scholarly journals Subsite mapping of enzymes. Depolymerase computer modelling

1976 ◽  
Vol 159 (1) ◽  
pp. 105-120 ◽  
Author(s):  
J D Allen ◽  
J A Thoma
Keyword(s):  
Goodness Of Fit ◽  
Computer Modelling ◽  
Bond Cleavage ◽  
Calculated Data ◽  
Simulated Data ◽  
Binding Energies ◽  
Rate Coefficients ◽  
Minimization Procedure ◽  
Squared Residuals ◽  
Subsite Mapping

We have developed a depolymerase computer model that uses a minimization routine. The model is designed so that, given experimental bond-cleavage frequencies for oligomeric substrates and experimental Michaelis parameters as a function of substrate chain length, the optimum subsite map is generated. The minimized sum of the weighted-squared residuals of the experimental and calculated data is used as a criterion of the goodness-of-fit for the optimized subsite map. The application of the minimization procedure to subsite mapping is explored through the use of simulated data. A procedure is developed whereby the minimization model can be used to determine the number of subsites in the enzymic binding region and to locate the position of the catalytic amino acids among these subsites. The degree of propagation of experimental variance into the subsite-binding energies is estimated. The question of whether hydrolytic rate coefficients are constant or a function of the number of filled subsites is examined.

scholarly journals Subsite mapping of enzymes. Application of the depolymerase computer model to two α-amylases

1976 ◽  
Vol 159 (1) ◽  
pp. 121-132 ◽  
Author(s):  
J D Allen ◽  
J A Thoma
Keyword(s):  
Experimental Data ◽  
Computer Model ◽  
Rate Coefficient ◽  
Bond Cleavage ◽  
Preceding Paper ◽  
Rate Coefficients ◽  
Binding Region ◽  
Enzyme Binding ◽  
Chain Lengths ◽  
Subsite Mapping

In the preceding paper (Allen and Thoma, 1976) we developed a depolymerase computer model, which uses a minimization routine to establish a subsite map for a depolymerase. In the present paper we show how the model is applied to experimental data for two alpha-amylases. Michaelis parameters and bond-cleavage frequencies for substrates of chain lengths up to twelve glucosyl units have been reported for Bacillus amyloliquefaciens, and a subsite map has been proposed for this enzyme [Thoma et al. (1971) J. Biol. Chem. 246, 5621-5635]. By applying the computer model to the experimental data, we have arrived at a ten-subsite map. We find that a significant improvement in this map is achieved by allowing the hydrolytic rate coefficient to vary as a function of the number of occupied subsites comprising the enzyme-binding region. The bond-cleavage frequencies, the enzyme is found to have eight subsites. A partial subsite map is arrived at, but the entire binding region cannot be mapped because Michaelis parameters are complicated by transglycosylation reactions. The hydrolytic rate coefficients for this enzyme are not constant.

Inelastic processes in oxygen–hydrogen collisions

2019 ◽  
Vol 487 (4) ◽  
pp. 5097-5105 ◽  
Author(s):  
A K Belyaev ◽  
Ya V Voronov ◽  
A Mitrushchenkov ◽  
M Guitou ◽  
N Feautrier
Keyword(s):  
Cross Sections ◽  
Short Range ◽  
Calculated Data ◽  
Current Method ◽  
Quantum Probability ◽  
Rate Coefficients ◽  
Stellar Spectra ◽  
Internuclear Distances ◽  
Excitation Processes ◽  
Ionic States

