Balancing the chemical equations and their steady-state approximations in the complex reaction mechanism: linear algebra techniques

2020 ◽  
Vol 10 (12) ◽  
pp. 5247-5252 ◽  
Author(s):  
Faisal Sultan ◽  
Muhammad Shahzad ◽  
Mehboob Ali ◽  
Wajiha Adnan ◽  
Waqar Azeem Khan
Keyword(s):  
Steady State ◽  
Reaction Mechanism ◽  
Linear Algebra ◽  
Complex Reaction ◽  
Chemical Equations

scholarly journals Serine acetyltransferase of Escherichia coli: substrate specificity and feedback control by cysteine

2003 ◽  
Vol 375 (3) ◽  
pp. 745-752 ◽  
Author(s):  
V. John HINDSON
Keyword(s):  
Escherichia Coli ◽  
Steady State ◽  
Reaction Mechanism ◽  
Binding Site ◽  
Ternary Complex ◽  
Random Order ◽  
Hydroxyl Group ◽  
Acyl Donor ◽  
Complex Reaction ◽  
Serine Acetyltransferase

Although SAT (serine acetyltransferase) of Escherichia coli, which catalyses the first step in cysteine synthesis, proceeds via a random-order ternary complex reaction mechanism [Hindson and Shaw (2003) Biochemistry 42, 3113–3119], it has been suggested that the nearly identical enzyme from Salmonella typhimurium might involve an acetyl-enzyme intermediate [Leu and Cook (1994) Protein Peptide Lett. 1, 157–162]. In this study the alternative acetyl acceptor threonine and the alternative acyl donor, propionyl-CoA were used to further investigate the reaction mechanism of SAT from E. coli. Steady-state kinetic data and dead-end inhibition studies were again diagnostic of a random-order ternary complex reaction mechanism for alternative substrates. Since earlier kinetic studies with SAT from S. typhimurium suggested that cysteine competes with acetyl-CoA for binding, rather than serine with which it is isostructural, the specificity of the serine-binding pocket was assessed with three substrate mimics; β-hydroxypropionic acid, glycine and ethanolamine. The data show that SAT interacts productively with the amino and hydroxymethyl moieties of serine, whereas the carboxyl group provides an essential contribution to binding strongly, supporting a view that cysteine will interact productively at the serine-binding site. Furthermore, since the hydroxymethyl contact region of the serine-binding site appears able to accommodate the methylene and acetyl moeties of threonine and O-acetyl-serine respectively, the site is unlikely to provide obligatory short-range contacts with the hydroxyl group of serine, a prerequisite for exclusion of cysteine. Such a proposal is supported by the results of micro-calorimetric studies which show that cysteine competes with serine for binding to SAT rather than with CoA. It follows that tight binding of cysteine at the serine-binding site near the catalytic centre may be the effector of a substantial reduction in the affinity of SAT for CoA, yielding the observed pattern of steady-state inhibition and the mechanism by which cysteine mediates effective end-product control of its synthesis.

Determination of Complex Reaction Mechanisms

2006 ◽  
Author(s):  
John Ross ◽  
Igor Schreiber ◽  
Marcel O. Vlad
Keyword(s):  
Reaction Mechanism ◽  
Reaction Mechanisms ◽  
Reaction Pathway ◽  
Chemical Species ◽  
Rate Coefficients ◽  
Chemical System ◽  
Evolutionary Development ◽  
Complex Reaction ◽  
Oscillatory Reactions

In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of Complex Reaction Mechanisms authors John Ross, Igor Schreiber, and Marcel Vlad present several systematic approaches for obtaining information on the causal connectivity of chemical species, on correlations of chemical species, on the reaction pathway, and on the reaction mechanism. Basic pulse theory is demonstrated and tested in an experiment on glycolysis. In a second approach, measurements on time series of concentrations are used to construct correlation functions and a theory is developed which shows that from these functions information may be inferred on the reaction pathway, the reaction mechanism, and the centers of control in that mechanism. A third approach is based on application of genetic algorithm methods to the study of the evolutionary development of a reaction mechanism, to the attainment given goals in a mechanism, and to the determination of a reaction mechanism and rate coefficients by comparison with experiment. Responses of non-linear systems to pulses or other perturbations are analyzed, and mechanisms of oscillatory reactions are presented in detail. The concluding chapters give an introduction to bioinformatics and statistical methods for determining reaction mechanisms.

Reaction mechanism of rat-liver ADH with ethanol and NAD in the steady state

1977 ◽  
Vol 2 (3) ◽  
pp. 171-177 ◽  
Author(s):  
M. Feraudi ◽  
M. Kohlmeier ◽  
G. Schmolz
Keyword(s):  
Steady State ◽  
Reaction Mechanism ◽  
Rat Liver

scholarly journals Unveiling the Rate-Limiting Step of the Bc1 Complex Reaction Mechanism

2019 ◽  
Vol 116 (3) ◽  
pp. 419a
Author(s):  
Angela M. Barragan ◽  
Alexander V. Soudackov ◽  
Zaida Luthey-Schulten ◽  
Klaus Schulten ◽  
Sharon Hammes-Schiffer ◽  
...  
Keyword(s):  
Reaction Mechanism ◽  
Complex Reaction ◽  
Bc1 Complex ◽  
Rate Limiting Step ◽  
Limiting Step ◽  
Rate Limiting

Graphical rules of steady-state reaction systems

1981 ◽  
Vol 59 (4) ◽  
pp. 737-755 ◽  
Author(s):  
Chou Kuo-Chen ◽  
Sture Forsen
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Mathematical Proof ◽  
Complex Reaction ◽  
Consecutive Reaction ◽  
Reaction Systems ◽  
First Order ◽  
Mathematical Proofs ◽  
Pseudo First Order ◽  
Manual Calculation

Four rules to deal with first-order or pseudo-first-order steady-state reaction systems are presented.By means of Rule 1, we can immediately write down the apparent rate constants of consecutive reaction systems. This rule is actually the same as the "Rule of Thumb" proposed by Gilbert, but here its mathematical proof is given.Rule 2 and Rule 3 may serve to derive the apparent rate constants of various complex reaction systems. In comparison with the general algebraic methods, these two rules can simplify laborious calculations that would otherwise be tedious and liable to errors.Rule 4 presents a new schematic method to calculate the concentrations of the reactants. The new method, in simplifying the calculation of complex problems, is extraordinarily efficacious in comparison with the existing schematic methods. For complex mechanisms which are too complicated to be treated with the general manual calculation method, the practical calculations show that we can easily write down the desired results by means of Rule 4.In addition, Rules 2, 3, and 4 include corresponding check formulae, by use of which we can avoid missing subgraphs to be counted. Their advantages will be manifested particularly in dealing with complex mechanisms.The mathematical proofs of these rules are given in the Appendices.

Optimal control of a plug flow reactor with a complex reaction mechanism

1993 ◽  
Vol 97 (45) ◽  
pp. 11689-11695 ◽  
Author(s):  
Atipat Rojnuckarin ◽  
Christodoulos A. Floudas ◽  
Herschel Rabitz ◽  
Richard A. Yetter
Keyword(s):  
Optimal Control ◽  
Reaction Mechanism ◽  
Flow Reactor ◽  
Plug Flow ◽  
Plug Flow Reactor ◽  
Complex Reaction
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