scholarly journals Mathematical Analysis of a Prototypical Autocatalytic Reaction Network

Life ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 42 ◽  
Author(s):  
Ekaterina V. Skorb ◽  
Sergey N. Semenov
Keyword(s):  
Exponential Growth ◽  
Mutual Exclusion ◽  
Reaction Network ◽  
Catalytic Cycle ◽  
Rate Laws ◽  
Experimental Systems ◽  
State Approximation ◽  
Steady State Approximation ◽  
Kinetics Of ◽  
Autocatalytic Networks

Network autocatalysis, which is autocatalysis whereby a catalyst is not directly produced in a catalytic cycle, is likely to be more common in chemistry than direct autocatalysis is. Nevertheless, the kinetics of autocatalytic networks often does not exactly follow simple quadratic or cubic rate laws and largely depends on the structure of the network. In this article, we analyzed one of the simplest and most chemically plausible autocatalytic networks where a catalytic cycle is coupled to an ancillary reaction that produces the catalyst. We analytically analyzed deviations in the kinetics of this network from its exponential growth and numerically studied the competition between two networks for common substrates. Our results showed that when quasi-steady-state approximation is applicable for at least one of the components, the deviation from the exponential growth is small. Numerical simulations showed that competition between networks results in the mutual exclusion of autocatalysts; however, the presence of a substantial noncatalytic conversion of substrates will create broad regions where autocatalysts can coexist. Thus, we should avoid the accumulation of intermediates and the noncatalytic conversion of the substrate when designing experimental systems that need autocatalysis as a source of positive feedback or as a source of evolutionary pressure.

scholarly journals Enzyme kinetics and metabolic control. A method to test and quantify the effect of enzymic properties on metabolic variables

1990 ◽  
Vol 269 (3) ◽  
pp. 697-707 ◽  
Author(s):  
L Acerenza ◽  
H Kacser
Keyword(s):  
Enzyme Concentration ◽  
Time Dependent ◽  
Experimental Systems ◽  
State Approximation ◽  
Metabolic Systems ◽  
Steady State Approximation ◽  
Before And After ◽  
Factor Alpha ◽  
Metabolic Variables ◽  
Time Invariant

It is usual to study the sensitivity of metabolic variables to small (infinitesimal) changes in the magnitudes of individual parameters such as an enzyme concentration. Here, the effect that a simultaneous change in all the enzyme concentrations by the same factor alpha (Co-ordinate-Control Operation, CCO) has on the variables of time-dependent metabolic systems is investigated. This factor alpha can have any arbitrary large value. First, we assume, for each enzyme measured in isolation, the validity of the steady-state approximation and the proportionality between reaction rate and enzyme concentration. Under these assumptions, any time-invariant variable may behave like a metabolite concentration, i.e. S alpha = Sr (S-type), or like a flux, i.e. J alpha = alpha Jr (J-type). The subscripts r and alpha correspond to the values of the variable before and after the CCO respectively. Similarly, time-dependent variables may behave according to S alpha (t/alpha) = Sr (t) (S-type) or to J alpha (t/alpha) = alpha J r (t) (J-type). A method is given to test these relationships in experimental systems, and to quantify deviations from the predicted behaviour. A positive test for deviations proves the violation of some of the assumptions made. However, the breakdown of the assumptions in an enzyme-catalysed reaction, studied in isolation, may or may not affect significantly the behaviour of the system when the component reaction is embedded in the metabolic network.

scholarly journals The Kinetics of the Oxidation of Lysine by μ-Peroxo-Bridged Binuclear Cobalt (III) Complex of Succinimide in Aqueous Hydrochloric Acid Medium

2017 ◽  
Vol 2 (1) ◽  
pp. 37-43
Author(s):  
Ahmed Adetoro ◽  
Suleiman O. Idris ◽  
Ameh D. Onu ◽  
Friday G. Okibe
Keyword(s):  
Ionic Strength ◽  
Outer Sphere ◽  
Hydrogen Ions ◽  
First Order ◽  
Hydrochloric Acid Medium ◽  
State Approximation ◽  
Steady State Approximation ◽  
Probable Reaction ◽  
Electron Transfer Processes ◽  
Kinetics Of