ABSTRACT New accurate theoretical rate coefficients for (de)-excitation and charge transfer in low-energy O + H, O+ + H− and O− + H+ collisions are reported. The calculations of cross-sections and rate coefficients are performed by means of the quantum probability current method, using full configuration interaction ab initio electronic structure calculations that provide a global description of all 43 lowest molecular states from short to asymptotic internuclear distances. Thus, both long- and short-range non-adiabatic regions are taken into account for the first time. All the doublet, quartet and sextet OH molecular states, with excitation energy asymptotes up to 12.07 eV, as well as the two lowest ionic states with the asymptotes O−H+ and O+H− are treated. Calculations are performed for the collision energy range 0.01–100eV and the temperature range 1 000–10 000 K. The mechanisms underlying the processes are analysed: it is shown that the largest rate coefficients, with values exceeding 10−8 cm3 s−1, are due to ionic–covalent interactions present at large internuclear distances, while short-range interactions play an important role for rates with moderate values involved in (de)-excitation processes. As a consequence, a comparison of the present data with previously published results shows that differences of up to several orders of magnitude exist for rate coefficients with moderate values. It is worth pointing out the relatively large rate coefficients for triplet–quintuplet oxygen transitions, as well as for transitions between the O$(\rm 2p^{3}3s\, ^{5}$So) and O$(\rm 2p^{3}3p\, ^{5}$P) levels of the oxygen triplet and H(n = 2) levels. The calculated data are important for modelling stellar spectra, leading to accurate oxygen abundances.

scholarly journals Stacks of Azobenzene Stars: Self-Assembly Scenario and Stabilising Forces Quantified in Computer Modelling

Molecules ◽  
2019 ◽  
Vol 24 (23) ◽  
pp. 4387 ◽  
Author(s):  
Vladyslav Savchenko ◽  
Markus Koch ◽  
Aleksander S. Pavlov ◽  
Marina Saphiannikova ◽  
Olga Guskova
Keyword(s):  
Self Assembly ◽  
Density Functional ◽  
Computer Modelling ◽  
Light Stimulus ◽  
Dipole Moments ◽  
Intermolecular Forces ◽  
Binding Energies ◽  
The Self ◽  
Assembly Mechanism ◽  
Lateral Displacements

In this paper, the columnar supramolecular aggregates of photosensitive star-shaped azobenzenes with benzene-1,3,5-tricarboxamide core and azobenzene arms are analyzed theoretically by applying a combination of computer simulation techniques. Without a light stimulus, the azobenzene arms adopt the trans-state and build one-dimensional columns of stacked molecules during the first stage of the noncovalent association. These columnar aggregates represent the structural elements of more complex experimentally observed morphologies—fibers, spheres, gels, and others. Here, we determine the most favorable mutual orientations of the trans-stars in the stack in terms of (i) the π – π distance between the cores lengthwise the aggregate, (ii) the lateral displacements due to slippage and (iii) the rotation promoting the helical twist and chirality of the aggregate. To this end, we calculate the binding energy diagrams using density functional theory. The model predictions are further compared with available experimental data. The intermolecular forces responsible for the stability of the stacks in crystals are quantified using Hirshfeld surface analysis. Finally, to characterize the self-assembly mechanism of the stars in solution, we calculate the hydrogen bond lengths, the normalized dipole moments and the binding energies as functions of the columnar length. For this, molecular dynamics trajectories are analyzed. Finally, we conclude about the cooperative nature of the self-assembly of star-shaped azobenzenes with benzene-1,3,5-tricarboxamide core in aqueous solution.

scholarly journals How well does your model fit the data?

2001 ◽  
Vol 3 (1) ◽  
pp. 49-55 ◽  
Author(s):  
M. J. Hall
Keyword(s):  
Data Mining ◽  
Goodness Of Fit ◽  
Computer Modelling ◽  
Synthetic Data ◽  
Model Fit ◽  
Coefficient Of Determination ◽  
Input Output

Despite almost five decades of activity on the computer modelling of input–output relationships, little general agreement has emerged on appropriate indices for the goodness-of-fit of a model to a set of observations of the pertinent variables. The coefficient of efficiency, which is closely allied in form to the coefficient of determination, has been widely adopted in many data mining and modelling exercises. Values of this coefficient close to unity are taken as evidence of good matching between observed and computed flows. However, studies using synthetic data have demonstrated that negative values of the coefficient of efficiency can occur both in the presence of bias in computed outputs, and when the computed volume of flow greatly exceeds the observed volume of flow. In contrast, the coefficient of efficiency lacks discrimination for cases close to perfect reproduction. In the latter case, a coefficient based upon the first differences of the data proves to be more helpful.

