The spleen colony technique. I. Correction for the overlap effect and sources of error in CFU-s determination

A linear model for the errors of the 'spleen colony' assay for haemopoietic stem cells has been derived. The components emerging from the model are interpreted and practical recommendations given for interpreting measurements made with this assay. The model permits correction for the effect of overlapping colonies and gives average errors for single measurements of the number of CFU-s. More reliable and more precise information can be obtained using this model. The spleen colony technique detects a population of immature precursor cells designated as CFU-s (Till & McCulloch, 1961). The relative error of measurement is often large when compared with the changes in the phenomena studied. Consequently a better knowledge of the errors of this technique is highly desirable. This paper should be regarded as an extension of the previous analysis of Till (1972). The theory for the errors of the spleen colony technique was applied to 905 determinations of the CFU-s numbers performed on random-bred mice. Data from random-bred mice rather than those from inbred mice have been used because the error components can be expected to be larger and, consequently, more easily detectable. The model of errors has also been validated using data published by Till (1972) and has subsequently been applied to data from several inbred mice strains (Znojil & Necas, 1988).     

Herbivores and the Spatial Distributions of the Phytoplankton. II. Estimating Grazing in Planktonic Environments

Large errors are made when laboratory measurements of the ingestion rate of herbivorous zoo-plankton are used to estimate grazing in planktonic environments. The errors arise because the spatial heterogeneity in natural plankton distributions is greater than the heterogeneity present in laboratory experiments. Two probability models are developed for extrapolating laboratory measurements of ingestion to planktonic environments. Both models require sample statistics of the plankton distributions, and these are estimated from sampling studies of the small scale distribution of marine plankton. One model predicts laboratory measurements overestimate the ration obtained by an individual copepod by 30 %. A second model predicts errors exceeding ±50 % are possible when laboratory measurements are used to estimate the grazing by a population of cope-pods.     

Residential magnetic fields predicted from wiring configurations: II. Relationships To childhood leukemia.

Case-control data on childhood leukemia in Los Angeles County were reanalyzed with residential magnetic fields predicted from the wiring configurations of nearby transmission and distribution lines. As described in a companion paper, the 24-h means of the magnetic field's magnitude in subjects' homes were predicted by a physically based regression model that had been fitted to 24-h measurements and wiring data. In addition, magnetic field exposures were adjusted for the most likely form of exposure assessment errors: classic errors for the 24-h measurements and Berkson errors for the predictions from wire configurations. Although the measured fields had no association with childhood leukemia (P for trend=.88), the risks were significant for predicted magnetic fields above 1.25 mG (odds ratio=2.00, 95% confidence interval=1.03-3.89), and a significant dose-response was seen (P for trend=.02). When exposures were determined by a combination of predictions and measurements that corrects for errors, the odds ratio (odd ratio=2.19, 95% confidence interval=1.12-4.31) and the trend (p =.007) showed somewhat greater significance. These findings support the hypothesis that magnetic fields from electrical lines are causally related to childhood leukemia but that this association has been inconsistent among epidemiologic studies due to different types of exposure assessment error. In these data, the leukemia risks from a child's residential magnetic field exposure appears to be better assessed by wire configurations than by 24-h area measurements. However, the predicted fields only partially account for the effect of the Wertheimer-Leeper wire code in a multivariate analysis and do not completely explain why these wire codes have been so often associated with childhood leukemia. The most plausible explanation for our findings is that the causal factor is another magnetic field exposure metric correlated to both wire code and the field's time-averaged magnitude.     

