling of these phosphate groups, in order to determine: (a) the steady-state rates of the interconversions of phosphatidylinositol, PtdIns4P and PtdIns(4,5)P2; and (b) the fractions of the total cellular complement of PtdIns4P and PtdIns(4,5)P2 that participate in this steady-state turnover. The experimental data most closely fit a pattern of PtdIns4P and PtdIns(4,5)P2 turnover in which one-quarter of the total cellular complement of each lipid is in the metabolic pool that participates in rapid metabolic turnover, with rate constants of 0.028 min-1 for the interconversion of PtdIns and PtdIns4P, and of 0.010 min-1 for the PtdIns4P/PtdIns(4,5)P2 cycle. These rate constants represent metabolic fluxes of approx. 2.1 nmol of lipid/h per ml of packed erythrocytes between PtdIns and PtdIns4P and of approx. 5.7 nmol/h per ml of cells between PtdIns4P and PtdIns(4,5)P2.

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

scholarly journals Mechanism of a Disassembly Driven Sensing System Studied by Stopped-Flow Kinetics

2021 ◽  
Author(s):  
Cara Gallo ◽  
Suma S. Thomas ◽  
Allison Selinger ◽  
Fraser Hof ◽  
Cornelia Bohne
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Artificial Saliva ◽  
Global Analysis ◽  
Dissociation Rate ◽  
Stopped Flow ◽  
Steady State Fluorescence ◽  
Saliva Analysis ◽  
Binding Isotherms ◽  
Dissociation Rate Constants

<div> Mechanistic studies were carried out on the kinetics for the assembly of a DimerDye (DD12) and the binding of the monomeric DimerDye (DD1) with nicotine in aqueous buffer and artificial saliva. DD12 is non-fluorescent, while monomeric DD1 and DD1-nicotine fluoresce. Binding isotherms were determined from steady-state fluorescence experiments. The report includes measurements of the steady-state fluorescence at pHs 2.2, 6.3 and 12.1, and stopped-flow kinetic data for the homodimerization forming DD12 and DD1-nicotine formation in buffer and artificial saliva. Analysis of the homodimerization kinetics led to the recovery of the association and dissociation rate constants for DD12. These rate constants were used in the global analysis for the coupled kinetics for DD1-nicotine formation, which led to the determination of the association and dissociation rate constants for nicotine binding to DD1.</div>

scholarly journals A much better replacement of the Michaelis–Menten equation and its application

2019 ◽  
Vol 12 (01) ◽  
pp. 1950008
Author(s):  
Banghe Li ◽  
Bo Li ◽  
Yuefeng Shen
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Polynomial Equation ◽  
Mass Action ◽  
Reaction Process ◽  
Quasi Steady State ◽  
State Laws ◽  
New Equation ◽  
Reaction Processes ◽  
State Assumption

Michaelis–Menten equation is a basic equation of enzyme kinetics and gives acceptable approximations of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to Michaelis–Menten curve (8). This curve is derived from Quasi-Steady-State Assumption (QSSA), which has been proved always true and called Quasi-Steady-State Law by Banghe Li et al. [Quasi-steady state laws in enzyme kinetics, J. Phys. Chem. A 112(11) (2008) 2311–2321]. Here, we found a polynomial equation with total degree of four [Formula: see text] (14), which gives more accurate approximation of the reaction process in two aspects: during the quasi-steady-state of the reaction, Michaelis–Menten curve approximates the reaction well, while our equation [Formula: see text] gives better approximation; near the end of the reaction, our equation approaches the end of the reaction with a tangent line the same to that of the reaction process trajectory simulated by mass action, while Michaelis–Menten curve does not. In addition, our equation [Formula: see text] differs to Michaelis–Menten curve less than the order of [Formula: see text] as [Formula: see text] approaches [Formula: see text]. By considering the above merits of [Formula: see text], we suggest it as a replacement of Michaelis–Menten curve. Intuitively, this new equation is more complex and harder to understand. But, just because of its complexity, it provides more information about the rate constants than Michaelis–Menten curve does. Finally, we get a better replacement of the Michaelis–Menten equation by combing [Formula: see text] and the equation [Formula: see text].

scholarly journals Thermodynamic Driving Forces and Chemical Reaction Fluxes; Reflections on the Steady State

Molecules ◽  
2020 ◽  
Vol 25 (3) ◽  
pp. 699 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Steady State ◽  
Chemical Reaction ◽  
Driving Force ◽  
Driving Forces ◽  
Point Of View ◽  
Fluid Mixtures ◽  
Similar Work ◽  
Chemical Potentials ◽  
Thermodynamic Driving Force ◽  
Reacting Systems

Molar balances of continuous and batch reacting systems with a simple reaction are analyzed from the point of view of finding relationships between the thermodynamic driving force and the chemical reaction rate. Special attention is focused on the steady state, which has been the core subject of previous similar work. It is argued that such relationships should also contain, besides the thermodynamic driving force, a kinetic factor, and are of a specific form for a specific reacting system. More general analysis is provided by means of the non-equilibrium thermodynamics of linear fluid mixtures. Then, the driving force can be expressed either in the Gibbs energy (affinity) form or on the basis of chemical potentials. The relationships can be generally interpreted in terms of force, resistance and flux.

scholarly journals A structural property for reduction of biochemical networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anika Küken ◽  
Philipp Wendering ◽  
Damoun Langary ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Model Reduction ◽  
Structural Property ◽  
Large Scale ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Reduced Models ◽  
Metabolic Phenotypes ◽  
Genome Scale

AbstractLarge-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

scholarly journals Proteolytic removal of three C-terminal residues of actin alters the monomer-monomer interactions

1993 ◽  
Vol 289 (3) ◽  
pp. 897-902 ◽  
Author(s):  
M Mossakowska ◽  
J Moraczewska ◽  
S Khaitlina ◽  
H Strzelecka-Golaszewska
Keyword(s):  
Electron Microscopy ◽  
Steady State ◽  
Ionic Strength ◽  
Rate Constants ◽  
Initial Rate ◽  
Critical Concentration ◽  
Rate Of Polymerization ◽  
Low Ionic Strength ◽  
Hydrolysis Of

Homogeneous preparations of actin devoid of the three C-terminal residues were obtained by digestion of G-actin with trypsin after blocking proteolysis at other sites by substitution of Mg2+ for the tightly bound Ca2+. Removal of the C-terminal residues resulted in the following: an enhancement of the Mg(2+)-induced hydrolysis of ATP in low-ionic-strength solutions of actin; an increase in the critical concentration for polymerization; a decrease in the initial rate of polymerization; and an enhancement of the steady-state exchange of subunits in the polymer. Electron microscopy indicated an increased fragility of the filaments assembled from truncated actin. The results suggest that removal of the C-terminal residues increases the rate constants for monomer dissociation from the polymer ends and from the oligomeric species.

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