An alternative to the goodness of fit

2016 ◽  
Vol 72 (6) ◽  
pp. 696-703 ◽  
Author(s):  
Julian Henn
Keyword(s):  
Experimental Data ◽  
Goodness Of Fit ◽  
Systematic Errors ◽  
Data Sets ◽  
Alternative Measure ◽  
Data Set ◽  
Statistical Errors ◽  
Entire Data ◽  
Squared Residuals ◽  
The Ideal

An alternative measure to the goodness of fit (GoF) is developed and applied to experimental data. The alternative goodness of fit squared (aGoFs) demonstrates that the GoF regularly fails to provide evidence for the presence of systematic errors, because certain requirements are not met. These requirements are briefly discussed. It is shown that in many experimental data sets a correlation between the squared residuals and the variance of observed intensities exists. These correlations corrupt the GoF and lead to artificially reduced values in the GoF and in the numerical value of thewR(F2). Remaining systematic errors in the data sets are veiled by this mechanism. In data sets where these correlations do not appear for the entire data set, they often appear for the decile of largest variances of observed intensities. Additionally, statistical errors for the squared goodness of fit, GoFs, and the aGoFs are developed and applied to experimental data. This measure shows how significantly the GoFs and aGoFs deviate from the ideal value one.

An Adjustment to the Time-Rescaling Method for Application to Short-Trial Spike Train Data

2003 ◽  
Vol 15 (11) ◽  
pp. 2565-2576 ◽  
Author(s):  
Matthew C. Wiener
Keyword(s):  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Simulated Data ◽  
Interval Censoring ◽  
Trial Data ◽  
Observation Window ◽  
Neural Data ◽  
Conditional Intensity Function ◽  
Spike Train Data

It is important to validate models of neural data using appropriate goodness-of-fit measures. Models summarizing some response features—for example, spike count distributions or peristimulus time histograms—can be assessed using standard statistical tools. Measuring the fit of a full point-process model of spike trains is more difficult. Recently, Barbieri, Quirk, Frank, Wilson, and Brown (2001) and Brown, Barbieri, Ventura, Kass, and Frank (2002) presented a method for rescaling time so that if an underlying description correctly describes the conditional intensity function of a point process, the rescaling will convert the process into a homogeneous Poisson process. The corresponding interevent intervals are exponential with mean 1 and can be transformed to be uniform; tests of the uniformity of the transformed intervals are thus tests of how well the model fits the data. When the lengths of interevent intervals are comparable to the length of the observation window, as can happen in common neurophysiology paradigms using short trials, the fact that long intervals cannot be observed (are censored) can cause the tests based on time rescaling to reject a correct model inappropriately. This article presents a simple adjustment to the time-rescaling method to account for interval censoring, avoiding inappropriate rejection of acceptable models for short-trial data. We illustrate the adjustment's effect using both simulated data and short-trial data from monkey primary visual cortex.

scholarly journals Binary orbits from combined astrometric and spectroscopic data

2018 ◽  
Vol 618 ◽  
pp. A100 ◽  
Author(s):  
L. B. Lucy
Keyword(s):  
Spectroscopic Data ◽  
Goodness Of Fit ◽  
Simulated Data ◽  
Statistical Properties ◽  
Posterior Distributions ◽  
Stellar Astronomy ◽  
Estimation Problems

An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components’ masses and for the binary’s parallax. One thousand independent repetitions of the simulation demonstrate that the 1- and 2-σ credibility intervals for these fundamental quantities have close to the correct coverage fractions. In addition, the simulations allow the investigation of the statistical properties of a Bayesian goodness-of-fit criterion and of the corresponding p-value. The criterion has closely similar properties to the traditional χ2 test for minimum-χ2 solutions.

scholarly journals Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 55
Author(s):  
Vytaras Brazauskas ◽  
Sahadeb Upretee
Keyword(s):  
Value At Risk ◽  
Goodness Of Fit ◽  
Risk Measures ◽  
Probability Distributions ◽  
Simulated Data ◽  
Information Criteria ◽  
Asymptotic Distributions ◽  
Parametric Estimation ◽  
Goodness Of Fit Tests ◽  
Transfer Strategies