Miniaturized receptor binding assays: complications arising from ligand depletion

The advent of miniaturized assay formats has made possible the screening of large numbers of compounds against a single target, known as high-throughput screening. Despite this clear advantage, assay miniaturization also increases the risk of ligand depletion, where the actual concentration of free ligand is significantly lower than that added. This, in turn, complicates the interpretation of data from such assays, potentially introducing significant error if not recognized. In this study, the effects of reducing assay volume on radioligand Kd and competitor Ki values have been investigated, using the muscarinic M(3) receptor as a model system. It was found that assay miniaturization caused dramatic effects, with up to a 30-fold underestimation of ligand affinity. A theoretical model was developed and shown to accurately predict both the degree of ligand depletion in any given assay volume and the effect of this depletion on affinity estimates for competing ligands. Importantly, it was found that in most cases, errors introduced by ligand depletion could be largely corrected for by the use of appropriate analysis methods. In addition to those previously described by others, the authors propose a simple method capable of correcting errors in competition binding experiments performed in conditions of ligand depletion.     

Model-based inference of neutralizing antibody avidities against influenza virus

To assess the response to vaccination, quantity (concentration) and quality (avidity) of neutralizing antibodies are the most important parameters. Specifically, an increase in avidity indicates germinal center formation, which is required for establishing long-term protection. For influenza, the classical hemagglutination inhibition (HI) assay, however, quantifies a combination of both, and to separately determine avidity requires high experimental effort. We developed from first principles a biophysical model of hemagglutination inhibition to infer IgG antibody avidities from measured HI titers and IgG concentrations. The model accurately describes the relationship between neutralizing antibody concentration/avidity and HI titer, and explains quantitative aspects of the HI assay, such as robustness to pipetting errors and detection limit. We applied our model to infer avidities against the pandemic 2009 H1N1 influenza virus in vaccinated patients (n = 45) after hematopoietic stem cell transplantation (HSCT) and validated our results with independent avidity measurements using an enzyme-linked immunosorbent assay with urea elution. Avidities inferred by the model correlated with experimentally determined avidities (ρ = 0.54, 95% CI = [0.31, 0.70], P < 10⁻⁴). The model predicted that increases in IgG concentration mainly contribute to the observed HI titer increases in HSCT patients and that immunosuppressive treatment is associated with lower baseline avidities. Since our approach requires only easy-to-establish measurements as input, we anticipate that it will help to disentangle causes for poor vaccination outcomes also in larger patient populations. This study demonstrates that biophysical modelling can provide quantitative insights into agglutination assays and complement experimental measurements to refine antibody response analyses.     

基于修正的亚像元模型的植被覆盖度估算

植被覆盖度是陆地生态过程模型、气象和气候模型的一项重要参数.通过消除植被类型分类精度以及遥感影像噪声带来的误差,结合实际测量值确定了归一化植被指数(NDVI)的最大值和最小值,修正了亚像元模型,并通过计算北京市植被覆盖度对模型进行了验证. 结果表明: 修正后模型的模拟值与实测值非常接近,尤其是对植被类型一致但密度有不同变化的草本植被, 但对乔木植被覆盖度的估算误差相对较大,这可能与遥感影像分辨率、植被破碎度及采用的混合像元模型有关.     

Sources of measurement error in assays of EROD activity of fish for biological effects monitoring

The paper describes the technical, procedural and biological aspects of 7-ethoxyresorufin O-deethylase (EROD) activity measurements in dab, Limanda limanda, from the North Sea. Several sources of measurement error in assays of EROD activity measurements for biological effects monitoring exercises could be defined, particularly for assay conditions, sample storage and sampling. In addition to variability caused by technical errors, biological features inherent in the surveyed fish may lead to even more severe errors in EROD activity measurements. This is particularly true of the choice of sampling time. Disregarding the species-specific spawning periods may lead to a loss of activity by a factor of as much as 90 in females and 40 in males, thus making it necessary to design sampling surveys appropriately. Received: 14 April 1999 / Received in revised form: 10 July 1999 / Accepted: 15 July 1999     

Bayesian analysis of serial dilution assays

In a serial dilution assay, the concentration of a compound is estimated by combining measurements of several different dilutions of an unknown sample. The relation between concentration and measurement is nonlinear and heteroscedastic, and so it is not appropriate to weight these measurements equally. In the standard existing approach for analysis of these data, a large proportion of the measurements are discarded as being above or below detection limits. We present a Bayesian method for jointly estimating the calibration curve and the unknown concentrations using all the data. Compared to the existing method, our estimates have much lower standard errors and give estimates even when all the measurements are outside the "detection limits." We evaluate our method empirically using laboratory data on cockroach allergens measured in house dust samples. Our estimates are much more accurate than those obtained using the usual approach. In addition, we develop a method for determining the "effective weight" attached to each measurement, based on a local linearization of the estimated model. The effective weight can give insight into the information conveyed by each data point and suggests potential improvements in design of serial dilution experiments.     

