Modeling particle transport by bubbles for performance guidelines in airlift fermentors

A calculation method has been developed to model the statistical transport of biological particles in bubble-driven flows, with special reference to the biokinetics of environmental excursions experienced by individual cells, aggregated cells, or immobilization beads in airlift bioreactors. Interim developments on modeling the transport of such particles in concentric tube devices are reported. The calculation is driven by user-prescribed global parameters for the bioreactor geometry, bulk air flow rate, and particle parameters (size and slip speed). The algorithm calls on empirical data correlations for void fraction, bulk liquid flow rate, and bubble sizes and slip speeds, optimally selected from a large bibliographic database. The Monte Carlo algorithm concentrates on simulating particle transport in the bubbly riser flows.The packaged family of correlations and calculations represents, in effect, an expert system augmented by a transport simulation suited to characterizing the biokinetic response of cells cultured in airlift bioreactors.     

田间作物蒸腾量测算方法研究

本文依据Penman-Monteith方法对田间蒸腾量的测算进行了探讨,从理论上分析并导出蒸腾量的估算模式,对参数的估算也做了详细分析和讨论。最后用大屯农业生态系统试验站的观测资料对模式进行验证,结果表明,采用本模式计算田间蒸腾量效果很好。     

The biennial life strategy in a random environment

A discrete-time population model with two age classes is studied which describes the growth of biennial plants in a randomly varying environment. A fraction of the oldest age class delays its flowering each year. The solution of the model involves products of random matrices. We calculate the exact mean and variance of the long-run geometric growth rate assuming a gamma distribution for the random number of offspring per flowering plant after one year. It is shown, both by analytical calculation and numerical examples, that it is profitable for the population to delay its flowering, in the sense that the average growth rate increases and the extinction probability decreases. The optimal values of the flowering fraction depend upon the environmental and model parameters.     

A distributed parameter model for an airlift fermentor. Effects of pressure

A previously presented model for an airlift fermentor is extended by considering the variations of pressure along the tubes. The fluid dynamics of the system is represented with the acid of correlations obtained from experiments. Only oxygen concentrations are considerations are considered. The influences of the various parameters affecting the system are analyzed. The model allows prediction of oxygen concentrations in the different points of an airlift fermentor and calculation of the best values of the gas flow rate.     

Mathematical modeling of an aqueous film coating process in a Bohle Lab-Coater: Part 2: Application of the model

For the prediction of the air and product temperatures, the product moisture, and the air humidity during a coating process in a Bohle Lab-Coater, a model was developed. The purpose of this work was to determine the limit moisture, the critical moisture, and the constant for the exchange rate between both zones and to use these values for other sets of experiments to test the model. The adaptation of the 3 parameters (limit moisture, critical moisture, and exchange rate constant), was done by calculation of the product temperature in both zones for several sets of parameters in order to minimize the sum of square deviation between the calculated and the measured product temperatures. This set of parameters was used to test the validity of the model. By applying the model, the product temperature could be predicted based on the product, process, and equipment-related parameters. Hence, the model can be used to theoretically investigate the influence of different process paramaters. The mean difference between the predicted, and measured product temperatures in the steady state is ≈2 up to 3 K using the determined parameter set for the limit moisture, the critical moisture, and the exchange rate constant. The model is useful for the prediction of the air and product temperatures, the product moisture, and air humidity during a coating process in the Bohle Lab-Coater using round, biconvex tablets.     

Analytic solution to steady-state radial diffusion of a substrate with first-order reaction kinetics in the tissue of a Krogh's cylinder

It is often useful to calculate the concentration profile for a substrate undergoing reaction in the tissue surrounding a capillary. In this paper, we consider a model geometry consisting of a long straight cylinder of tissue surrounding a capillary. Substrate diffuses radially out of the capillary through the tissue, with consumption of substrate in the tissue directly proportional to substrate concentration (i.e., first-order reaction kinetics). The model is extended to include the case where a cylinder of necrotic tissue surrounds a metabolically active inner tissue cylinder. A simple analytic solution is derived, and concentration profiles are generated for various combinations of parameters. Compared to the case where substrate consumption is independent of concentration, this model predicts much more rapid depletion of substrate near the capillary interface. This can have significant implications for the calculation of the hypoxic fraction (e.g., tissue with pO(2)<0.5-5 mmHg) when tumor oxygenation is modeled. The model also permits calculation of the limiting substrate concentration for cell viability when the reaction rate constant is known and vice versa.     

