Two-step Reversible Reaction Research Articles

Mathematical and sensitivity analysis for chemical species in multistep dynamical system: A computational study

This study presents a significant contribution to the field of chemical kinetics by providing a detailed analysis of a multi-step chemical kinetic process using ordinary differential equations (ODEs). The aim is to describe complex chemical processes' kinetics and the steady-state behavior of chemical species. The research employs reduction techniques to simplify the model by separating fast and slow processes based on their time scales, with a focus on a two-step reversible reaction mechanism. Special consideration is given to the phase flow of solution trajectories near equilibrium points, providing a clear depiction of system behavior. MATLAB simulations demonstrate the physical properties of observed data, while sensitivity analysis reveals parameters' impact on species behavior. Overall, this study enhances our understanding of chemical kinetics and offers insights into modeling complex reaction processes, with implications for various applications in chemistry and related fields.

Computing the solution trajectories, steady state approximation, and sensitivity analysis in complex chemical reaction mechanism

Ordinary differential equations are often employed in chemical kinetics mathematical modeling. The theoretical results for a model of a multi-step chemical kinetic process are presented in this article. This model seeks to describe both the complicated kinetics of complex chemical processes and the steady state behavior of chemical species. Reduction techniques are used to divide fast and slow processes according to their time scales, which simplifies the model. As a result, the quick processes are removed, making the slow processes the main emphasis of a reduced-dimensional model. The paper concentrates on a two-step reversible reaction mechanism for model reduction, which reduces the complexity of the entire reaction process. The phase flow of solution trajectories close to equilibrium points is also given special consideration in the analysis as it offers a clear and pertinent depiction of the behavior of the system. The physical properties of the observed data are further shown via MATLAB simulations. Sensitivity analysis computes parameters, revealing their impact on species behavior, visually presenting the parameter impact.

Dynamics of two-step reversible enzymatic reaction under fractional derivative with Mittag-Leffler Kernel.

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.

Methanolysis of Poly(lactic Acid) Using Catalyst Mixtures and the Kinetics of Methyl Lactate Production

Polylactic acid (PLA) is a leading bioplastic of which the market share is predicted to increase in the future; its growing production capacity means its end-of-life treatment is becoming increasingly important. One beneficial disposal route for PLA is its chemical recycling via alcoholysis. The alcoholysis of PLA leads to the generation of value-added products alkyl lactates; this route also has potential for a circular economy. In this work, PLA was chemically recycled via methanolysis to generate methyl lactate (MeLa). Four commercially available catalysts were investigated: zinc acetate dihydrate (Zn(OAc)2), magnesium acetate tetrahydrate (Mg(OAc)2), 4-(dimethylamino)pyridine (DMAP), and triazabicyclodecene (TBD). Dual catalyst experiments displayed an increase in reactivity when Zn(OAc)2 was paired with TBD or DMAP, or when Mg(OAc)2 was paired with TBD. Zn(OAc)2 coupled with TBD displayed the greatest reactivity. Out of the single catalyst reactions, Zn(OAc)2 exhibited the highest activity: a higher mol% was found to increase reaction rate but plateaued at 4 mol%, and a higher equivalent of methanol was found to increase the reaction rate, but plateaued at 17 equivalents. PLA methanolysis was modelled as a two-step reversible reaction; the activation energies were estimated at: Ea1 = 25.23 kJ∙mol−1, Ea2 = 34.16 kJ∙mol−1 and Ea-2 = 47.93 kJ∙mol−1.

Investigation of hot jet on active control of oblique detonation waves

The hot jet injection is utilized to actively control the oblique detonation wave, such as initiating and stabilizing an oblique detonation wave at a desired position that is shorter than the length of induction zone, and adjust the height of the oblique detonation wave at the exit of combustor when the oblique detonation wave engine is working on off-design flight conditions. The fifth order Weighted Essentially Non-Oscillatory (WENO) scheme and a two-step reversible reaction mechanism of the stoichiometric H2/Air are adopted in the simulations. With the help of hot jet injection, the transition from inert oblique shock wave to the oblique detonation wave immediately occurs near the position of hot jet injection, and consequently the length of combustor can be reduced. The angle of oblique detonation wave also decreases as the hot jet injection approaches the nose of wedge. Additionally, the height of the oblique detonation wave at the exit of combustor can be flexibly adjusted, and also depends on the injection position and the strength of the hot jet. If the velocity of the hot jet is too weak to directly trigger the overall oblique detonation wave at the position of injection, increasing the injection pressure will improve the strength of the hot jet and results in a successful transition.

C-matrix and invariants in chemical kinetics: A mathematical concept

To treat a realistic chemical system, such as a liquid phase dehydrogenation reaction, a chemical scheme, which describes the chemical kinetics in terms of the small number of reaction progress variables is needed. Based on the matrix algebra, we analyse the key components, elements and reactions in the mechanism, C-matrix. Reduction techniques exploit the time-scale separation into fast and slow modes by computing the dimension reduced model via the elimination of fast mode subjecting them to the slow one. The two-step reversible reaction mechanism is considered for model reduction and to simplify the complexity of reaction mechanisms. They give a meaningful picture, but for maximum clarity, the phase flow of the solution trajectories near the equilibrium point is exploited. The Lyapunov function is applied for the stability analysis. To describe the physical behaviour of the reaction mechanism, graphical results are measured while refinement of the initial approximation is tabulated at the end.