AbstractKinetics of oxidation of Lysine (Lys) and mechanisms by μ-peroxo bis[bis(ethylenediamine)succinimidato-dicobalt(III)]dinitratedihydrate; [LCo(μ-O2)CoL](NO3)2.2H2O (L = suc(en)2), hereafter the complex, was investigated at 420 nm wavelength of maximum absorption of the complex under the conditions hydrogen ions concentration = 1.8 × 10−2 mol dm−3, temperature = 24 ± 1 °C, [LCo(μ-O2)CoL2+] = 1.4 × 10−4 mol dm−3 and ionic strength = 0.5 mol dm−3. First order in [LCo(μ-O2)CoL2+] and [Lys] were obtained but inverse first order in [H+]. The proposed overall rate equation is as shown:$$Rate = ({{k_1 } \over {k_2 }} + {{K_1 k_3 } \over {k_4 }}{1 \over {[H^ + ]}})[LCo(\mu O_2 )CoL^{2 + } ][Lys]$$Rate of the reaction decreases when hydrogen ions concentration increase and exhibited converse effect with increase in concentration of ionic strength from 0.1 – 1.3 mol dm−3. Added cations and anions affected the reaction rate and the Michaelis-Menten plot passed through the origin indicating no absence of intermediate complex in the electron transfer processes. Putting all the results obtained together, the most probable reaction mechanism is in favour of outer-sphere and an appropriate rate law is established using steady state approximation.

scholarly journals The Kinetics of the Oxidation of Lysine by μ-Peroxo-Bridged Binuclear Cobalt (III) Complex of Succinimide in Aqueous Hydrochloric Acid Medium

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
A Adetoro ◽  
S.O. Idris ◽  
A.D. Onu ◽  
F.G Okibe
Keyword(s):  
Ionic Strength ◽  
Outer Sphere ◽  
Hydrogen Ions ◽  
First Order ◽  
Hydrochloric Acid Medium ◽  
State Approximation ◽  
Steady State Approximation ◽  
Probable Reaction ◽  
Electron Transfer Processes ◽  
Kinetics Of

Abstract Kinetics of oxidation of Lysine (Lys) and mechanisms by μ-peroxo bis[bis(ethylenediamine)succinimidato-dicobalt(III)]dinitratedihydrate; [LCo(μ-O2)CoL](NO3)2.2H2O (L = suc(en)2), hereafter the complex, was investigated at 420 nm wavelength of maximum absorption of the complex under the conditions hydrogen ions concentration = 1.8 × 10-2 mol dm-3, temperature = 24 ± 1 °C, [LCo(μ-O2)CoL2+] = 1.4 × 10-4 mol dm-3 and ionic strength = 0.5 mol dm-3. First order in [LCo(μ- O2)CoL2+] and [Lys] were obtained but inverse first order in [H+]. The proposed overall rate equation is as shown: Rate of the reaction decreases when hydrogen ions concentration increase and exhibited converse effect with increase in concentration of ionic strength from 0.1 - 1.3 mol dm-3. Added cations and anions affected the reaction rate and the Michaelis-Menten plot passed through the origin indicating no absence of intermediate complex in the electron transfer processes. Putting all the results obtained together, the most probable reaction mechanism is in favour of outer-sphere and an appropriate rate law is established using steady state approximation.

Synthesis and Kinetics of Highly Substituted Piperidines in the Presence of Tartaric Acid as a Catalyst

2018 ◽  
Vol 21 (4) ◽  
pp. 302-311
Author(s):  
Younes Ghalandarzehi ◽  
Mehdi Shahraki ◽  
Sayyed M. Habibi-Khorassani
Keyword(s):  
Ambient Temperature ◽  
Tartaric Acid ◽  
Aromatic Aldehydes ◽  
One Pot ◽  
Rate Determining Step ◽  
State Approximation ◽  
Solvent Free Conditions ◽  
Steady State Approximation ◽  
Absorbance Changes ◽  
The One

Aim & Scope: The synthesis of highly substituted piperidine from the one-pot reaction between aromatic aldehydes, anilines and β-ketoesters in the presence of tartaric acid as a catalyst has been investigated in both methanol and ethanol media at ambient temperature. Different conditions of temperature and solvent were employed for calculating the thermodynamic parameters and obtaining an experimental approach to the kinetics and mechanism. Experiments were carried out under different temperature and solvent conditions. Material and Methods: Products were characterized by comparison of physical data with authentic samples and spectroscopic data (IR and NMR). Rate constants are presented as an average of several kinetic runs (at least 6-10) and are reproducible within ± 3%. The overall rate of reaction is followed by monitoring the absorbance changes of the products versus time on a Varian (Model Cary Bio- 300) UV-vis spectrophotometer with a 10 mm light-path cell. Results: The best result was achieved in the presence of 0.075 g (0.1 M) of catalyst and 5 mL methanol at ambient temperature. When the reaction was carried out under solvent-free conditions, the product was obtained in a moderate yield (25%). Methanol was optimized as a desirable solvent in the synthesis of piperidine, nevertheless, ethanol in a kinetic investigation had none effect on the enhancement of the reaction rate than methanol. Based on the spectral data, the overall order of the reaction followed the second order kinetics. The results showed that the first step of the reaction mechanism is a rate determining step. Conclusion: The use of tartaric acid has many advantages such as mild reaction conditions, simple and readily available precursors and inexpensive catalyst. The proposed mechanism was confirmed by experimental results and a steady state approximation.

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