Rate Constants Of Elementary Steps Research Articles

Kinetic study on the molecular mechanism of light-driven inward proton transport by schizorhodopsins

Schizorhodopsins (SzRs) are light-driven inward proton pumping membrane proteins. A H+ is released to the cytoplasmic solvent from the chromophore, retinal Schiff base (RSB), after light absorption, and then another H+ is bound to the RSB at the end of photocyclic reaction. However, the mechanistic detail of H+ transfers in SzR is almost unknown. Here we studied the deuterium isotope effect and the temperature dependence of the reaction rate constants of elementary steps in the photocycles of SzRs. The former indicated that deprotonation and reprotonation of RSB is mainly accomplished by H+ hopping between heavy atoms with similar H+ affinity. Furthermore, the temperature dependence of the rate constants revealed that most of H+ transfer events have a high entropy barrier. In contrast, the activation enthalpy and entropy of extremely thermostable SzR (MsSzR) are significantly higher than other types of SzRs (SzR1 and MtSzR) suggesting that its highly thermostable structure is optimized with at the cost of slower reaction rates at ambient temperatures.

Automation of chemical kinetics: Status and challenges

Driven by synergic advancements in high performance computing and theory, the capability to estimate rate constants from first principles has evolved considerably recently. When this knowledge is coupled with a procedure to determine a list of all reactions relevant to describe the evolution of a reacting system, it becomes possible to envision a methodology to predict theoretically the reaction kinetics. However, if a thorough examination of all possible reaction channels is desired, the number of reactions for which a rate constant estimate is needed can become quite large. This determines the need for rate constant estimation automation. In the present work, the status of this rapidly evolving field is reviewed, with emphasis on recent advancements and present challenges. Thermochemistry is the field where automation is most advanced. Entropies, heat capacities, and enthalpies can be determined efficiently with accuracy comparable to experiments for most chemical species containing a limited number of atoms, while machine learning can be used to improve the computational predictions for large chemical species using reduced computational resources. Several approaches have been proposed to automatically investigate the reactivity over complex potential energy surfaces, while rate constants for elementary steps can be determined accurately for several reaction classes, such as abstraction, addition, beta-scission, and isomerization. Kinetic mechanisms can be automatically generated using methodologies that differ for level of complexity and required physical insight. Among the challenges that are still to be met are the estimation of rate constants for intrinsically multireference reaction classes, such as barrierless processes, the containment of the number of reactions to screen in mechanism development, and the integration of the existing automated software. It is suggested that the synergy between experiment and theory should evolve towards a stage where experiments are focused on the estimation of parameters where theoretical tools are least predictive, and vice versa.

Kinetics and Mechanisms of Protein Adsorption and Conformational Change on Hematite Particles.

Adsorption kinetics and conformational changes of a model protein, bovine serum albumin (BSA, 0.1, 0.5, or 1.0 g/L), on the surface of hematite (α-Fe2O3) particles in 39 ± 9, 68 ± 9, and 103 ± 8 nm, respectively, were measured using attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. As the particle size increases, the amount of adsorbed BSA decreases, but the loss in the helical structure of adsorbed BSA increases due to the stronger interaction forces between adsorbed BSA and the larger particles. On 39 or 68 nm hematite particles, refolding of adsorbed BSA can be induced by protein-protein interactions, when the protein surface coverage exceeds certain critical values. Two-dimensional correlation spectroscopy (2D-COS) analysis of time-dependent ATR-FTIR spectra indicate that the increase in the amount of adsorbed BSA occurs prior to the loss in the BSA helical structure in the initial stage of adsorption processes, whereas an opposite sequence of the changes to BSA conformation and surface coverage is observed during the subsequent refolding processes. Desorption experiments show that replacing the protein solution with water can quench the refolding, but not the unfolding, of adsorbed BSA. A kinetic model was proposed to quantitatively describe the interplay of adsorption kinetics and conformational change, as well as the effects of particle size and initial protein concentration on the rate constants of elementary steps in protein adsorption onto a mineral surface.

Systematic Application of the Principle of Detailed Balancing to Complex Homogeneous Chemical Reaction Mechanisms.

