Reduced kinetic models of neutral transport in the tokamak plasma

A method for constructing reduced models of neutrals transport for problems with a reduced dimension has been proposed on the basis of the kinetic equation. The case of a cylindrically symmetric plasma column, which is a good approximation for the tokamak geometry, has been thoroughly analyzed. For this geometry, the kinetic model of neutrals in the isotropic approximation is implemented using an algorithm based on energy grouping of neutrals; this algorithm for atomic hydrogen isotopes is integrated in the ASTRA code.     

A new device for measuring diffusional restrictions and modelling substrate inhibition in a starch-glucoamylase system

An experimental device that quantifies the diffusional properties of polysaccharides solution, in a simple and reproducible way, and an equation relating these properties to solute concentration, is proposed. Using this model to analyse the kinetic profile of the hydrolysis of starch with glucoamylase, is substrate inhibition completely reduced to phenomena that depends on the reological properties of the reacting mixture. The experimental device and kinetic model can be applied to contrast hypothetical substrate inhibitions in any enzymatic system.     

Some experiments on the primary electron acceptor in reaction centres from Rhodopseudomonas sphaeroides.

The bacterial reaction center absorbance change at 450 nm (A-450) assigned to an anionic semiquinone, has been suggested as a candidate for the reduced form of the primary electron acceptor in bacterial photosynthesis. In reaction centers of Rhodopseudomonas sphaeroides we have found kinetic discrepancies between the decay of A-450 and the recovery of photochemical competence. In addition, no proton uptake is measurable on the first turnover, although subsequent ones elicit one proton bound per electron. These results are taken to indicate that the acceptor reaction after a long dark period may be different for the first turnover than for subsequent ones. It is suggested that A-450 is still a likely candidate for the acceptor function but that in reaction centers, additional quinone may act as an adventitious primary acceptor when the "true" primary acceptor is reduced. Alternatively, the primary acceptor may act in a "ping-pong" fashion with respect to subsequent photoelectrons.     

Multi-stage regulation, a key to reliable adaptive biochemical pathways.

A general "multi-stage" regulation model, based on linearly connected regulatory units, is formulated to demonstrate how biochemical pathways may achieve high levels of accuracy. The general mechanism, which is robust to changes in biochemical parameters, such as protein concentration and kinetic rate constants, is incorporated into a mathematical model of the bacterial chemotaxis network and provides a new framework for explaining regulation and adaptiveness in this extensively studied system. Although conventional theories suggest that methylation feedback pathways are responsible for chemotactic regulation, the model, which is deduced from known experimental data, indicates that protein interactions downstream of the bacterial receptor complex, such as CheAs and CheZ, may play a crucial and complementary role.     

Kinetic theory of a gas-discharge positive column and wall sheath

The positive column and wall sheath in a gas discharge are studied with allowance for ion collisions in a plasma and ion reflection from a solid surface under conditions of incomplete ion neutralization. The kinetic equation for ions in a positive column is reduced to a Fredholm equation of the second kind. This makes it possible to solve the kinetic equation using a resolvent and thereby derive a single integrodifferential equation for the potential, which is referred to as a generalized plasma-sheath equation. Specific versions of the plasma-sheath equation are obtained that take into account charge exchange of the ions in a plasma and the thermal spread in velocities of the ionization-produced ions.     

Comprehensive Spectroscopic,Steady State,and Transient Kinetic Studies of a Representative Siderophore-associated Flavin Monooxygenase

Many siderophores used for the uptake and intracellular storage of essential iron contain hydroxamate chelating groups. Their biosyntheses are typically initiated by hydroxylation of the primary amine side chains of l-ornithine or l-lysine. This reaction is catalyzed by members of a widespread family of FAD-dependent monooxygenases. Here the kinetic mechanism for a representative family member has been extensively characterized by steady state and transient kinetic methods, using heterologously expressed N⁵-l-ornithine monooxygenase from the pathogenic fungus Aspergillus fumigatus. Spectroscopic data and kinetic analyses suggest a model in which a molecule of hydroxylatable substrate serves as an activator for the reaction of the reduced flavin and O₂. The rate acceleration is only ∼5-fold, a mild effect of substrate on formation of the C4a-hydroperoxide that does not influence the overall rate of turnover. The effect is also observed with the bacterial ornithine monooxygenase PvdA. The C4a-hydroperoxide is stabilized in the absence of hydroxylatable substrate by the presence of bound NADP⁺ (t_½ = 33 min, 25 °C, pH 8). NADP⁺ therefore is a likely regulator of O₂ and substrate reactivity in the siderophore-associated monooxygenases. Aside from the activating effect of the hydroxylatable substrate, the siderophore-associated monooxygenases share a kinetic mechanism with the hepatic microsomal flavin monooxygenases and bacterial Baeyer-Villiger monooxygenases, with which they share only moderate sequence homology and from which they are distinguished by their acute substrate specificity. The remarkable specificity of the N⁵-l-ornithine monooxygenase-catalyzed reaction suggests added means of reaction control beyond those documented in related well characterized flavoenzymes.     

