Lucenz simulator: A tool for the teaching of enzyme kinetics

Low sidelobe levels may be a crucial factor in the success of achieving high gain using linear receiving arrays, since the level of the sidelobes determines the degree to which noisy nearby sources can be prohibited from interfering with the detection of a weak source on a different azimuth. In real world experiments at sea, one frequently operates with an array which has not only errors in amplitude and phase between channels but also dead elements. The effect of random errors in both amplitude and phase is to yield a sidelobe level of the average beam pattern which is the sum of the error-free pattern and an additional level due to the random errors. The sidelobe level due to the random errors depends upon the details of the amplitude shading function, the distribution function from which the random errors are drawn, and increases with the mean square value of the errors. Thus, given rms values of amplitude and phase errors, there is a practical limit to which the sidelobes can be reduced by amplitude shading the array. The effect of element failure on the sidelobe level can be drastic and depends on the sum of the amplitude weights of the dead elements. Thus, a failure of a highly-weighted element will have a greater effect on the sidelobe level than the failure of two or three whose combined weights are less. [Work supported by NAVMAT.]

The RNA-dependent RNA polymerase NS5B is a key enzyme of the replication of hepatitis C virus (HCV) and a major therapeutic target. Applying a novel continuous assay with highly purified protein and a fluorescent RNA-template we provide for the first time a comprehensive mechanistic description of the enzymatic reaction. Using fluorescence spectroscopy, the kinetics of NS5B was confirmed to consist of two half-reactions, namely substrate binding and turnover. Determining the binding constants of the substrates and the rate constants of individual reaction steps, NS5B was shown to bind the template single-stranded RNA with high affinity (nanomolar range) and in a stepwise process that reflects the substrate positioning. As demonstrated by CD, NTP(s) binding caused a tertiary structural change of the enzyme into an active conformation. The second half-reaction was dissected into a sequential polymerization and a subsequent, rate-limiting product release reaction. Taking advantage of these tools, we analyzed the mechanism of action of the NS5B inhibitor HCV-796, which was shown to interfere with the formation of double-stranded RNA by blocking the second half-reaction.

A method of model discrimination and parameter estimation in enzyme kinetics is proposed. The experimental design and analysis of the model are carried out simultaneously and the stopping rule for experimentation is deduced by the experimenter when the probabilities a posteriori indicate that one model is clearly superior to the rest. A FORTRAN77 program specifically developed for joint designs is given. The method is very powerful, as indicated by its usefulness in the discrimination between models. For example, it has been successfully applied to three cases of enzyme kinetics (a single-substrate Michaelian reaction with product inhibition, a single-substrate complex reaction and a two-substrate reaction). By using this method the most probable model and the estimates of the parameters can be obtained in one experimental session. The FORTRAN77 program is deposited as Supplementary Publication SUP 50134 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5.

In an interesting paper "The Effect of Random Errors in Gravity Data on Second Derivative Values," Thomas A. Elkins (1952) points out the need for eliminating the random component of gravity data before proceeding to interpret them with the aid of second derivative maps. There is a prima facie case for the elimination of random errors, if only to ensure reliability in results. The need, however, becomes more apparent if it is remembered: a. that the Second Derivative method of interpreting gravity (or magnetic) data is one of high resolving power, and b. that, therefore, errors creeping into those data may considerably vitiate the interpretation of those data.

Based on the works of Ruze and Vu, a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors. In this model, both nonuniform root mean square (rms) surface errors and nonuniform illumination functions are employed. In addition, the model incorporates the dependence on F/D in the construction of the solution. The mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna, the geometrical rms surface value is known. It is shown that closed-form expressions can then be derived, which result in a very efficient computational method for the average power pattern. Detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels. The results clearly demonstrate that as sidelobe levels decrease, their dependence on the surface rms/ \lambda becomes much stronger and, for a specified tolerance level, a considerably smaller rms/ \lambda is required to maintain the low sidelobes within the required bounds.

SAXS Ensemble Refinement of ESCRT-III CHMP3 Conformational Transitions

The effect of random errors in the steering vector of an Applebaum adaptive array is examined. Each component of the steering vector is assumed to have a random error component uncorrelated between elements. The array output signal-to-interferenceplus-noise ratio (SINR) is computed as a function of the error variance. It is shown that the array output SINR becomes more sensitive to steering vector errors as more elements are added to the array and as the received desired signal power becomes larger. The variance of the steering vector error that may be tolerated depends on the required desired signal dynamic range. The larger the dynamic range that must be accommodated, the smaller the error variance must be.

Errors are inevitable in the implementation of any complex process. Here we examine the effect of random errors on Single Transferable Vote (STV) elections, a common approach to deciding multi-seat elections. It is usually expected that random errors should have nearly equal effects on all candidates, and thus be fair. We find to the contrary that random errors can introduce systematic bias into election results. This is because, even if the errors are random, votes for different candidates occur in different patterns that are affected differently by random errors. In the STV context, the most important effect of random errors is to invalidate the ballot. This removes far more votes for those candidates whose supporters tend to list a lot of preferences, because their ballots are much more likely to be invalidated by random error. Different validity rules for different voting styles mean that errors are much more likely to penalise some types of votes than others. For close elections this systematic bias can change the result of the election.