A study of the change in conductivity of the neuronal membrane caused by a generator potential using a method of computer modeling

Injection of cAMP induces in snail neurons generator potential, which is related to an increase of sodium and decrease of potassium permeability of the neuron outer membrane. A model is proposed which takes into account cAMP diffusion inside the neuron from the injection place and interaction of these molecules with the intercellular system controlling permeability of the outer membrane. Resulting impulse generation induces calcium ions current through the outer membrane. The model also considers calcium diffusion toward cAMP and its effect on the rate of the enzyme work destroying cAMP. Agreement between the calculations of ionic current I(t) and the experiment permits determination of the model parameters and calculation of the observed change of time distribution of nerve impulses when calcium input is significant.     

Economic values of rabbit traits in different production systems

In animal breeding, genetic parameters along with economic weights (EWs) of traits are applied. Profit functions currently used to calculate rabbit traits’ EWs do not consider nutrient requirements based on animal weight, growth rate and doe reproductive status. Therefore, the aim of this study was to develop a flexible bioeconomic model of rabbit-production systems and implement it in a computer programme in order to calculate economic values and relative EWs for rabbit traits. The bioeconomic model includes calculation of the doe age structure in the stationary state of a doe population; calculation of progeny structure; modelling growth, digestible energy, feed and water requirements for does in different reproductive statuses and for all progeny groups using a normative approach; calculation of the total feed and non-feed costs, revenues and profit per doe and per year; calculation of marginal economic values for up to 20 production and functional traits and estimation of the relative EWs of selected traits. The application of the programme is shown through an example calculation of trait economic values for a typical Czech commercial rabbit-production system. The trait economic value expresses the change in profit per doe and per year when the trait mean is increased by one unit. The programme developed is primarily useful for selection purposes in rabbit-breeding systems. Using this programme, some economic analyses of the impact of production, management and economic circumstances on the economic efficiency of various rabbit-production systems can also be performed.     

An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.     

Monitoring of the Membrane Potential in Proteoliposomes with Incorporated Cytochrome-c Oxidase Using the Fluorescent Dye Indocyanine

A method has been developed to monitor changes of the membrane potential across vesicle membranes in real time. Using the potential-sensitive fluorescent dye indocyanine and on the basis of a water/lipid redistribution model, a calculation procedure has been introduced to estimate the membrane potential in vesicles with incorporated cytochrome-c oxidase. Physical parameters, such as vesicle size distribution and density of the lipid bilayer were estimated and used as calculation parameters. By extrapolation of the transient potential change to zero time, the initial rate of the potential change (dU/dt) could be calculated. It is also shown, that the initial potential change (dU/dt) may be used to study the proton/electron stoichiometry of cytochrome-c oxidase incorporated in the vesicles. Received: 28 September 1995/Revised: 6 February 1996     

Optimization and evaluation of vegetation photosynthesis and respiration model using the measurements collected from the forest site of subtropical coniferous-evergreen

 碳循环模型参数的确定和优化对生态系统净CO₂交换(NEE)的模型计算至关重要。该文利用2010–2012年ChinaFLUX千烟洲站点的通量观测资料, 对植被光合呼吸模型(VPRM)的参数进行了优化。通过比较两种不同的拟合方案, 发现利用传统光响应方程得到的参数不适用于VPRM, 而利用模型自身反演方案拟合得到的参数最大光量子效率(λ)达0.203, 大于C₃植物平均值, 但与其他相关研究结果吻合。采用VPRM模型反演方案优化得到的参数后, VPRM能较准确地模拟千烟洲站不同季节的NEE。其对全年半小时NEE模拟的平均误差为–0.86 μmol·m^–2·s^–1, 相关系数为0.72。模型可准确地模拟生长旺季NEE平均日变化, 但低估了非生长旺季白天吸收峰值约52%。通过个例分析发现, VPRM模型可以准确模拟晴天条件下NEE的时间变化, 但对阴雨天条件下NEE的模拟还存在较大的不确定性。该研究将有助于进一步改进CO₂通量及浓度的区域数值模拟。     