It is not uncommon for proposed complex reaction mechanisms to violate the principle of detailed balancing. Here, we draw attention to three ways in which such violations can occur: reversible reaction loops where the rate constants do not attain closure, illegal loops, and reversible steps having rate equations in the forward and reverse directions that are inconsistent with the equilibrium expressions. We present two simple methods to test whether a proposed mechanism is consistent with the first two aspects of the principle of detailed balancing. Both methods are restricted to closed homogeneous isothermal reactions having mechanisms that consist of stoichiometrically balanced reaction steps. The first method is restricted to mechanisms in which all reaction steps are reversible; values of Δf G° are assigned to all reaction species, equilibrium constants are then computed for all steps, and all rate constants for elementary steps are constrained by the relationship Keq = kf/ kr. The second method is applicable to mechanisms that can consist of a series of reversible and/or irreversible reaction steps. One first examines the subset of reversible steps to determine whether any of these steps are stoichiometrically equivalent to a combination of any of the other steps. If so, the forward and reverse rate expressions must yield equilibrium constants that are in agreement with the stoichiometric relationships. Next, the complete set of steps is examined to look for "illegal reaction loops". Both of these procedures are performed by constructing matrices that represent the stoichiometries of the various reaction steps and then performing row reductions to identify basis sets of loops. A method based on linear programming is described that determines whether a mechanism contains any illegal loops. These methods are applied in the analysis of several published reaction mechanisms.

Catalytic consequences of cation and anion substitutions on rate and mechanism of oxidative coupling of methane over hydroxyapatite catalysts

The identity and rate constants of elementary steps in primary reactions of oxidative coupling of methane (OCM) over Pb2+ and/or F− substituted hydroxyapatite (HAP, Pb-HAP, HAP-F, and Pb-HAP-F) catalysts have been studied. The rigorous kinetics analysis suggests that HAP and HAP-F initiated the reaction between adsorbed methane and O2 following Langmuir-Hinshelwood behavior. The Pb-HAP and Pb-HAP-F, however, enabled the reaction between gaseous methane and adsorbed O2 in the Eley-Rideal mechanism. The F− substitution of OH− weakened both O2 adsorption and CH bond activation, leading to low methane conversion and slightly higher C2H6 selectivity. The substitution of Ca2+ by Pb2+ weakened both methane and oxygen adsorptions, but maintained CH bond activation and raised C2H6 selectivity. The present analysis explored for the first time the effects of cation and/or anion in HAP on OCM reactions in which the analysis has been detailed and quantified in the nature of the mechanism-based kinetic models.

Automation of the information content analysis of kinetic parameters

The aim of this work has been to automate the analysis of kinetic measurements in solving inverse problems in order to recognize the number and form of the independent combinations of reaction rate constants. Software for determining the basis of nonlinear parametric functions of the kinetic parameters of a mathematical model for the mechanism of a complex chemical reaction has been developed and described. The main stages of program construction with the use of a search algorithm for the independent combinations of the rate constants of elementary steps in the mechanism of a complex chemical reaction based on experimental data on the concentrations of reactants are considered.

Mechanism of the reaction between N,N′-diphenyl-1,4-benzoquinone diimine and thiophenol in n-propanol

We studied the kinetics of the reaction between N,N′-diphenyl-1,4-benzoquinone diimine and thiophenol in n-propanol at 343 K and compared the results with the same data for the chlorobenzene medium. The replacement of chlorobenzene with n-propyl alcohol increases the reaction rate by one order of magnitude. The order of the reaction with respect to thiophenol was determined to be 1.0 in both solvents, and the order of the reaction with respect to quinone diimine decreases from 1.5 to 1.2 on passing from chlorobenzene to n-propanol. In contrast to the reaction in chlorobenzene, where the radical chain mechanism is realized, the reaction in n-propanol simultaneously proceeds via a radical chain channel and a heterolytic channel. In the absence of an initiator and at equal reactant concentrations of ∼10−4 mol/L, the reaction rates in both pathways are commensurable. The chain reaction is characterized by short chains whose length is a few units. Chain generation in the absence of an initiator occurs by the direct bimolecular reaction between the reactants, whose rate constant in n-propanol is one order of magnitude higher than that in chlorobenzene, which is explained by the high polarity of the transition state in this endothermic homolytic reaction. The reaction mechanism was proposed, and, for this mechanism, the rate constants of elementary steps were determined.

SurfKin: an ab initio kinetic code for modeling surface reactions.

In this article, we describe a C/C++ program called SurfKin (Surface Kinetics) to construct microkinetic mechanisms for modeling gas-surface reactions. Thermodynamic properties of reaction species are estimated based on density functional theory calculations and statistical mechanics. Rate constants for elementary steps (including adsorption, desorption, and chemical reactions on surfaces) are calculated using the classical collision theory and transition state theory. Methane decomposition and water-gas shift reaction on Ni(111) surface were chosen as test cases to validate the code implementations. The good agreement with literature data suggests this is a powerful tool to facilitate the analysis of complex reactions on surfaces, and thus it helps to effectively construct detailed microkinetic mechanisms for such surface reactions. SurfKin also opens a possibility for designing nanoscale model catalysts.

