Equations Of Chemical Kinetics Research Articles

In vivo translation rates can substantially delay the cotranslational folding of the Escherichia coli cytosolic proteome

A question of fundamental importance concerning protein folding in vivo is whether the kinetics of translation or the thermodynamics of the ribosome nascent chain (RNC) complex is the major determinant of cotranslational folding behavior. This is because translation rates can reduce the probability of cotranslational folding below that associated with arrested ribosomes, whose behavior is determined by the equilibrium thermodynamics of the RNC complex. Here, we combine a chemical kinetic equation with genomic and proteomic data to predict domain folding probabilities as a function of nascent chain length for Escherichia coli cytosolic proteins synthesized on both arrested and continuously translating ribosomes. Our results indicate that, at in vivo translation rates, about one-third of the Escherichia coli cytosolic proteins exhibit cotranslational folding, with at least one domain in each of these proteins folding into its stable native structure before the full-length protein is released from the ribosome. The majority of these cotranslational folding domains are influenced by translation kinetics which reduces their probability of cotranslational folding and consequently increases the nascent chain length at which they fold into their native structures. For about 20% of all cytosolic proteins this delay in folding can exceed the length of the completely synthesized protein, causing one or more of their domains to switch from co- to posttranslational folding solely as a result of the in vivo translation rates. These kinetic effects arise from the difference in time scales of folding and amino-acid addition, and they represent a source of metastability in Escherichia coli's proteome.

The mechanism of non-linear photochemical oscillations in the mesopause region

Abstract. The mechanism of generation of 2-day photochemical oscillations in the mesopause region (80–90 km) has been studied analytically. The initial system of equations of chemical kinetics describing the temporal evolution of O, O3, H, OH and HO2 concentrations with allowance for diurnal variations of solar radiation has been simplified successively to a system of two nonlinear first-order time equations with sinusoidal external forcing. The obtained system has a minimum number of terms needed for generation of 2-day oscillations. Linearization of this system near the period-doubling threshold permits separating explicitly a particular case of the Mathieu equation ẍ + α · sin ω t · x = 0, in which the first sub-harmonic (ω/2) of the exciting force starts to grow exponentially when the amplitude of external forcing (α) exceeds its threshold value. Finally, a system of two simplest differential equations with power-law nonlinearity has been derived that allows analytical investigation of the effect of arising of reaction-diffusion waves in the mesospheric photochemical system.

Kinetic modelling and analysis of amino acid formation mechanisms during bioconversion of plant raw material and organic wastes

Kinetic features are studied for biocatalytic conversion of a mixture of plant material and organic waste of plant origin. It is established that free amino acid formation in the course of biocatalytic conversion is described with sufficient accuracy by equations of formal chemical kinetics, and growth of microbial population is described by a classical Mono equation. Analysis of results in the course of kinetic simulation makes it possible to draw a conclusion about the complexity and multiplicity of free amino acid formation mechanisms, and also to carry out a series of laboratory tests for biocatalytic conversion.

Graph-theoretical method for determination of key substances in complex chemical reactions

Key substances are such that the concentrations of all other substances involved in the reaction are a lin� ear function of the set of these substances. A basic property of the set of differential equations of chemi� cal kinetics is that the number of existing independent linear laws of concentration conservation is no less than the number of chemical elements constituting the substances involved in the reaction [2]. Information on key substances is of crucial impor� tance in solving the inverse problems of identification of mechanisms of complex chemical reactions. A major challenge in solving such problems is insuffi� cient information provided by measurements [3, 4]. Hypothetical schemes of reaction mechanisms involve a large number of substances and reactions between them. Mathematical descriptions of these mecha� nisms are sets of differential equations in which the number of unknowns is equal to the number of sub� stances involved in reactions. At the same time, only some of these substances can be directly measured. There arises an inverse problem of determining the parameters of the set of differential equations (rate constants of chemical reactions) reproducing part of its solutions. A consequence of insufficient informa�

Analysis of chemical, electrochemical reactions and thermo-fluid flow in methane-feed internal reforming SOFCs: Part I – Modeling and effect of gas concentrations