Computational study of conformational changes in human 3-hydroxy-3-methylglutaryl coenzyme reductase induced by substrate binding

The enzyme 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGR) is mainly involved in the regulation of cholesterol biosynthesis. HMGR catalyses the reduction of 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA) to mevalonate at the expense of two NADPH molecules in a two-step reversible reaction. In the present study, we constructed a model of human HMGR (hHMGR) to explore the conformational changes of HMGR in complex with HMG-CoA and NADPH. In addition, we analysed the complete sequence of the Flap domain using molecular dynamics (MD) simulations and principal component analysis (PCA). The simulations revealed that the Flap domain plays an important role in catalytic site activation and substrate binding. The apo form of hHMGR remained in an open state, while a substrate-induced closure of the Flap domain was observed for holo hHMGR. Our study also demonstrated that the phosphorylation of Ser872 induces significant conformational changes in the Flap domain that lead to a complete closure of the active site, suggesting three principal conformations for the first stage of hHMGR catalysis. Our results were consistent with previous proposed models for the catalytic mechanism of hHMGR.Communicated by Ramaswamy H. Sarma

A NEW MOUSE MODEL TO UNRAVEL THE MECHANISM OF SIRT1 ACTIVATION

SIRT1 is an NAD+-dependent deacetylase and one of the seven-member family of sirtuins that play a key role in the regulation of metabolism, DNA repair, inflammation, chromatin structure, and aging in mammals. Activation of SIRT1 improves mitochondrial function, treats hyperglycemia and fatty liver in mice and provides cardioprotection. The SIRT1 deacetylase reaction is one of the most complicated in the biological world, carrying out a two-step reversible reaction involving a covalently attached peptidyl intermediate. In collaboration with the de Cabo lab, we reported that STACs can increase the mean and maximum lifespan of mice by up to 22%. In humans, SRT2104, was able to alleviate psoriasis. Whether STACs such as resveratrol and SRT1720 mediate their health benefits via direct SIRT1 activation remains an unsolved question in the field, but one that will help guide drug development. SIRT1-activating compounds (STACs) work by binding to the N terminus of SIRT1 and lowering the Km for the substrate. Mutation of the mE222 residue adjacent to the STAC binding domain (SCD) prevents SIRT1 activation. We have generated a knock-in mouse model that is a homozygous mutant for E222K and are using it to precisely determine which of the biological effects if STACs such as resveratrol are due to SIRT1 activation. These studies will determine which diseases STACs could treats in humans and how they can be improved to increase their potency.

Effect of SDS on kinetics for Co-Cyanex 272 complex in a neutral micellar phase

Cobalt extraction by Cyanex 272, Bis(2,4,4-trimethylpentyl)phosphinic acid, (HR) in micellar solution has been shown to be a two-step reversible reaction and the reaction rate constants for the forward and reverse reactions have been obtained. In this investigation the influence of the addition of anionic surfactants, Sodium Dodecyl Sulphate (SDS), on the rate of extraction of cobalt from the aqueous phase by Cyanex 272 in the micelle phase was investigated. The anion surfactant (SDS) was found to increase the rate of extraction. This could be mainly ascribed to the increase in the local concentration of cobalt at the interface generated by the electrostatic surface potential with added surfactant. The effect of charge on the reaction rate has been modelled based on the electrostatic surface potential generated by the added surfactant.

Diastereoselective Imine-Bond Formation through Complementary Double-Helix Formation

Optically active amidine dimer strands having a variety of chiral and achiral linkers with different stereostructures are synthesized and used as templates for diastereoselective imine-bond formations between two achiral carboxylic acid monomers bearing a terminal aldehyde group and racemic 1,2-cyclohexanediamine, resulting in a preferred-handed double helix stabilized by complementary salt bridges. The diastereoselectivity of the racemic amine is significantly affected by the chirality of the amidine residues along with the rigidity and/or chirality of the linkers in the templates. NMR and kinetic studies reveal that the present imine-bond formation involves a two-step reversible reaction. The second step involves formation of a preferred-handed complementary double helix assisted by the chiral amidine templates and determines the overall reaction rate and diastereoselectivity of the amine.

Binding of nitric oxide to water-soluble iron(III) porphyrins

Binding equilibrium of NO to three water-soluble iron(III) porphyrins was examined spectrophotometrically in aqueous solution. Effects of electron-donor ability and hydrophobicity of porphyrin on the NO binding were discussed on the basis of the thermodynamic data for the binding. In aqueous and organic mixed solvents, NO binding to 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrinatoiron(III) was found to be a two-step reversible reaction. With increasing the NO partial pressure, the Fe(III) complex firstly produces Fe(III)–NO species, followed by generation of Fe(II)–NO species. The results suggest that water would play an essential role in this phenomenon.

Kinetic Study of Aryl Substitutions with Lithium Organocopper Reagents

Lithium organocuprates can undergo substitution with alkyl and aryl halides which form direct carbon-carbon bond coupling. Like many other organometallic reagents, however, the mechanisms of these reactions are still unknown. This paper presents preliminary work for the kinetic study of substitution in simple aryl iodides with lithium dimethylcuprate. The experimental results suggested the presence of a stable intermediate. A two-step reversible reaction model was employed to calculate the reaction rate in each step. It was found that the second step is the rate-determining step. Along with a discussion of the intermediate structure, a mechanism is proposed to account for both the experimental and theoretical results.

Substitution of phosphine in the complex [RhCl(cyclooctadiene)(phosphine)] by 1-hexene

The substitution of phosphine in the [RhCl(COD)(phosphine)] complex (1), where phosphine is PPh3 or 1/2 BPS-2 [bis(diphenylphosphinoethyl)tetramethyldisiloxane] and COD is cycloocta-1,5-diene, by 1-hexene is a two-step reversible reaction. All individual rate constants and equilibrium constants were determined spectrophotometrically and associative mechanism occurring via the formation of five-coordinated [RhCl(COD)(phosphine)(1-hexene)] (2) was inferred. The rate-determining step changes from the first- to the second-one as the concentration of 1-hexene increases. An excess of phosphine shifts the equilibrium towards complex (2).