The regularities of reversible chain reactions in the equilibrium state

The characteristics of dynamic equilibrium states in the experimentally studied reversible chain reactions of quinoneimines with hydroquinones and in some reversible chain reactions with similar mechanisms are discussed. The concentrations of radicals and non-radical participants were calculated. The equilibrium concentrations of the same reaction participants depend only on the initial reactant concentrations, being independent of the number of chain initiation-chain termination steps in the reaction mechanism. The results of mathematical modeling of reversible chain reactions using the experimentally determined rate constants for elementary steps of a reaction in the quinoneimine-hydroquinone system are presented. Expressions relating the equilibrium constants of elementary steps to each other and to the equilibrium constant of the total stoichiometric reaction are derived. Examples of other actual reversible chain reactions are presented, indicating that such reactions are widespread.

Analytical approach for estimating kinetics of elementary steps on transition metals: Tunneling, trends and Brönsted–Evans–Polanyi relation

An overall formulation of an adiabatic approach, which combines adsorption characteristics of reactants and products with an analytical method of searching for the saddle point (SP) on semi-empirical adiabatic potential energy surface (APES), is presented for studying surface reactions kinetics. The following cases are analyzed: (i and ii) breaking or formation of a chemical bond, (iii) diffusion hopping of a molecule on a metal surface, and (iv) subsurface penetration of a metal surface. Numerical results for the activation energies and rate constants of elementary steps of CO oxidation, oxygen dissociative adsorption and water dissociation on transition metals (Pt, Pd, etc.) at the zero-coverage limit are presented. Specifically, the reaction energy dependencies of the kinetic characteristics like activation energy are presented as Brönsted–Evans–Polanyi relation. Moreover, the effect of tunneling along reaction coordinate is shown to be significant for several steps. The calculated diffusitivities of CO on (111) surfaces of several metals are correlated with the corresponding adsorption energies. The mechanism of subsurface oxygen penetration in a cluster resembling a (111) palladium surface is investigated. Approximate dependence of the activation energy of the oxygen subsurface diffusion on surface coverage is suggested.

Kinetics of the gas-phase thermal chlorination of methane

Based on information concerning the rate constants of elementary steps corrected with consideration for experimental data obtained under laboratory, pilot-plant, and industrial conditions, the kinetics of the gas-phase process of thermal chlorination of methane was considered. The form of the rate equation of the process depends on the mode of chain termination. Of four possible variants, cross termination with the participation of a chlorine atom and a hydrocarbon radical and quadratic-law termination on hydrocarbon radicals are significant under industrial conditions. The fractions of the participation of either of these variants at various degrees of chlorine conversion were determined. Rate equations were found to describe the chlorination of methane, methyl chloride, methylene chloride, and chloroform with cross and quadratic-law chain terminations. The overall kinetic order of these equations with respect to reactants was 1.5. Combined equations that imply the simultaneous occurrence of cross and quadratic-law chain terminations were proposed.

Reversible chain reaction between N,N′-diphenyl-1,4-benzoquinonediimine and 2,5-dichlorohydroquinone: Kinetics, mechanism, and the rate constants of elementary steps

The kinetics of the reversible chain reaction between N,N′-diphenyl-1,4-benzoquinonediimine and 2,5-dichlorohydroquinone was studied in chlorobenzene at 298 and 343 K. Experiments in the presence of an initiator proved that the reaction proceeds via a chain mechanism with a chain length of ∼104 to 105 units, depending on the reactant and initiator concentrations and temperature. The reaction rate first increases and then decreases with increasing concentrations of the reaction products (N,N′-diphenyl-1,4-phenylenediamine and 2,5-dichloroquinone) due to the pronounced reversibility of the chain termination and propagation steps involving the reaction products. The reaction orders with respect to the components were determined. The rate constants and activation energies of most of the elementary steps of the forward and backward chain reactions were determined or reliably estimated. Induction periods were observed for the first time in the reversible chain reactions in the quinoneimine + hydroquinone systems. The induction periods are due to the long time required for the establishment of the steady-state radical concentrations in the system.

Kinetic heterogeneity of the active sites of titanium-containing catalytic systems in the stereospecific polymerization of isoprene

The kinetic heterogeneity of the active sites of titanium-containing catalytic systems in the stereospecific polymerization of isoprene was studied based on solving inverse problems for the molecular-weight distribution of polyisoprene with the use of the Tikhonov regularization method. It was found that from two to four types of active sites can occur depending on the nature of the organoaluminum compound used in the catalytic system. The rate constants of elementary steps of the polymerization process for particular types of active sites were obtained for the first time by solving inverse kinetic problems.