Direct internal reforming solid oxide fuel cells (DIR SOFCs) have complicated distributions of temperature and species concentrations due to various chemical and electrochemical reactions. The details of these properties are studied by a 3-D numerical simulation in this work. The simulation modeling used governing equations (mass, momentum, energy and species balance equations) generally suitable to porous medium with porosity variable of zero (solid), 0.3 (porous medium) and 1.0 (fluid). Chemical kinetics equations for the internal reforming and shift reactions based on the Langmuir–Hinshelwood model were incorporated. Hydrogen and carbon monoxide oxidations were considered both participating in electrochemical reactions. The experimentally measured current density–potential curves were compared with the simulation data to validate the code, which revealed that the simulation model was able to predict the dilution effect of nitrogen and the mass transfer under high current densities. It is found that the temperature dramatically declined near the fuel inlet with strong endothermic reactions, but it increased along the fluid flow with electrochemically exothermic reactions. A low steam-to-carbon ratio (SCR) led to high steam reforming and water gas shift reaction rates, which generated a greater amount of hydrogen. Therefore, current density increased with low SCR. The average current density due to carbon monoxide electrochemical oxidation varies from 205.3 A/m2 under an SCR of 2.0 to 47.6 A/m2 under an SCR of 4.0. The average current density due to hydrogen electrochemical oxidation was 5535.4 A/m2 under an SCR of 2.0, which was 27 times higher than that of carbon monoxide. The total current density ranged from 5740.8 A/m2 under an SCR of 2.0 to 2268.9 A/m2 under an SCR of 4.0.

MiRNA regulatory circuits in ES cells differentiation: a chemical kinetics modeling approach.

MicroRNAs (miRNAs) play an important role in gene regulation for Embryonic Stem cells (ES cells), where they either down-regulate target mRNA genes by degradation or repress protein expression of these mRNA genes by inhibiting translation. Well known tables TargetScan and miRanda may predict quite long lists of potential miRNAs inhibitors for each mRNA gene, and one of our goals was to strongly narrow down the list of mRNA targets potentially repressed by a known large list of 400 miRNAs. Our paper focuses on algorithmic analysis of ES cells microarray data to reliably detect repressive interactions between miRNAs and mRNAs. We model, by chemical kinetics equations, the interaction architectures implementing the two basic silencing processes of miRNAs, namely “direct degradation” or “translation inhibition” of targeted mRNAs. For each pair (M,G) of potentially interacting miRMA gene M and mRNA gene G, we parameterize our associated kinetic equations by optimizing their fit with microarray data. When this fit is high enough, we validate the pair (M,G) as a highly probable repressive interaction. This approach leads to the computation of a highly selective and drastically reduced list of repressive pairs (M,G) involved in ES cells differentiation.

Ionization mechanism in a direct current discharge plasma in an argon-oxygen mixture

We present the results of calculating the charged particle formation and decay rates in a dc discharge positive column in argon-oxygen mixture. The calculations are based on a combined solution to the Boltzmann equation; vibration kinetics equations for the ground state of the O2 molecule; and chemical kinetics equations for Ar and O atoms, O2 molecule, and their excited states under the experimentally determined reduced electric field strength, E/N, for various gas phase compositions, currents, and pressures. The role is clarified of particular components in the ionization processes. Electron and positive ion decay is shown to take place predominantly at the reactor walls on which they fall due to joint diffusion. The negative oxygen ions affect the diffusion rate.

A conducting macroparticle in dense electronegative gas under thermionic emission

The consequences of thermionic emissions from the surfaces of small metal particles present as a rarefied suspension in a dense electronegative gas are studied, including the attachment of electrons to neutral molecules, the presence of electron and ion currents on a particle and the electric charge formation of the latter. Calculations are carried out in the temperature range of 1000–2000 K, where the ionization of the host gas can be neglected. The attachment reaction is considered based on chemical kinetics equations. The distribution of electron and ion densities and their currents in the vicinity of the particle, as well as the shielding of the particle charge, are discussed. The subject is considered in a hydrodynamic approximation.

Application of Genetic Algorithm in Chemical Reaction Kinetics

In this paper, a summary of Genetic Algorithm methods developed recent years applied in chemical reaction kinetics was presented. The applications of the Genetic Algorithm in reduction of the chemical reaction kinetics, estimation of the chemical kinetic parameters and calculation of the chemical kinetic equations were expounded here. Eventually, the confronted problem and developing trend of the application of Genetic Algorithm methods in chemical kinetics were reviewed.

A Modified Implicit Iterative Difference Algorithm for Stiff Chemical Kinetic Equations in Complex Combustion System

The splitting-operator method has been widely used in the numerical simulation of complex combustion system with its high computation efficiency. The main difficult encountered in the method is how to integrate the stiff chemical kinetics ordinary differential equation (ODE) efficiently and accurately in each grid node of flow field. Although several ODE software packages such as LSODE and VODE have very predominant performance in integrating stiff and non-stiff case, it couldn’t ensure the positivity of mass fraction in integrating stiff chemical kinetic ODE. A detail liquid rocket hypergolic bipropellant combination of Monomethylhydrazine (MMH)/Red Fuming Nitric Acid (RFNA) chemical mechanism consisting of 550 elementary reactions among 83 species was constituted basing on several relevant literatures firstly. And then a modified implicit iterative difference algorithm with variable time steps was developed to tackle the problem of mass fraction non-positive. The results from the integration of MMH /nitrogen tetroxide (NTO) chemical kinetic ODE indicate that the algorithm is always retain stability and positive value of mass fraction. The time step length would also be automatically adjusted at different chemical reaction time in the algorithm to keep its computational efficiency.