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as in pricing of extreme events, developing reserve estimates, designing risk transfer strategies, and allocating capital. In this paper, we present the empirical nonparametric and two types of parametric estimators of quantiles at various levels. For parametric estimation, we employ the maximum likelihood and percentile-matching approaches. Asymptotic distributions of all the estimators under consideration are derived when data are left-truncated and right-censored, which is a typical loss variable modification in insurance. Then, we construct relative efficiency curves (REC) for all the parametric estimators. Specific examples of such curves are provided for exponential and single-parameter Pareto distributions for a few data truncation and censoring cases. Additionally, using simulated data we examine how wrong quantile estimates can be when one makes incorrect modeling assumptions. The numerical analysis is also supplemented with standard model diagnostics and validation (e.g., quantile-quantile plots, goodness-of-fit tests, information criteria) and presents an example of when those methods can mislead the decision maker. These findings pave the way for further work on RECs with potential for them being developed into an effective diagnostic tool in this context.

ESTIMATION OF EXTREME QUANTILES: EMPIRICAL TOOLS FOR METHODS ASSESSMENT AND COMPARISON

2000 ◽  
Vol 07 (01) ◽  
pp. 75-94 ◽  
Author(s):  
J. DIEBOLT ◽  
M.-A. EL-AROUI ◽  
V. DURBEC ◽  
B. VILLAIN
Keyword(s):  
Goodness Of Fit ◽  
Simulated Data ◽  
Real Data ◽  
Data Sets ◽  
Data Set ◽  
Extreme Quantiles ◽  
Maintenance Policies ◽  
Simulated Data Sets ◽  
Industrial Context

When extreme quantiles have to be estimated from a given data set, the classical parametric approach can lead to very poor estimations. This has led to the introduction of specific methods for estimating extreme quantiles (MEEQ's) in a nonparametric spirit, e.g., Pickands excess method, methods based on Hill's estimate of the Pareto index, exponential tail (ET) and quadratic tail (QT) methods. However, no practical technique for assessing and comparing these MEEQ's when they are to be used on a given data set is available. This paper is a first attempt to provide such techniques. We first compare the estimations given by the main MEEQ's on several simulated data sets. Then we suggest goodness-of-fit (Gof) tests to assess the MEEQ's by measuring the quality of their underlying approximations. It is shown that Gof techniques bring very relevant tools to assess and compare ET and excess methods. Other empirical criterions for comparing MEEQ's are also proposed and studied through Monte-Carlo analyses. Finally, these assessment and comparison techniques are experimented on real-data sets issued from an industrial context where extreme quantiles are needed to define maintenance policies.

Quantifying annual patterns in the frequency of mammalian births: do goodness-of-fit tests provide adequate inferences?

2012 ◽  
Vol 60 (6) ◽  
pp. 381 ◽  
Author(s):  
Evan Watkins ◽  
Julian Di Stefano
Keyword(s):  
Sample Size ◽  
Effect Size ◽  
Statistical Power ◽  
Goodness Of Fit ◽  
A Priori ◽  
Simulated Data ◽  
Maximum Effect ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Power Studies

Hypotheses relating to the annual frequency distribution of mammalian births are commonly tested using a goodness-of-fit procedure. Several interacting factors influence the statistical power of these tests, but no power studies have been conducted using scenarios derived from biological hypotheses. Corresponding to theories relating reproductive output to seasonal resource fluctuation, we simulated data reflecting a winter reduction in birth frequency to test the effect of four factors (sample size, maximum effect size, the temporal pattern of response and the number of categories used for analysis) on the power of three goodness-of-fit procedures – the G and Chi-square tests and Watson’s U2 test. Analyses resulting in high power all had a large maximum effect size (60%) and were associated with a sample size of 200 on most occasions. The G-test was the most powerful when data were analysed using two temporal categories (winter and other) while Watson’s U2 test achieved the highest power when 12 monthly categories were used. Overall, the power of most modelled scenarios was low. Consequently, we recommend using power analysis as a research planning tool, and have provided a spreadsheet enabling a priori power calculations for the three tests considered.

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