Efficient step size selection for the tau-leaping simulation method

The tau-leaping method of simulating the stochastic time evolution of a well-stirred chemically reacting system uses a Poisson approximation to take time steps that leap over many reaction events. Theory implies that tau leaping should be accurate so long as no propensity function changes its value "significantly" during any time step tau. Presented here is an improved procedure for estimating the largest value for tau that is consistent with this condition. This new tau-selection procedure is more accurate, easier to code, and faster to execute than the currently used procedure. The speedup in execution will be especially pronounced in systems that have many reaction channels.     

Multinomial tau-leaping method for stochastic kinetic simulations

We introduce the multinomial tau-leaping (MtauL) method for general reaction networks with multichannel reactant dependencies. The MtauL method is an extension of the binomial tau-leaping method where efficiency is improved in several ways. First, tau-leaping steps are determined simply and efficiently using a priori information and Poisson distribution-based estimates of expectation values for reaction numbers over a tentative tau-leaping step. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper-bound estimation of the number of times a particular reaction occurs. Together, these features allow larger time steps where the numbers of reactions occurring simultaneously in a multichannel manner are estimated accurately using a multinomial distribution. Furthermore, we develop a simple procedure that places a specific upper bound on the total reaction number to ensure non-negativity of species populations over a single multiple-reaction step. Using two disparate test case problems involving cellular processes--epidermal growth factor receptor signaling and a lactose operon model--we show that the tau-leaping based methods such as the MtauL algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude.     

A combined explicit-implicit method for high accuracy reaction path integration

We present the use of an optimal combined explicit-implicit method for following the reaction path to high accuracy. This is in contrast to most purely implicit reaction path integration algorithms, which are only efficient on stiff ordinary differential equations. The defining equation for the reaction path is considered to be stiff, however, we show here that the reaction path is not uniformly stiff and instead is only stiff near stationary points. The optimal algorithm developed in this work is a combination of explicit and implicit methods with a simple criterion to switch between the two. Using three different chemical reactions, we combine and compare three different integration methods: the implicit trapezoidal method, an explicit stabilized third order algorithm implemented in the code DUMKA3 and the traditional explicit fourth order Runge-Kutta method written in the code RKSUITE. The results for high accuracy show that when the implicit trapezoidal method is combined with either explicit method the number of energy and gradient calculations can potentially be reduced by almost a half compared with integrating either method alone. Finally, to explain the improvements of the combined method we expand on the concepts of stability and stiffness and relate them to the efficiency of integration methods.     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

An automatic photometric method with high precision by gradually diluting a sample

An automatic photometric method to increase the precision of measurement is proposed, which is based on the injection of a very small volume of sample by rotary valve and the subsequent homogeneous mixing in a small reaction cell made of glass of the sample with a color-developing reagent gradually delivered by a syringe piston pump until the absorbance of the mixture approaches 0.434, where the lowest relative error in the concentration locates. This photometric method is characteristic of uniformly high precision, low sample and reagent consumption, and high sampling rate of 30 samples per h. The other advantages of this method include easy calibration with only one standard solution and no strict requirements on photometric components. While applied for the determination of cobalt ranging from 0.21 to 1.43 g 1(-1), the relative standard deviations are all below 0.4%.     

An automatic back titration method for microchemical analysis

An automatic back titration method for microchemical analysis is introduced, which is based on conventional volumetric analysis's principle and the use of flow injection analysis apparatus for the automation and microminiaturization of the process. The sample and a known, but excess amount of a calibrated reagent solution are injected and propelled into a titration cell, where their reaction takes place. The excess of the reagent is then titrated with a titrant containing an indicator and the end point is monitored photometrically. Since homogeneous mixing in the titration cell is obtained magnetically in the whole process, there is a linear relationship between the analyte's concentration and the volume of the titrant consumed. Nickel in the range of 10-70 g 1(-1) is determined by the above method, in which 30 microl of sample and 500 microl of EDTA are injected and the excess of EDTA is titrated with a standard zinc salt solution containing xylenol orange which could be blocked by nickel ion in a direct titration. This method is characteristic of low sample and reagent consumption, high sampling rate as high as 45 samples h(-1), negligible effect of sample's viscosity, small carry-over effect (lower than 0.14%), and very good precision, whose relative standard deviations are as small as 0.24%.     

Microdetermination of molybdenum by an automatic reaction-rate method

An automatic reaction-rate method is described for the microdetermination of molybdenum; the method is based on the hydrogen peroxide-iodide reaction which is catalyzed by molybdenum. The effect of reagent concentrations was studied and the maximum tolerable amounts of interfering ions were determined. Procedures for the determination of 0.01–0.15 μg and 0.1–1.0 μg molybdenum per milliliter are given ; 0.036–2.5 μg of molybdenum could be determined with relative errors of about 2%.     

Ultramicrodetermination of iridium by an automatic reaction-rate method

Summary An automatic spectrophotometric kinetic method is described for the ultramicrodetermination of iridium, based on its accelerating effect on the periodate photodecomposition. The time required for the reaction to consume a fixed amount of periodate is measured automatically and related directly to the iridium concentration. Ultramicroamounts of iridium in the range 80–800 ng (1.0×10^–7-1.0 x 10^–6 M) were determined with an average error of about 2%. The relative standard deviation for a 100-ppb iridium sample was 1.8%.