Stochastic simulation of population balance models with disparate time scales: Hybrid strategies

The Monte Carlo methods have been an effective tool for the numerical solution of population balance models (PBMs). They are particularly useful for complex multidimensional problems. Less attention has been paid to solving population balance models where some species are away from the thermodynamic limit (very dilute or finite) and other species can be considered deterministic (high concentration). These types of problem often result in a stochastic system with rates spanning orders of magnitude for different mechanisms. Using the exact Monte Carlo solution to solve these types of problem is very inefficient because of the simulation time spent sampling fast events. These fast events are associated with species with large populations for which a single event does not change the population appreciably. This frequent sampling of fast events becomes a bottleneck during a simulation in which many single MC steps are required to make an appreciable change in the population. In this work, a hybrid solution strategy is developed to effectively solve this type of problem. The method implements the self-consistent fast/slow partitions used to solve stochastic equations in chemical kinetics. One strategy is found on the capacity of a coarse-grained Markov model called particle ensemble random product (PERP) to accelerate the simulation of fast events of PBMs (Chem. Eng. Sci. 63, 7649–7664; Chem. Eng. Sci. 63, 7665–7675). A second strategy approximates the fast events using mass conservation equations. These models are coupled with the exact MC simulation of slow events. Two extreme cases of heterocoagulation are studied to demonstrate these hybrid strategies.

Comparison of different models for non-equilibrium CO2 flows in a shock layer near a blunt body

The paper presents results of a numerical simulation of a supersonic two-dimensional (2D) viscous flow containing CO2 molecules near a spacecraft entering the Mars atmosphere. The gas–dynamic equations in the shock layer are coupled to the equations of non-equilibrium vibrational and chemical kinetics in the five-component mixture CO2/CO/O2/C/O. Transport and relaxation processes in the flow are studied on the basis of the rigorous kinetic theory methods; the developed transport algorithms are incorporated in the numerical scheme. The influence of the vibrational excitation of CO2 and chemical reactions on the gas flow parameters and heat transfer is analyzed. The obtained results are compared with those found using two simplified models based on the two-temperature and one-temperature vibrational distributions in CO2. The accuracy of the simplified models and the limits of their validity within the shock layer are evaluated. The effect of bulk viscosity in a flow near a re-entry body is discussed. The role of different diffusion processes, chemical reactions, and surface catalytic properties in a flow of the considered mixture in the shock layer is estimated.

Combination of micro- and macroscopic descriptions of the kinetics of chemical reactions and processes of vibrational energy exchange in a multicomponent gas mixture

Chemical and vibrational kinetics equations for a multicomponent reacting gas mixture constructed by combining microscopic (level-by-level) and macroscopic (mode) descriptions are presented. A mixture of diatomic molecules, anharmonic oscillators, which interact with each other and other generally polyatomic components is treated as a subsystem described microscopically, that is, in the form of equations of balance of vibrational state populations. The subsystem of polyatomic components is considered macroscopically, that is, in the form of equations for component concentrations and mean vibrational mode energies. The kinetic equations obtained this way for a system as a whole correctly describe interactions between components considered microscopically and macroscopically.

Laminar flame and acoustic waves in two-dimensional flow

The complete system of fluid dynamics equations describing the development of instability of a reaction front in a two-dimensional flow in reversed time are reduced to a closed system of equations of front dynamics by using Lagrangian variables and integrals of motion. The system can be used to analyze processes behind the front without solving the complete system of fluid dynamics and chemical kinetics equations. It is demonstrated how the gas density disturbances induced by the moving front can be described in the adiabatic approximation.