Idealized atomic coordinates of yeast phenylalanine transfer RNA.

The atomic coordinates are given for yeast phenylalanine transfer RNA in the orthorhombic crystal form. The structure has been refined by fitting to successively improved electron density maps at 2.7 Å resolution. The model fitting has been accomplished by using an interactive computer graphics system to minimize the errors inherent in manual model building and coordinate measurements, using an optical comparator. The atomic coordinates have then been “idealized” to make bond distances, bond angles, steric conformation and non-bonded contacts close to standard values, while constraining the model to fit the electron density maps.     

Spectral compensation for flow cytometry: visualization artifacts, limitations, and caveats.

BACKGROUND: In multicolor flow cytometric analysis, compensation for spectral overlap is nearly always necessary. For the most part, such compensation has been relatively simple, producing the desired rectilinear distributions. However, in the realm of multicolor analysis, visualization of compensated often results in unexpected distributions, principally the appearance of a large number of events on the axis, and even more disconcerting, an inability to bring the extent of compensated data down to "autofluorescence" levels. MATERIALS AND METHODS: A mathematical model of detector measurements with variable photon intensities, spillover parameters, measurement errors, and data storage characteristics was used to illustrate sources of apparent error in compensated data. Immunofluorescently stained cells were collected under conditions of limiting light collection and high spillover between detectors to confirm aspects of the model. RESULTS: Photon-counting statistics contribute a nonlinear error to compensated parameters. Measurement errors and log-scale binning error contribute linear errors to compensated parameters. These errors are most apparent with the use of red or far-red fluorochromes (where the emitted light is at low intensity) and with large spillover between detectors. Such errors can lead to data visualization artifacts that can easily lead to incorrect conclusions about data, and account for the apparent "undercompensation" previously described for multicolor staining. CONCLUSIONS: There are inescapable errors arising from imperfect measurements, photon-counting statistics, and even data storage methods that contribute both linearly and nonlinearly to a "spreading" of a properly compensated autofluorescence distribution. This phenomenon precludes the use of "quadrant" statistics or gates to analyze affected data; it also precludes visual adjustment of compensation. Most importantly, it is impossible to properly compensate data using standard visual graphical interfaces (histograms or dot plots). Computer-assisted compensation is required, as well as careful gating and experimental design to determine the distinction between positive and negative events. Finally, the use of special staining controls that employ all reagents except for the one of interest (termed fluorescence minus one, or "FMO" controls) becomes necessary to accurately identify expressing cells in the fully stained sample.     

Enzyme immunoassay of serum testosterone.

An enzyme immunoassay of serum testosterone using the testosterone-glucoamylase complex is described. Testosterone was estimated by the enzyme immunoassay after extraction with hexan: ether (4:1) for serum from men and additional thin layer chromatographic step for serum from women. The within and between assay errors, measured as the coefficient of variation were 11.1 percent (n=8) and 12.0 percent (n=12). The sensitivity of this assay was 0.25 ng. The mean testosterone concentration (+/- SD) in 19 normal men and 4 normal cycling women were 5.3 +/- 1.8 and 0.52 +/- 0.12 ng/ml, respectively. The level of testosterone found by the present assay compared favorably with those obtained by other methods.     