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Zusammenfassung Eine automatische, spektrophotometrische, kinetische Methode für die Ultramikrobestimmung von Iridium wurde beschrieben, die auf dessen beschleunigender Wirkung auf die Lichtzersetzung von Perjodat beruht. Die für den Verbrauch einer bestimmten Perjodatmenge erforderliche Zeit wird automatisch gemessen und unmittelbar in Beziehung zur Iridiumkonzentration gesetzt. 10^–7 bis 10^–6 M Iridium (80–800 ng) lassen sich auf etwa 2% genau bestimmen. Die relative Standardabweichung für 100 ppb Ir beträgt 1,8%.

     

Ultramicrodetermination of manganese by an automatic reaction-rate method

Summary An automatic spectrophotometric reaction-rate method is described for the ultramicrodetermination of manganese(II). The method is based on the potassium periodate-diethylaniline reaction which is catalyzed by manganese. The time required for the reaction to produce a small fixed amount of colored product is measured automatically and related directly to the manganese concentration. Maximum tolerable amounts of interfering ions were determined. Ultramicro amounts of manganese in the range 3–30 ng were determined with relative errors of about 2% and measurement times of 15–150 seconds. The coefficient of variation was 1.0%. The method was applied for the determination of manganese in natural waters.

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Zusammenfassung Eine automatische spektrophotometrische Methode der Reaktionszeitmessung für die Ultramikrobestimmung von Mangan(II) wurde beschrieben. Sie beruht auf der durch Mn katalysierten Umsetzung von Kaliumperjodat mit Diäthylanilin. Die für die Bildung einer bestimmten kleinen Menge gefärbten Produktes nötige Zeit wird automatisch gemessen und daraus auf die Mn-Konzentration geschlossen. Die maximal erlaubten Mengen störender Ionen wurden ermittelt. Mangan läßt sich in Mengen von 3 bis 30 ng mit einem relativen Fehler von ungefähr 2% bestimmen. Die zu messenden Reaktionszeiten betragen dann 15 bis 150 Sekunden. Der Variationskoeffizient beträgt 1,0%. Die Methode wurde zur Mn-Bestimmung in natürlichen Wässern verwendet.

     

A method for automatic impedance measurement and analysis

In this communication, we describe an experimental arrangement for sequential impedance measurements which has an experimental time comparable to that of techniques using integral transforms. This method has the advantage of simplicity of operation. A computer analysis of the data is also described.     

An automatic absorptiometric method for the determination of nitrate

A method has been developed for the determination of nitrate with the Technicon Autoanalyser in the range 2–10 p.p.m. The method depends on the reduction of nitrate to nitrite by hydrazine in alkaline solution, with copper as a catalyst. The nitrite produced diazotises sulphanilamide and the product is coupled with N-(1-naphthyl) ethylenediamine, to give a red dye, the absorbance of which is measured at 550 mμ. A relative standard deviation of 3–4% is obtained.     

催化动力学-流动注射停流分光光度法测定微量汞的研究

设计了分光光度自动分析系统的硬、软件 ,利用汞 ( )对藏红 T-碘化钾体系的催化褪色作用 ,建立了微量汞的催化动力学 -流动注射停流分光光度自动测定方法。Hg( )含量在 0～ 6.0 μg/m L范围内符合比尔定律 ,检出限为 3.5×1 0 -7g/m L,分析频率为 2 0 s/h。方法用于合成样品及污水中汞的测定 ,回收率为95.6%和 98.5% ,相对标准偏差为 5.1 %和 4.5% ( n=9     

Determination of potassium by an automatic ultraviolet absorptiometric method

An automatic ultraviolet absorptiometric method has been developed for the determination of potassium. The method involves precipitation of potassium by addition of a known excess of sodium tetraphenylborate, removal of the potassium tetraphenylborate precipitate by filtration, and measurement of the excess of sodium tetraphenylborate in the filtrate by means of its absorbance at 254 mμ;. Most of the apparatus, including a continuous filter, is standard AutoAnalyzer equipment but a Uvicord ultraviolet absorptiometer replaces the conventional colorimeter. Build-up of precipitate in the system is eliminated by immersing the mixing coils in an ultrasonic bath which is actuated intermittently by a simple timing mechanism. The method is especially suitable for potassium analysis in production plant where flame photometer results are sometimes affected by fertilizer dust in the air surrounding the burner.     

A quantitative CE method to analyse tau protein isoforms using coated fused silica capillaries

We evaluated the potential of CE to analyse different isoforms of unphosphorylated recombinant tau protein and for separating one phosphorylated tau from the respective unphosphorylated protein. Different capillary coatings such as polyacrylamide, poly‐(ethylene oxide) and polybrene (PB) were evaluated to overcome the poor efficiencies obtained with fused‐silica capillary. Although peak asymmetry values were quite similar for the three investigated coatings, the peak efficiencies were 35‐fold and 5‐fold higher with PB coating than with polyacrylamide and poly(ethylene oxide) coatings, respectively. The recovery percentage (over 97%) was satisfactory and confirmed the efficacy of PB coating to limit the adsorption of tau protein to capillary walls. Moreover, PB coating produced higher repeatability for migration times (RSD values <1.2%) in comparison to the neutral coatings. The potential of PB‐modified capillary in producing high resolutive separations of one phosphorylated tau isoform from its unphosphorylated counterpart and of a mixture of phosphorylated and unphosphorylated tau peptides was demonstrated with 50 mM phosphate buffer pH 3.0. The separation of unphosphorylated tau isoform 352 (Tau‐352) from Tau‐352 phosphorylated in vitro by the mitogen‐activated protein kinase ERK2, was accomplished in less than 15 min.