Degradabilidade dos agentes quelantes EDTA e EDDS após aplicação no solo

Este trabalho objetivou avaliar a degradabilidade dos quelantes EDTA e EDDS por meio do monitoramento da respiração do solo. Os quelantes foram aplicados em dois solos, um Cambissolo Háplico contaminado por metais pesados e um Latossolo Vermelho-Amarelo não contaminado. Três doses de cada quelante (250, 500 e 750 mg kg-1) e uma dose de glicose foram aplicadas em ambos os solos testados, com três repetições cada uma. A degradação dos quelantes foi determinada por meio da quantificação do CO2 emanado do início até o término do ensaio. As equações de cinética química não se ajustaram satisfatoriamente para ambos os quelantes no Latossolo, enquanto para o Cambissolo Háplico resultaram em valores de meia-vida entre 12-16 dias para o EDDS e de 6 dias para o EDTA. Nesse período, a quantidade degradada de EDTA foi de 15% somente. Para o Latossolo o EDTA foi responsável pela menor taxa de degradação, próxima de zero, ocorrida na menor dose, e o EDDS pela maior taxa (135%), ocorrida na maior dose. Para o Cambissolo Háplico, a menor taxa de degradação (19,2%) coube ao EDTA na maior dose e a maior taxa (211,4%), ao EDDS na menor dose. Ambos os quelantes tiveram redução da taxa de degradação com o aumento de suas respectivas doses, exceto com a aplicação da menor dose do EDDS (250 mg kg-1). Contudo, a degradabilidade do EDDS continuou maior que a verificada com a aplicação do EDTA.

The Dynamics of Combustion Products' Flow in a Ring Nozzle with a Half-Closed Cavity

Complex results are presented in numerical and experimental flow dynamic research and thrust characteristics of jet engine model thrust device with ring nozzle working on equilibrium combustion products of acetylene-air mixtures. Experiments with thrust device models were performed in a pulse aerodynamic laboratory facility. Calculations of viscous flow were based on a program complex including the programs of Navier-Stokes equations and numerical integration for various models of gas environment added by the equations of chemical kinetics. As a result, the main details of flow dynamic, stationary flow structure, and thrust characteristics of the ring nozzle have been established. The comparison of experimental and calculated data has been made to verify the mathematical models and computation method.

Analytical derivation of moment equations in stochastic chemical kinetics

The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e. the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.

An integral approach to considering the evolution of a microwave streamer

We present a model of a microwave streamer based on analytical relations that allows its evolution to be described both during its elongation along the external electric field and after its stop. The equations for the electric field amplitude at the streamer center, the equations that describe the dynamics of the longitudinal and transverse sizes, and the equations of plasma chemical kinetics are self-consistently solved in terms of this model. Comparison with numerical 2D simulations of the electrostatic stage in air is made. We derive simple analytical relations that allow the power released in a plasma channel to be estimated on the fly. Almost the entire energy contribution is shown to be made after the termination of the streamer elongation.

Why a master sintering curve model can be applied to the sintering of nano-sized particles?

The master sintering curve model ( MSC) has been widely applied to both the analysis and prediction of the sintering behavior of many powder materials, including nanocrystalline powder. However, since the conventional sintering theories are only true for submicron-sized or larger particles, it should not be applicable to the sintering of nano-sized particles. This work aims to provide an explanation as to why the MSC is capable of predicting nano-sized particle sintering. A comparison with another kinetic model, i.e., the master kinetics curve ( MKC), which was derived from general chemical kinetic equation, reveals that MSC is almost identical except for a 1/ T term in the equation. The analysis of sintering data also shows that the ability of both MSC and MKC are almost equal, and that the values of apparent activation energy provided by both two models are similar too. In previous researches, it is also found that the MSC can be applied to non-sintering systems. These results show that the ability of prediction of the MSC is strongly related to the integration of an Arrhenius type equation. However, because the MSC cannot determine the mechanism of the sintering process, the apparent activation energy Q a may not represent any physical meaning. In summary, MSC may be a “universal” analytical tool for many reaction systems, and its success is definitely not due to its sintering origin but rather to its Arrhenius type form.

Ammonia volatilization in soil treated with tannery sludge

The utilization of tannery sludge in agricultural areas can be an alternative for its disposal and recycling. Despite this procedure may cause the loss of nitrogen by ammonia volatilization, there is no information about this process in tropical soils. For two years a field experiment was carried out in Rolândia (Paraná State, Brazil), to evaluate the amount of NH3 volatilization due to tannery sludge application on agricultural soil. The doses of total N applied varied from zero to 1200kgha−1, maintained at the surface for 89days, as usual in this region. The alkalinity of the tannery sludge used was equivalent to between 262 and 361g CaCO3 per kg. Michaelis–Menten equation was adequate to estimate NH3–N volatilization kinetics. The relation between total nitrogen applied as tannery sludge and the potentially volatilized NH3–N, calculated by the chemical-kinetics equation resulted in an average determination coefficient of 0.87 (P>0.01). In this period, the amount of volatilized NH3 was more intense during the first 30days; the time to reach half of the maximum NH3 volatilization (Km) was 13 an 9days for the first and second experiments, respectively. The total loss as ammonia in the whole period corresponded in average to 17.5% of the total N applied and to 35% of the NH4+–N present in the sludge. If tannery sludge is to be surface applied to supply N for crops, the amounts lost as NH3 must be taken into consideration.