Linear constrain relations in biochemical reaction systems III. Sequential application of data reconciliation for sensitive detection of systematic errors

This article presents a method to test the presence of relatively small systematic measurement errors; e.g., those caused by inaccurate calibration or sensor drift. To do this, primary measurements-flow rates and concentrations-are first translated into observed conversions, which should satisfy several constraints, like the laws of conservation of chemical elements. This study considers three objectives: 1.Modification of the commonly used balancing technique to improve error sensitivity to be able to detect small systematic errors. To this end, the balancing technique is applied sequentially in time.2.Extension of the method to enable direct diagnosis of errors in the primary measurements instead of diagnosing errors in the observed conversions. This was achieved by analyzing how individual errors in the primary measurements are expressed in the residual vector.3.Derivation of a new systematic method to quantitatively determine the sensitivity of the error, is that error size at which the expected value of the chisquare test function equals its critical value.The method is applied to industrial data demonstrating the effectiveness of the approach. It was shown that, for most possible error sources, a systematic errors of 2% to 5% could be detected. In given application, the variation of the N-content of biomass was appointed to be the cause of errors. (c) 1994 John Wiley & Sons, Inc.     

Calibration of the "Flock of Birds" electromagnetic tracking device and its application in shoulder motion studies.

In this paper the applicability in terms of measurement accuracy of the "Flock of Birds" six D.O.F. electromagnetic tracking device in shoulder research is investigated. Position measurements in a workspace of approximately 1 m3 were performed using a stylus. The andom error at the stylus tip appeared to be 1.86, 1.98 and 2.54 mm for x-, y- and z-coordinate, respectively. The error caused by distortion of the magnetic field by metal in the concrete of especially the floor was 20.8, 22.2 and 20.4 mm for the x-, y- and z-coordinate, respectively. Calibration and leaving out the measurements closest to the floor lowered this error to 2.07, 2.38 and 2.35 mm. Orientation errors of the shoulder bones evolving from the measurement inaccuracy were estimated from repeated measurements of shoulder bony landmarks of ten subjects by means of the stylus. These errors were generally below 2 degrees. This is lower than found for the same measurements using a spatial linkage digitizer. It is concluded that the "Flock of Birds" is a useful tool for shoulder kinematic studies.     

Testing for differentially-expressed genes by maximum-likelihood analysis of microarray data.

Although two-color fluorescent DNA microarrays are now standard equipment in many molecular biology laboratories, methods for identifying differentially expressed genes in microarray data are still evolving. Here, we report a refined test for differentially expressed genes which does not rely on gene expression ratios but directly compares a series of repeated measurements of the two dye intensities for each gene. This test uses a statistical model to describe multiplicative and additive errors influencing an array experiment, where model parameters are estimated from observed intensities for all genes using the method of maximum likelihood. A generalized likelihood ratio test is performed for each gene to determine whether, under the model, these intensities are significantly different. We use this method to identify significant differences in gene expression among yeast cells growing in galactose-stimulating versus non-stimulating conditions and compare our results with current approaches for identifying differentially-expressed genes. The effect of sample size on parameter optimization is also explored, as is the use of the error model to compare the within- and between-slide intensity variation intrinsic to an array experiment.     

Optimized estimation of respiratory impedance by signal averaging in the time domain.

The spontaneous breathing of a subject during measurements of respiratory impedance (Zrs) by the forced oscillation technique (FOT) induces errors that result in biased impedance estimates, especially at low frequencies. Although in standard measurements this bias may be avoided by using special impedance estimators, there are two applications of FOT for which such estimators are not useful: when a head generator is used and when measurements are made during intubation. In this paper we describe a data-processing procedure for unbiased impedance estimation for all FOT setups. The proposed estimator (Z) was devised for pseudorandom excitation and is based on time-domain signal averaging before frequency analysis. The performance of estimator Z was first analyzed by computer simulation of a head generator setup and a setup including an endotracheal tube to measure (2-32 Hz) a resistance-inertance-elastance model mimicking Zrs of a healthy subject. Second, Z was assessed during real measurements in 16 healthy subjects. The results obtained in the simulation (e.g., error in elastance was reduced from 15.6% with most conventional estimators to 3.3% with Z in simulation of head generator setup) and in the measurements in subjects (differences of less than 1.6% between Z and a reference) confirmed the theoretical lack of bias of Z and its practical suitability for the different FOT setups. In addition to its applicability in the situations in which no other unbiased estimators are available, estimator Z is also advantageous in most conventional applications of FOT, since it requires much less computing time and thus allows on-line Zrs measurements.     