Rate constants of elementary steps of the reversible chain reaction of N-phenyl-1,4-benzoquinonemonoimine with 2,5-dichlorohydroquinone

The kinetics of reversible chain reactions in quinoneimine-hydroquinone systems has first been studied for the reaction of N-phenyl-1,4-benzoquinonemonoimine with 2,5-dichloro-hydroquinone used as an example. The dependences of the reaction rate on the concentration of the initial reactants, initiator, and each product were studied. The reliable estimates of the rate constants of 11 (of 12) elementary steps of this reaction were obtained from the experimental data using the earlier derived formulas and the method of equal concentrations developed in the present work.

Elementary Steps of the Cross-Bridge Cycle in Fast-Twitch Fiber Types from Rabbit Skeletal Muscles

To understand the molecular mechanism underlying the diversity of mammalian skeletal muscle fibers, the elementary steps of the cross-bridge cycle were investigated in three fast-twitch fiber types from rabbit limb muscles. Skinned fibers were maximally Ca2+-activated at 20°C and the effects of MgATP, phosphate (P, Pi), and MgADP were studied on three exponential processes by sinusoidal analysis. The fiber types (IIA, IID, and IIB) were determined by analyzing the myosin heavy-chain isoforms after mechanical experiments using high-resolution SDS-PAGE. The results were consistent with the following cross-bridge scheme: ▪ where A is actin, M is myosin, D is MgADP, and S is MgATP. All states except for those in brackets are strongly bound states. All rate constants of elementary steps (k2, 198–526s−1; k−2, 51–328s−1; k4, 13.6–143s−1; k−4, 13.6–81s−1) were progressively larger in the order of type IIA, type IID, and type IIB fibers. The rate constants of a transition from a weakly bound state to a strongly bound state (k−2, k4) varied more among fiber types than their reversals (k2, k−4). The equilibrium constants K1 (MgATP affinity) and K2 (=k2/k−2, ATP isomerization) were progressively less in the order IIA, IID, and IIB. K4 (=k4/k−4, force generation) and K5 (Pi affinity) were larger in IIB than IIA and IID fibers. K1 showed the largest variation indicating that the myosin head binds MgATP more tightly in the order IIA (8.7mM−1), IID (4.9mM−1), and IIB (0.84mM−1). Similarly, the MgADP affinity (K0) was larger in type IID fibers than in type IIB fibers.

The carboligation reaction of acetohydroxyacid synthase II: Steady-state intermediate distributions in wild type and mutants by NMR

The thiamin diphosphate (ThDP)-dependent enzyme acetohydroxyacid synthase (AHAS) catalyzes the first common step in branched-chain amino acid biosynthesis. By specific ligation of pyruvate with the alternative acceptor substrates 2-ketobutyrate and pyruvate, AHAS controls the flux through this branch point and determines the relative rates of synthesis of isoleucine, valine, and leucine, respectively. We used detailed NMR analysis to determine microscopic rate constants for elementary steps in the reactions of AHAS II and mutants altered at conserved residues Arg-276, Trp-464, and Met-250. In Arg276Lys, both the condensation of the enzyme-bound hydroxyethyl-ThDP carbanion/enamine (HEThDP) with the acceptor substrates and acetohydroxyacid release are slowed several orders of magnitude relative to the wild-type enzyme. We propose that the interaction of the guanidinium moiety of Arg-264 with the carboxylate of the acceptor ketoacid provides an optimal alignment of substrate and HEThDP orbitals in the reaction trajectory for acceptor ligation, whereas its interaction with the carboxylate of the covalent HEThDP-acceptor adduct plays a similar role in product release. Both Trp-464 and Met-250 affect the acceptor specificity. The high preference for ketobutyrate in the wild-type enzyme is lost in Trp464Leu as a consequence of similar forward rate constants of carboligation and product release for the alternative acceptors. In Met250Ala, the turnover rate is determined by the condensation of HEThDP with pyruvate and release of the acetolactate product, whereas the parallel steps with 2-ketobutyrate are considerably faster. We speculate that the specificity of carboligation and product liberation may be cumulative if the former is not completely committed.

