Combination Of Rate Constants Research Articles

Sensitivity Analysis of Thermal Degradation of Plastic Waste Using Statistically Assumed Exponential Factors and Activation Energies.

The rise in the production of plastic waste has prompted the exploration of various recovery options instead of landfilling, burning, and other unethical ways of decomposing. The experimentally generated rate constants for the thermal processing of plastic waste do not yield enough liquid fuels and gases for commercial-scale usage. It is imperative to predict kinetic rate constants statistically using an appropriate combination of activation energies (E a) and frequency factors (A o) for the optimized thermal valorization of plastic waste. This approach also assists in controlling the selectivity and quantity of the pyrolysis products. A statistical kinetic model was tested to find the best combination of rate constants from different combinations of E a and A o to pyrolyze the high-density polyethylene. Two series of E a and A o were first assumed using R software. These series were then used to predict kinetic rate constants and analyze their sensitivity independently using MATLAB. The rate constants were varied from their originally predicted values during the sensitivity analysis. It was found that the rate constant k(7) dominated the other predicted rate constants where high oil and gas yields were concerned. The gas yield increased from lower to higher extreme positions in the range of 60%-74% with the first series and from 65% to 81% with the second series. The maximum oil content was found around 74% and 65% with the first series and second series, respectively.

Development and automation of algorithm for determining basis of nonlinear parameter functions of kinetic constants

Mathematical modeling of catalytic processes is necessary for the complete and accurate description, as well as for controlling the quality and physicochemical studied of catalysts. In the paper, theoretical issues of industrial catalysis are discussed. The work is devoted to theoretical graph analysis of informativity of kinetic parameters of the model of a complex chemical reaction. The aim is the development and automation of algorithm for determining basis of nonlinear parameter functions in solving inverse problems of chemical kinetics in order to define the number and form of independent combinations of rate constants of elementary stages. A program package for analysis of informativity of kinetic parameters of the mathematical model of a complex catalytic reaction is developed and described. The obtained functional relations between the kinetic parameters can be useful for experimentalists in physicochemical interpretation and analysis of mechanisms of chemical reactions. In other words, the proposed method allows independent combinations of kinetic constants to be distinguished that results in shortening the number of the model parameters and, as a consequence, enhance the accuracy of the mathematical model. The mechanism of hydrogen oxidation over a platinum catalyst is given as an example of the use of the software.

On the different experimental manifestations of two-state 'induced-fit' binding of drugs to their cellular targets.

'Induced-fit' binding of drugs to a target may lead to high affinity, selectivity and a long residence time, and this mechanism has been proposed to apply to many drugs with high clinical efficacy. It is a multistep process that initially involves the binding of a drug to its target to form a loose RL complex and a subsequent isomerization/conformational change to yield a tighter binding R'L state. Equations with the same mathematical form may also describe the binding of bivalent antibodies and related synthetic drugs. Based on a selected range of 'microscopic' rate constants and variables such as the ligand concentration and incubation time, we have simulated the experimental manifestations that may go along with induced-fit binding. Overall, they validate different experimental procedures that have been used over the years to identify such binding mechanisms. However, they also reveal that each of these manifestations only becomes perceptible at particular combinations of rate constants. The simulations also show that the durable nature of R'L and the propensity of R'L to be formed repeatedly before the ligand dissociates will increase the residence time. This review may help pharmacologists and medicinal chemists obtain preliminary indications for identifying an induced-fit mechanism.

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.

Initial Stages of the Pyrolysis of Polyethylene.