最小成本为目标函数时最优循环量的确定

由于超滤无相变,操作条件温和,能耗低等优点,使其在生物医药领域取得日益广泛的应用,尤其在价格昂贵的生物制品等热敏性生物活性物质的分离、浓缩和纯化中显示出极大优越性,已引起人们的广泛重视。然而,超滤优势的充分发挥受到许多因素的制约。在影响超滤的众多操作因素中,保留液循环量即膜面速度是其中最重要的因素之一,特别是当膜应用于中试或工业化生产后,最优循环量(膜面     

Nonstationary model of an axisymmetric mirror trap with nonequilibrium plasma

The DOL nonstationary model intended to describe plasma processes in axisymmetric magnetic mirror traps is considered. The model uses averaging over the bounce period in order to take into account the dependence of plasma parameters on the coordinate along the facility axis. Examples of calculations of trap parameters by means of the DOL code based on this model are presented. Among the features of the DOL model, one can single out two points: first, the capability of calculating the terms of the collision integral with the use of a non-Maxwellian scattering function while evaluating the distribution function of fast ions and, second, concerning the background plasma, the capability of calculating the longitudinal particle and energy fluxes in confinement modes with the particle mean free path being on the order of the trap length. The influence of the scattering function approximation used to calculate the collision integral on the solution to the kinetic equation is analyzed. The dependences of plasma parameters on the power of heating injectors and the length of the fast-ion turning zone are presented as calculation examples. The longitudinal profile of the fusion reaction rate in the case of a trap with a long fast-ion turning zone is shown to depend strongly on the input parameters of the model.     

Theoretical investigation of axial and local particle size distribution on expanded bed adsorption process

The general rate model was developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial variation of bed porosity, particle size distribution (PSD), external and intraparticle mass transfer, and dispersion in liquid and solid phase. The analysis of the influence of the model parameters on dynamic capacity (DC) was investigated. The simulation results showed that major impact on dynamic capacity is exerted by intraparticle mass transfer (particle diameter and pore diffusivity). The external mass transfer resistance and dispersion parameters have secondary effect on DC. The replacement of axial PSD by the mean particle diameter results in error in calculation of DC, which increases remarkably with the increase of mean particle diameter. The PSD can promote a very slow approaching of plateau concentration by breakthrough curves. It was shown also that axial bed porosity variation could be replaced by average porosity with negligible error for DC calculations.     

Voltage dependence of Na channel blockage by amiloride: Relaxation effects in admittance spectra

Summary Amiloride, present in the mucosal solution, causes the appearance of a distinct additional dispersion in the admittance spectrum of the apical membrane of toad urinary bladder. The parameters of this dispersion (characteristic frequency. amplitude) change with amiloride concentration and with membrane voltage. They allow the calculation of the overall rate constants for Na channel blockage by the positively charged form of amiloride. and the voltage dependence of these rate constants. The on-rate of blockage increases and the off-rate decreases when the membrane surface to which cationic amiloride has access, is made more positive. This result is suggestive of a blocking model where the cationic amidino group of amiloride, depending on its charge, senses 10 to 13% of the membrane voltage while invading the channel entrance by a single-step process, and rests at an electrical distance corresponding to 24 to 30% of membrane voltage while occupying the blocking position.     

Reactive extraction of penicillin G in a pilot plant Karr-column III. Modelling and simulation of the extraction process

Summary The longitudinal concentration profiles of penicillin the continuous aqueous phase of a pilot plant Karr-column of 7.6 m height was calculated by a mathematic model consisting of reaction rate and cascase models. Satisfactory agreements between calculated and measured profiles were found. The identified mass transfer coefficients are identical in the bench-scale and pilot plant columns, in the model medium and fermentation medium as well as at different stroke frequencies. The specific interfacial area are strongly influenced by these parameters. The model can be used for calculation of penicillin extraction columns of different sizes. For the layout of the columns, hydrodynamic data are needed, which, however, cannot yet be calculated on a theoretical basis.     