The effect of a constant synchronization error on PN systems has been studied by Gill [1]. His results are generalized here for random synchronization errors, and extended to PSK systems using decision directed channel measurements [2]. In both cases, it is shown that the effect of random synchronization errors is to reduce the effective input signal power and to introduce an additional self-noise. The effect is minimized when the synchronization error has zero mean and can easily be evaluated in terms of circuit parameters.

Stereo vision (SV) is a widely used measurement technology, while accuracy is one of its most critical properties. Currently, modeling the volumetric error of the SV system is a way to improve measurement accuracy. This article proposes an accurate volumetric error modeling method for submeter SV systems. An analytical expression of the volumetric error considering the effect of random error is developed at first. To accurately evaluate the measurement error of SV systems, a platform consisting of a laser tracker and a robot is established, and an error evaluation method is proposed. Since the random error is coupled with the measurement error and impacts the accuracy of the volumetric error model, we propose an error decoupling method to separate the random error from the measurement error by only a single measurement. Finally, the accuracy of the proposed method is verified through simulations and experiments.

The kinetic compensation effect states that there is a linear relationship between Arrhenius parameters ln A and E for a family of related processes. It is a widely observed phenomenon in many areas of science, notably heterogeneous catalysis. This paper explores one of the mathematical, rather than physicochemical, explanations for the compensation effect and for the isokinetic relationship. It is demonstrated, both theoretically and by numerical simulations, that random errors in kinetic data generate an apparent compensation effect (sometimes termed the statistical compensation effect) when the true Arrhenius parameters are constant. Expressions for the gradient of data points on a plot of ln A against E are derived when experimental kinetic data are analysed by linear regression, by non-linear regression and by weighted linear regression. It is shown that the most appropriate analysis technique depends critically on the error structure of the kinetic data. Whenever data points on a plot of ln A against E are in a straight line with a gradient close to 1/RT, then confidence ellipses should be calculated for each data point to investigate whether the apparent compensation effect arises from random errors in the kinetic measurements or has some other origin.

Random errors due to the positioning of the coil blocks in superconducting magnets introduce error multipoles. Because the coil blocks are close to the limiting beam aperture, the multipoles are a sensitive function of the closed orbit. The consequences of this effect for the accumulation of current in high energy superconducting storage rings is discussed.

O objetivo deste trabalho foi estimar a proporção de ensaios com significância para efeito de blocos, cultivares e do atendimento às pressuposições de normalidade e aleatoriedade do erro, homogeneidade das variâncias do erro entre cultivares e a aditividade do modelo necessárias para os testes de hipótese. Também foi objetivo a quantificação do efeito do não atendimento das pressuposições sobre a diferença mínima significativa (DMS), obtida pelo teste de Tukey em nível de 5% de probabilidade. Foram analisados 307 ensaios da rede estadual de competição de cultivares de milho do Estado do Rio Grande do Sul no período de 1993 e 1996. Dos ensaios de competição de cultivares de milho, 85,67% apresentaram efeito significativo para cultivares e, nestes, a média da DMS era igual a 30,28%. O não atendimento às pressuposições para os testes de hipótese ocorreu em baixa freqüência e aumentou a DMS. A falta de aditividade no modelo ocorreu em 8,75% dos ensaios e não modificou a DMS, sendo a transformação indicada ineficiente para a redução da DMS. A causa da falta de aleatoriedade dos erros em 9,88% dos ensaios foi a variabilidade entre as unidades experimentais e/ou o bloqueamento em posição inadequada à variabilidade espacial da fertilidade no local do ensaio.

Abstract. Atmospheric turbidity is an important parameter for assessing the air pollution in local areas, as well as being the main parameter controlling the attenuation of solar radiation reaching the Earth's surface under cloudless sky conditions. Among the different turbidity indices, the Ångström turbidity coefficient β is frequently used. In this work, we analyse the performance of three methods based on broad-band solar irradiance measurements in the estimation of β. The evaluation of the performance of the models was undertaken by graphical and statistical (root mean square errors and mean bias errors) means. The data sets used in this study comprise measurements of broad-band solar irradiance obtained at eight radiometric stations and aerosol optical thickness measurements obtained at one co-located radiometric station. Since all three methods require estimates of precipitable water content, three common methods for calculating atmospheric precipitable water content from surface air temperature and relative humidity are evaluated. Results show that these methods exhibit significant differences for low values of precipitable water. The effect of these differences in precipitable water estimates on turbidity algorithms is discussed. Differences in hourly turbidity estimates are later examined. The effects of random errors in pyranometer measurements and cloud interferences on the performance of the models are also presented. Examination of the annual cycle of monthly mean values of β for each location has shown that all three turbidity algorithms are suitable for analysing long-term trends and seasonal patterns.

The effects of random errors and of nonconstant heat of vaporization upon the estimation of the second and third law heats of vaporization are examined. The most important conclusion is that the often noticed marked improvement in precision of the third law heat over that for the second law heat is real and is a natural consequence of the difference between the two estimators. The effects of systematic errors upon the two heats are not investigated here. Other results of interest, but of less importance because of the small magnitude of the effects, include: (1) the two heats are negatively correlated, (2) the second law heat is generally biased, (3) the third law heat is not the minimum variance unbiased estimator of the heat of vaporization, and (4) the standard deviation obtained from least squares fitting consistently overestimates the true standard deviation, but by a negligible amount. Any reversible process for which the equilibrium constant, is treated by a similar procedure is governed by the same considerations. The results apply approximately at any temperature although the stimulus for these considerations comes from high temperature chemistry.