An experimental study of the kinetics of the initial stages of the pyrolysis of high-density polyethylene (PE) was performed. Quantitative yields of gas-phase products (C1-C8 alkanes and alkenes) and functional groups within the remaining polyethylene melt (methyl, vinyl, vinylene, vinylidene, and branching sites) were obtained as a function of time (0-20 min) at five temperatures in the 400-440 °C range. Gas chromatography and NMR ((1)H and (13)C) were used to detect the gas- and condensed-phase products, respectively. Modeling of polyethylene pyrolysis was performed, with the primary purpose of determining the rate constants of several critical reaction types important at the initial pyrolysis stages. Detailed chemical mechanisms were created (short and extended mechanisms) and used with both the steady-state approximation and numerical integration of the differential kinetic equations. Rate constants of critical elementary reactions (C-C backbone scission, two kinds of H-atom transfer, radical addition to the double bond, and beta-scission of tertiary alkyl radicals) were adjusted, resulting in an agreement between the model and the experiment. The values of adjusted rate constants are in general agreement with those of cognate reactions of small molecules in the gas phase, with the exception of the rate constants of the backbone C-C scission, which is found to be approximately 1-2 orders of magnitude lower. This observation provides tentative support to the hypothesis that congested PE melt molecular environment impedes the tumbling motions of separating fragments in C-C bond scission, thus resulting in less "loose" transition state and lower rate constant values. Sensitivity of the calculations to selected uncertainties in model properties was studied. Values and estimated uncertainties of four combinations of rate constants are reported as derived from the experimental results via modeling. The dependence of the diffusion-limited rate constant for radical recombination on the changing molecular mass of polyethylene was explicitly quantified and included in the extended kinetic mechanism, which appears critical for the agreement between modeling and experiment, particularly the agreement between the experimental and the calculated activation energies for product formation rates. Calculations were performed to estimate the contribution to the overall rate of radical recombination of the "reaction diffusion" phenomenon, where recombination is driven not by the actual motion of the recombining radical sites but rather by the migration of the radical site through PE melt due to rapid hydrogen transfer; this contribution was shown to be negligible for the conditions of the current work.

Competition enhances stochasticity in biochemical reactions

We study stochastic dynamics of two competing complexation reactions (i) A + B↔AB and (ii) A + C↔AC. Such reactions are common in biology where different reactants compete for common resources--examples range from binding enzyme kinetics to gene expression. On the other hand, stochasticity is inherent in biological systems due to small copy numbers. We investigate the complex interplay between competition and stochasticity, using coupled complexation reactions as the model system. Within the master equation formalism, we compute the exact distribution of the number of complexes to analyze equilibrium fluctuations of several observables. Our study reveals that the presence of competition offered by one reaction (say A + C↔AC) can significantly enhance the fluctuation in the other (A + B↔AB). We provide detailed quantitative estimates of this enhanced fluctuation for different combinations of rate constants and numbers of reactant molecules that are typical in biology. We notice that fluctuations can be significant even when two of the reactant molecules (say B and C) are infinite in number, maintaining a fixed stoichiometry, while the other reactant (A) is finite. This is purely due to the coupling mediated via resource sharing and is in stark contrast to the single reaction scenario, where large numbers of one of the components ensure zero fluctuation. Our detailed analysis further highlights regions where numerical estimates of mass action solutions can differ from the actual averages. These observations indicate that averages can be a poor representation of the system, hence analysis that is purely based on averages such as mass action laws can be potentially misleading in such noisy biological systems. We believe that the exhaustive study presented here will provide qualitative and quantitative insights into the role of noise and its enhancement in the presence of competition that will be relevant in many biological settings.