Measurement of biodegradability parameters for single unsubstituted and methylated polycyclic aromatic hydrocarbons in liquid bacterial suspensions

Substrate depletion experiments were conducted to characterize aerobic biodegradation of 20 single polycyclic aromatic hydrocarbons (PAHs) by induced Sphingomonas paucimobilis strain EPA505 in liquid suspensions. PAHs consisted of low molecular weight, unsubstituted, and methyl-substituted homologs. A material balance equation containing the Andrews kinetic model, an extension of the Monod model accounting for substrate inhibition, was numerically fitted to batch depletion data to estimate extant kinetic parameters including the maximal specific uptake rates, q(max), the affinity coefficients, K(S), and the substrate inhibition coefficients, K(I). Strain EPA505 degraded all PAHs tested. Applied kinetic models adequately simulated experimental data. A cell proliferation assay involving reduction of the tetrazolium dye WST-1 was used to evaluate the ability of strain EPA505 to utilize individual PAHs as sole energy and carbon sources. Of the 22 PAHs tested, 9 supported bacterial growth. Evaluation of the biokinetic data showed that q(max) correlated highly with transmembrane flux as theoretically estimated by a diffusion model, pointing to transmembrane transport as a potential rate-determining process. The biodegradability data generated in this study is essential for the development of quantitative structure-activity relationships (QSARs) for biodegradability and for modeling biodegradation of simple PAH mixtures.     

A self-consistent kinetic model of the stratification of plane and spherical low-pressure discharges in argon

A self-consistent kinetic model is used to describe the effect of stratification of the positive column of a plane and a spherical gas discharge in argon at low pressure. The model is based on solving the Boltzmann kinetic equation for the electron energy distribution function, the time-dependent ion continuity equation, and Poisson’s equation for the self-consistent electric field. The spatial distributions of the electron and ion densities and of the electric field in the positive column of a stratified discharge are determined. The kinetic mechanism for discharge stratification in noble gases at low pressures is explained in terms of the proposed model. The model makes it possible to describe the moving strata and to confirm the validity of the experimentally obtained dependence of the radii of the strata on their numbers in a spherical discharge.     

Inhibition-threshold substrate concentrations

A proposed substrate inhibition model (M. C. Tseng and M. Wayman, Can. J. Microbiol., 21 , 994 (1975)), ((1)) ((2)) derived from yeast growth rates has been applied to data for bacterial growth: Pseudomonas methanica grown on methanol and Arthrobacter AK19 grown on n-butanol. The model represents the experimental data very well.     

嗜酸氧化亚铁硫杆菌生长动力学方程的应用

基于Monod模型推导出了A．f的生长动力学方程模型,采用Gauss-Newton算法确定了在不同初始条件下细菌生长的动力学参数,即最大比生长速率‰、Monod常数K及R0。通过在不同初始条件下细菌生长特性的研究,得到了相应初始生长条件下以限制性底物亚铁离子浓度为表征的生长动力学方程,理论上揭示了动力学参数变化对细菌生长的影响规律,其中生长动力学方程的数值模拟与实验数据相吻合。     

A theoretical derivation of the Contois equation for kinetic modeling of the microbial degradation of insoluble substrates

Although developed as an empirical model to describe microbial growth on soluble substrates, the Contois equation has been widely accepted for kinetic modeling of insoluble substrate degradation. Yet, the mechanistic basis underlining these successful applications remains unanswered. Unlike soluble substrates that mainly cultivate suspended cultures, microbes cultivated on insoluble substrates have the populations that attach to the substrate surface or remain suspended in the bulk solution, while those attached usually grow faster than those suspended due to their proximity to food resources. This imbalanced growth provides a plausible explanation to the inverse relationship between microbial concentration and their specific growth rate as conveyed in the Contois equation. Based on a theoretical derivation, this study revealed that the Contois equation holds true only when attached microbes substantially obstruct the access of food to their suspended counterparts. On the other hand, when plentiful insoluble substrate surfaces are exposed for cell attachment, the Contois equation will be reduced back to the classic Monod equation.     

神经元网络动力学的统计物理方法

本文回顾了利用统计物理的方法研究神经元网络动力学的数学降维描述.以一个全兴奋性的“整合-发放”神经元网络为出发点,导出了描写神经元群体活动的概率分布函数的(2+1)-维对流-扩散方程.在没有引入任何新参数的情况下,讨论了如何利用moment closure scheme得到(1+1)-维的动力学方程.我们将此方程的预测...     