An extended kinetic analysis of valinomycin-induced Rb-transport through monoglyceride membranes

Summary The time course of the current following a voltage jump, which is applied to monoglyceride bilayers in the presence of valinomycin, shows two relaxation times. This is basically in agreement with a simple carrier model which has been described in full detail formerly. Relaxation times and amplitudes allow a calculation of the rate constants of the transport model. The presented data supplement an analysis which was hitherto based only on the slower relaxation process and on information derived from the nonlinearity of currentvoltage characteristics. The additional resolution of the faster relaxation time allowed an approximate determination of the voltage dependence of the translocation rate constant for the carrier-ion-complex and provided evidence for a small voltage dependence of the interfacial reaction. The dependence of the relaxation parameters on the ion concentration in the aqueous phase was interpreted assuming a saturation of the ion concentration at the reaction plane at high bulk concentrations.     

An extended kinetic analysis of valinomycin-induced Rb-transport through monoglyceride membranes.

The time course of the current following a voltage jump, which is applied to monoglyceride bilayers in the presence of valinomycin, shows two relaxation times. This is basically in agreement with a simple carrier model which has been described in full detail formerly. Relaxation times and amplitudes allow a calculation of the rate constants of the transport model. The presented data supplement an analysis which was hitherto based only on the slower relaxation process and on information derived from the nonlinearity of current-voltage characteristics. The additional resolution of the faster relaxation time allowed an approximate determination of the voltage dependence of the translocation rate constant for carrier-ion-complex and provided evidence for a small voltage dependence of the interfacial reaction. The dependence of the relaxation parameters on the ion concentration in the aqueous phase was interpreted assuming a saturation of the ion concentration at the reaction plane at high bulk concentrations.     

A Three-State Multi-Ion Kinetic Model for Conduction Properties of ClC-0 Chloride Channel

A three-state, multiion kinetic model was proposed to enable the conduction properties of the mammalian channel ClC-0 to be well characterized. Using this rate-theory based model, the current-voltage and conductance-concentration relations were obtained. The five parameters needed were determined by fitting the data of conduction experiments of the wild-type ClC-0 and its K519C mutant. The model was then tested against available calculation and simulation data, and the energy differences between distinct chloride-occupancy states computed agreed with an independent calculation on the binding free energies solved by using the Poisson-Boltzmann equation. The average ion number of conduction and the ion passing duration calculated closely resembled the values obtained from Brownian dynamics simulations. According to the model, the decrease of conductance caused by mutating residue K519 to C519 can be attributed to the effect of K519C mutation on translocation rate constants. Our study sets up a theoretical model for ion permeation and conductance in ClC-0. It provides a starting point for experimentalists to test the three-state model, and would help in understanding the conduction mechanism of ClC-0.     

不同步长尺度下BEPS碳循环模型的协同应用

小时步长的BEPSHourly模型可以模拟植被日内生态生理过程,但模型的结构及解算过程复杂耗时,常适用于站点尺度进行参数优化及总初级生产力(GPP)、净初级生产力(NPP)的日内变化分析;日步长的BEPSDaily模型解算日光合速率方法简单,不涉及众多的迭代过程,模型耗时较少,适用于模拟计算区域初级生产力及分析区域碳源/汇空间分布.本研究根据BEPSDaily及BEPSHourly各自的模型特点及适用性,提出了小时步长及日步长BEPS模型的协同应用研究方法.首先利用BEPSHourly模型在站点尺度进行主要光合作用参数——最大羧化速率(V_{c max})、最大电子传递速率(J_max)的优化,将优化后主要光合作用参数引入区域BEPSDaily模型进行参数修正,再基于优化修正后的区域BEPSDaily模型进行区域NPP估测.结果表明: 基于通量数据对光合作用主要参数进行优化可以提高模型的模拟能力;2011年,帽儿山地区不同森林类型的初级生产能力依次为阔叶林>针阔混交林>针叶林;本研究提出的不同步长尺度碳循环模型协同应用研究方法能够有效地进行主要光合作用参数的优化,模拟GPP、NPP的月平均日内变化,快速估测区域NPP并分析碳源/汇空间分布.