Reaction kinetics of toluene diisocynate and propanol by in situ FTIR

PurposeTo evaluate the effect of the concentrations of isocyanate group and hydroxyl group and hydroxyl group species on the rate constants of isocyanate‐propanol reaction, and to reveal the kinetics of isocyanate‐hydroxyl reaction.Design/methodology/approachThe in situ FTIR technique was employed to measure the group concentration evolutions, by which the rate constants were determined. Besides, the FTIR was used to detect the OH absorbance shifts during reaction and the OH absorbance at different concentrations. The kinetic mechanism of isocyanate‐propanol reaction was discussed with the combination of rate constants and FTIR spectra.FindingsA new reaction mechanism, alcohol association mechanism, was proposed that could explain many phenomena. It was revealed that the rate constant was independent of the isocyanate concentration, while the concentration and species of hydroxyl groups had apparent effects on the rate constants. It was possible to calculate the number averaged degree of association of propanol with alcohol association mechanism.Research limitations/implicationsThe associated n‐propanol molecules that reacted with isocyanate to form urethane were the associated dimer and trimer predominately, while the iso‐propanol was the dimer.Practical implicationsThe kinetics of isocyanate‐hydroxyl reaction and the alcohol association mechanism will be helpful to understand the preparation and curing of polyurethane, and their controls.Originality/valueA new reaction mechanism, alcohol association mechanism, was proposed that could explain many phenomena that might not be interpreted by other mechanisms. The mechanism could be employed to calculate the number averaged degree of association of alcohols.

Kinetic Investigation of Escherichia coli RNA Polymerase Mutants That Influence Nucleotide Discrimination and Transcription Fidelity

Recent RNA polymerase (RNAP) structures led to a proposed three-step model of nucleoside triphosphate (NTP) binding, discrimination, and incorporation. NTPs are thought to enter through the secondary channel, bind to an E site, rotate into a pre-insertion (PS) site, and ultimately align in the catalytic (A) site. We characterized the kinetics of correct and incorrect incorporation for several Escherichia coli RNAPs with substitutions in the proposed NTP entry pore (secondary channel). Substitutions of the semi-conserved residue betaAsp(675), which is >10A away from these sites, significantly reduce fidelity; however, substitutions of the totally conserved residues betaArg(678) and betaAsp(814) do not significantly alter the correct or incorrect incorporation kinetics, even though the corresponding residues in RNAPII crystal structures appear to be interacting with the NTP phosphate groups and coordinating the second magnesium ion in the active site, respectively. Structural analysis suggests that the lower fidelity of the betaAsp(675) mutants most likely results from reduction of the negative potential of a small pore between the E and PS sites and elimination of several structural interactions around the pore. We suggest a mechanism of nucleotide discrimination that is governed both by rotation of the NTP through this pore and subsequent rearrangement or closure of RNAP to align the NTP in the A site.

A Kinetic Study of the Intercalation of Ethidium Bromide into Poly(A)·Poly(U)

The equilibria and kinetics of the intercalation of ethidium bromide (EB) into poly(A).poly(U) have been studied in aqueous solution (pH = 7.0, 1 M NaCI, 25 °C) by spectrophotometry, spectrofluorimetry, and stopped-flow techniques. The analysis of the binding isotherms yields the site binding constant K = 2.6 x 10 4 M - 1 and the site size n = 2.2 base pairs, thus revealing the occurrence of intercalation according to the excluded site model. The salt dependence of the binding constant indicates that approximately one Na + counterion is displaced from the polymer by the binding of one ethidium ion. The kinetic curves are biexponential both in absorbance and in fluorescence. The results suggest the formation of two bound forms according to the reaction scheme D + S DS 1 and S + DS 1 DS I I + S, where k 1 = 5.9 x 10 4 M - 1 s - 1 , k - 1 = 8.7 s - 1 , k 2 = 1.8 x 10 5 M - 1 s - 1 , and k - 2 = 0.70 × 10 5 M - 1 s - 1 . The value of the equilibrium constant K, derived from kinetics as a combination of rate constants, agrees with that derived from equilibria. The behavior of the investigated RNA/ethidium system is compared with that of the DNAs/ethidium systems.

A mathematical model of solid-state thermo-oxidative stabilization of acrylic fibers

Following a brief review of the reactions that can occur during stabilization of acrylic precursor polymers for carbon fibers, a simplified mathematical model of stabilization in a solid fiber is developed and solved numerically in this study. Examples are given that show the results from this analysis to be entirely consistent with the trends observed in practice. Current optimization schemes for oxidative stabilization involve a trial-and-error approach in achieving the correct temperatures and stabilization time periods. The numerical model given here, fitted with the right combination of rate constants and reaction orders, could serve to replace current optimization procedures.