Investigation of the Properties of a Kinetic Mechanism Describing the Chemical Structure of RDX Flames. I. Role of Individual Reactions and Species

For description of the chemical structure of RDX flames, key reactions and species are selected by numerical solution of the system of equations describing one–dimensional flows of a viscous, heat–conducting, reacting gas at pressures of 0.5—90 atm. The kinetic mechanism consists of 263 elementary steps and 43 species. Literature data on rate constants of elementary steps are considered. Flame structure is calculated for RDX combustion under irradiation. Various reaction paths in the RDX vapor decompositon zone are considered. The effects of the mass flow rate and two–dimensional nature of the gas flow on the flame structure are discussed. Calculation results are compared to experimental data. The structure of various flame zones and the role of individual steps and species in the chemical process are investigated.

Unimolecular decay of the thiomethoxy cation, CH3S+: A computational study on the detailed mechanistic aspects

The unimolecular decay of the triplet thiomethoxy cation CH3S+, ion 1, has been investigated by density functional theory, ab initio, and Phase–space/Rice Ramsperger Kassel Marcus (PST/RRKM) calculations. We have first located on the singlet and triplet B3LYP/6-311+G(d,p) [C,H3,S]+ potential energy surfaces the energy minima and transition structures involved in the lowest energy decompositions of 1, including the loss of H, H2, and S. We have subsequently located the minimum energy points lying on the B3LYP/6-311+G(d,p) hyperline of intersection between the singlet and triplet surfaces, using a recently described steepest descent-based method [Theor. Chem. Acc. 99, 95 (1998)]. The total energies of all these species were refined by CCSD(T)/cc-pVTZ single-point calculations. The obtained potential energy surface has been used to outline the full kinetic scheme for the unimolecular decay of ion 1. The rate constants of the various elementary steps have been calculated by the PST and the RRKM theory. We used a nonadiabatic version of the latter to evaluate the rate constants of the elementary steps which involve a change in the total spin multiplicity. We found that the two kinetically favored decomposition channels are the loss of atomic hydrogen, with formation of 2CH2S+⋅, and molecular hydrogen, with formation of 1HCS+. The former process is predicted to prevail for ions 1 in the lowest rotational states and with an internal energy content of at least 60 kcal mol−1. The loss of H2 was found to be by far the prevailing process in the time scale of ca. 10−5 to ca. 10−6 s from the formation of 1. This is fully consistent with the experimentally observed exclusive loss of H2 by the CH3S+ ions which decompose in the “metastable” time window of the mass spectrometer. The loss of H2 from ion 1 with formation of 1HCS+ may occur by two distinct “spin-forbidden” paths, i.e., a simple concerted 1,1 H2 elimination or a 1,2 H shift followed by a 1,2 H2 elimination from the singlet mercaptomethyl ion 2. In the metastable time window, these two mechanisms may occur alternatively, depending on the degree of rotational excitation of 1.

Investigation of the Mechanism of Crossover Reaction of p‐Dicumyl chloride/BCl3/Isobutylene System by Glass Fiber Optic Photometry

AbstractA thorough kinetic investigation was done by measuring the optical density of reaction mixtures of the pDCC/BCl3 initiating system in the presence and in the absence of monomer and added salt at 500 nm and at −80°C. The absolute rate constants of elementary steps of the ion generation and cationation were evaluated by computer using a fitting method for determination of the parameters occurring in the kinetic model. The key activated species of the mechanism are identified to be colorless donor‐acceptor complexes. The color of reaction mixtures is caused by ionized species. On the basis of the calculations and other evidences, a well‐established mechanism is proposed. Both ‐tC‐Cl and ‐tC‐OH endgroups were found by MS/EI. GPC analysis of the reaction products indicates that the major product is dimer under the reaction conditions applied.

1] Transient kinetic approaches to enzyme mechanisms

Steady-state kinetics can provide information about the overall reaction pathway for multiple substrate reactions, the specificity of the enzyme for specific substrate structures, and lower bounds for the specific rate constants in a mechanism. However, the kinetic parameters measured are complex functions of the specific rate constants, so that individual rate constants rarely can be determined and little information is obtained about mechanistic intermediates. To elucidate the details of an enzymatic mechanism and to measure rate constants for elementary steps, kinetic experiments must be carried out at high enzyme concentrations where enzyme-substrate species are significantly populated and can be directly detected. Because enzymes are very efficient catalysts, fast reaction techniques are often needed to study the transient kinetics. This chapter is discusses transient kinetic studies to biochemists. First, the theoretical bases, for analyzing the rate equations, associated with typical mechanisms, are discussed in the chapter. Second, a brief description of the various types of stopped-flow, rapid quench, and temperature jump equipment is given. Finally, some examples of transient kinetic studies are described in the chapter.