Development of a fluorescence polarization assay for peptidyl-tRNA hydrolase

Peptidyl-tRNA hydrolase (Pth) activity ensures the rapid recycling of peptidyl-tRNAs that result from premature termination of translation. Historically, the hydrolyzing activity of Pth has been assayed with radiolabeled N-blocked aminoacyl-tRNAs in assay systems that require the separation of radiolabeled amino acid from the N-blocked aminoacyl-tRNA complex. In the present study, we describe the development of a kinetic fluorescence polarization (FP) assay that enables measurements of Pth activity without the need to separate bound and free tracer. The hydrolyzing activity of Pth was determined by measuring the change in polarization values that resulted from the cleavage of a fluorescently labeled substrate (BODIPY-Lys-tRNA(Lys)). The data were analyzed using an equation describing first-order dissociation and the results showed that the experimental data correlated well with the theoretical curve. A runs test of the residuals showed that the experimental data did not significantly differ from the first-order model. The assay is adaptable to a multiwell format and is sensitive enough to detect Pth-like activity in bacterial cell lysate. The Pth FP assay provides a homogeneous and kinetic format for measuring Pth activity in vitro.     

Kinetics mechanism of L-aspartate synthesis from ammonium fumarate catalyzed by free and immobilized cells of E. coli

A detailed study of kinetic peculiarities of the L-aspartate-ammonium-lyase reaction catalyzed by free and immobilized E. coli 85 cells incorporated into polyacrylamide gel, has been carried out. The effects of different types of bacterial cell "activation", substrate concentration and temperature on the reaction rate have been investigated. It was shown that the rate of the reaction is limited by the rate of the substrate transfer through the cell and cytoplasmic membranes and at sufficiently high values of the substrate can be described in terms of zero-order kinetics with respect to substrate and reaction products concentrations A kinetic model based on the diffuse and transfer processes of translocation of the aspartate-ammonium-lyase reaction participants through the cell and cytoplasmic membranes is proposed.     

A mathematical model for the kinetics of Methanobacterium bryantii M.o.H. considering hydrogen thresholds

We develop a kinetic model that builds on the foundation of classic Monod kinetics, but incorporates new phenomena such as substrate thresholds and survival mode observed in experiments with the H2-oxidizing methanogen Methanobacterium bryantii M.o.H. We apply our model to the experimental data presented in our companion paper on H2 thresholds. The model accurately describes H2 consumption, CH4 generation, biomass growth, substrate thresholds, and survival state during batch experiments. Methane formation stops when its Gibbs free energy is equal zero, although this does not interrupt H2 oxidation. The thermodynamic threshold for H2 oxidation occurs when the free energy for oxidizing H2 and transferring electrons to biomass is no longer negative, at approximately 0.4 nM. This threshold is not controlled by the Gibbs free energy equation of methanogenesis from H2 + HCO3- as we show in our companion paper. Beyond this threshold, the microorganisms shift to a low-maintenance metabolism called "the survival state" in response to extended H2 starvation; adding the starvation response as another new feature of the kinetic model. A kinetic threshold (or S (min)), a natural feature of the Monod kinetics, is also captured by the model at H2 concentration of around approximately 2,400 nM. S (min) is the minimum substrate concentration to maintain steady-state biomass concentration. Our model will be useful for interpreting threshold results and designing new studies to understand thresholds and their ecological implications.     

On the use of apparent kinetic parameters for immobilized enzyme with noncompetitive substrate inhibition

The use of a simple rate equation with apparent parameters to describe the kinetic behavior of an immobilized enzyme with noncompetitive substrate inhibition was assessed. To do so, the reaction rate was calculated as a function of the interfacial substrate concentration, and the results were used to identify the apparent kinetic parameters by nonlinear regression. This procedure was repeated for different values of the diffusional constraints and of the inhibition constant. The equation using apparent parameters can describe the global kinetic behavior, provided that the diffusional and inhibitory constraints are not too high. When the constraints are high, a Michaelis-Menten equation can be used to model the kinetics for interfacial concentrations lower than the concentration leading to the maximum reaction rate.     

Process model comparison and transferability across bioreactor scales and modes of operation for a mammalian cell bioprocess

A Monod kinetic model, logistic equation model, and statistical regression model were developed for a Chinese hamster ovary cell bioprocess operated under three different modes of operation (batch, bolus fed‐batch, and continuous fed‐batch) and grown on two different bioreactor scales (3 L bench‐top and 15 L pilot‐scale). The Monod kinetic model was developed for all modes of operation under study and predicted cell density, glucose glutamine, lactate, and ammonia concentrations well for the bioprocess. However, it was computationally demanding due to the large number of parameters necessary to produce a good model fit. The transferability of the Monod kinetic model structure and parameter set across bioreactor scales and modes of operation was investigated and a parameter sensitivity analysis performed. The experimentally determined parameters had the greatest influence on model performance. They changed with scale and mode of operation, but were easily calculated. The remaining parameters, which were fitted using a differential evolutionary algorithm, were not as crucial. Logistic equation and statistical regression models were investigated as alternatives to the Monod kinetic model. They were less computationally intensive to develop due to the absence of a large parameter set. However, modeling of the nutrient and metabolite concentrations proved to be troublesome due to the logistic equation model structure and the inability of both models to incorporate a feed. The complexity, computational load, and effort required for model development has to be balanced with the necessary level of model sophistication when choosing which model type to develop for a particular application. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2013