Kinetic constants of the acetylcholine (ACh) receptor reaction deduced from the rise in open probability after steps in ACh concentration

Outside-out patches of enzymatically dissociated adult and denervated mouse muscle fibers were superfused repetitively by pulses of acetylcholine (ACh) containing solution. Up to 300 channels opened simultaneously 300 microseconds after the beginning of a 1,000 microM ACh pulse corresponding to a peak current i of almost -1 nA. Single responses to ACh were averaged and the concentration dependence of i and of the rise time tr from 0.1 i to 0.9 i was measured. In adult receptors, i increased proportional to the second to third power of ACh concentration, whereas in embryonic-type receptors it was proportional to the first to the second power. tr increased from approximately 0.3 ms at 1,000 microM ACh to a plateau value of approximately 5 ms for adult and of approximately 10 ms for embryoniclike receptors at concentrations less than 10 microM ACh. The concentration dependence of i and tr was simulated using the standard model of ACh binding with different combinations of rate constants and two and three binding sites for ACh. The calculated curves were compared to the measurements and a set of well fitting rate constants was determined for adult and embryoniclike receptors. Three binding sites for ACh were necessary to fit the dose response for i for adult receptors. A method for deriving rate constants in a model of ACh-receptor interaction is described that avoids analysis of open-closed kinetics of single channels, which in rapid systems, as the ones studied here, are at the limit of the frequency response of the current measurement.

The effect of Mg2+ and guanine nucleotide exchange factor on the binding of guanine nucleotides to eukaryotic initiation factor 2.

A major site of regulation of polypeptide chain initiation is the binding of Met-tRNA to 40 S ribosomal subunits which is mediated by eukaryotic initiation factor 2 (eIF-2). The formation of ternary complex, eIF-2.GTP.Met-tRNA, is potently inhibited by GDP. Measurement of the parameters for guanine nucleotide binding to eIF-2 is critical to understanding the control of protein synthesis by fluctuations in cellular energy levels. We have compared the dissociation constants (Kd) of eIF-2.GDP and eIF-2.GTP and find that GDP has a 400-fold higher affinity for GDP than GTP. The Kd for GDP is almost an order of magnitude less than has been reported previously. The difference between the Kd values for the two nucleotides is the result of a faster rate constant for GTP release, the rate constants for binding being approximately equal. This combination of rate constants and low levels of contaminating GDP in preparations of GTP can explain the apparently unstable nature of eIF-2.GTP observed by others. Mg2+ stabilizes binary complexes slowing the rates of release of nucleotide from both eIF-2.GDP and eIF-2.GTP. The competition between GTP and GDP for binding to eIF-2.guanine nucleotide exchange factor complex has been measured. A 10-fold higher GTP concentration than GDP is required to reduce [32P] GDP binding to eIF-2.guanine nucleotide exchange factor complex by 50%. The relevance of this competition to the regulation of protein synthesis by energy levels is discussed.

Intracellular pH-regulating mechanism of the squid axon. Relation between the external Na+ and HCO-3 dependences.

The intracellular pH-regulating mechanism of the squid axon was examined for its dependence on the concentrations of external Na+ and HCO3-, always at an external pH (pHo) of 8.0. Axons having an initial intracellular pH (pHi) of approximately 7.4 were internally dialyzed with a solution of pH 6.5 that contained 400 mM Cl- and no Na+. After pHi had fallen to approximately 6.6, dialysis was halted, thereby returning control of pHi to the axon. With external Na+ and HCO-3 present, intracellular pH (pHi) increased because of the activity of the pHi-regulating system. The acid extrusion rate (i.e., equivalent efflux of H+, JH) is the product of the pHi recovery rate, intracellular buffering power, and the volume-to-surface ratio. The [HCO3-]o dependence of JH was examined at three fixed levels of [Na+]o: 425, 212, and 106 mM. In all three cases, the apparent Jmax was approximately 19 pmol X cm-2 X s-1. However, the apparent Km (HCO3-) was approximately inversely proportional to [Na+]o, rising from 2.6 to 5.4 to 9.7 mM as [Na+]o was lowered from 425 to 212 to 106 mM, respectively. The [Na+]o dependence of JH was similarly examined at three fixed levels of [HCO3-]o: 12, 6, and 3 mM. The Jmax values did not vary significantly from those in the first series of experiments. The apparent Km (Na+), however, was approximately inversely related to [HCO3-]o, rising from 71 to 174 to 261 mM as [HCO3-]o was lowered from 12 to 6 to 3 mM, respectively. These results agree with the predictions of the ion-pair model of acid extrusion, which has external Na+ and CO3= combining to form the ion pair NaCO3-, which then exchanges for internal Cl-. When the JH data are replotted as a function of [NaCO3-]o, data from all six groups of experiments fall along the same Michaelis-Menten curve, with an apparent Km (NaCO3-) of 80 microM. The ordered and random binding of Na+ and CO3= cannot be ruled out as possible models, but are restricted in allowable combinations of rate constants.

Investigation of T1-Relaxation by a Microwave Pulse Technique for HCCC15N Rotational Transitions

The pressure dependence of 1/T1 has been measured with a bridge type superhet spectrometer at room temperature for the rotational transitions (J, |M| ) = (1, 0)-(2, 0), (1, 1)-(2, 1), (2, 0) -(3,0), (2. 1)-(3, 1) and (2, 2)-(3, 2) of cyanoacetylene. HCCC15N. by using a π, τ, π/2 microwave pulse sequence method. In addition to the measurements on the pure gas, T1-relaxation has also been investigated for mixtures with H2, He, Ne and Ar. The results are used to derive linear combinations of rate constants for collision-induced transfer of rotational energy between |M| - resolved rotational levels of HCCC15N.

Transients and Cooperativity: A SLOW TRANSITION MODEL FOR RELATING TRANSIENTS AND COOPERATIVE KINETICS OF ENZYMES

A model is proposed to account for the occurrence of both slow transient kinetics and cooperativity in a monomeric, single-site enzyme. This slow transition model incorporates one reaction of the enzyme, in addition to normal catalytic steps, which is slower than other steps in the mechanism and is influenced by substrate. The slow reaction step may be an isomerization (conformation change), a dissociation-association, or binding of another ligand (modifier). Analysis of steady state kinetics and simulation studies for the slow isomerization mechanism have demonstrated that both positive and negative cooperativity can occur with either bursts or lags of enzyme activity. Examination of various combinations of rate constants have illustrated the dependence of cooperativity of the system on changes in certain rate constants. For example, a necessary condition for cooperativity in this model requires that both the binding and the isomerization steps of the mechanism be in a steady state but not at equilibrium. Modifiers could potentially shift the extent or type of cooperativity. The combination of slow transitions with homotropic, sitesite interaction could generate several types of complex, cooperative kinetics. Whenever a transient is observed in a progress curve the contribution of the slow transition model to cooperativity of the kinetics should be assessed. The results of binding studies, initial (pre-transition) velocity measurements, and the effects of factors (e.g. pH, temperature, modifiers) on the half-time of the transient should be capable of determining the extent of the contribution of the slow transition to cooperativity. A table of 10 enzymes which show both transients and cooperativity suggests that these phenomena do occur together and may be related mechanistically through the slow transition mechanism. Thus, in those cases in which a slow transition occurs, the transition may be responsible for nonlinear, double reciprocal plots of the steady state kinetics without requiring interactions between more than one site.