Continuous enzymatic assay for histone lysine methyltransferases

We describe a continuous peptide methylation assay using the Neurospora crassa Dim-5 histone H3 lysine 9 (H3K9) methyltransferase as a model system. The assay uses streptavidin FlashPlates coated with target peptide. Since no washing and pipeting steps were required after the addition of the enzyme/S-adenosyl-L-methionine (AdoMet) mixture to the microplate, a continuous readout of the reaction progress was possible. We show that this assay is highly reproducible (with errors in the order of +/- 3%). The continuous assay is well suited for the simultaneous analysis of up to 384 samples, thus allowing for a rapid screening of methylation rates of different substrates under different conditions or in the presence of inhibitors.     

Electrical properties of frog skeletal muscle fibers interpreted with a mesh model of the tubular system.

This paper presents the construction, derivation, and test of a mesh model for the electrical properties of the transverse tubular system (T-system) in skeletal muscle. We model the irregular system of tubules as a random network of miniature transmission lines, using differential equations to describe the potential between the nodes and difference equations to describe the potential at the nodes. The solution to the equations can be accurately represented in several approximate forms with simple physical and graphical interpretations. All the parameters of the solution are specified by impedance and morphometric measurements. The effect of wide circumferential spacing between T-system openings is analyzed and the resulting restricted mesh model is shown to be approximated by a mesh with an access resistance. The continuous limit of the mesh model is shown to have the same form as the disk model of the T-system, but with a different expression for the tortuosity factor. The physical meaning of the tortuosity factor is examined, and a short derivation of the disk model is presented that gives results identical to the continuous limit of the mesh model. Both the mesh and restricted mesh models are compared with experimental data on the impedance of muscle fibers of the frog sartorius. The derived value for the resistivity of the lumen of the tubules is not too different from that of the bathing solution, the difference probably arising from the sensitivity of this value to errors in the morphometric measurements.     

Centers and angles of rotation of body joints: A study of errors and optimization

Large variations are generally reported in the locations of centers of rotation (CR) for each of various joints in the human body. Some of these reports present conflicting results. This paper shows that this may be due in part to suboptimal experimental design as well as the phenomenon of error magnification. An algorithm is presented for computing the coordinates of the CR and the angle of rotation from the x, y coordinate measurements of two point markers on a moving body in two different positions. Error analysis is performed using a mathematical model that introduces systematically a positive or a negative error into each of the 8 x, y coordinates in all possible combinations, resulting in 256 CR locations. CR error zones are computed and graphed. Parametric analysis of the experimental set-up leads to optimization of the set-up. A typical case is analyzed and its errors computed. It is shown that small errors present in the measurements of the x, y coordinates of the markers are magnified to relatively large errors in the CR coordinates. In a suboptimal case, this magnification may be 30–50 times or more. The results show that, besides the magnitude of x, y coordinate errors, other factors responsible for determining the magnitude of errors in the location of the CR are: the magnitude of angle of rotation, the orientation of the markers with respect to the CR and their distances from the CR. In conjunction with the CR, the angle of rotation is also analyzed. Guidelines for optimal experimental set-up for minimizing the output errors are presented.     

The magnetic field of a single axon. A comparison of theory and experiment.

The magnetic field and the transmembrane action potential of a single nerve axon were measured simultaneously. The volume conductor model was used to calculate the magnetic field from the measured action potential, allowing comparison of the model predictions with the experimental data. After analyzing the experiment for all systematic errors, we conclude that the shape of the magnetic field can be accurately predicted from the transmembrane potential and, more importantly, the shape of the transmembrane potential can be calculated from the magnetic field. The data are used to determine ri, the internal resistance per unit length of the axon, to be 19.3 +/- 1.9 k omega mm-1, implying a value for the internal conductivity of 1.44 +/- 0.33 omega -1 m-1. Magnetic measurements are compared with standard bioelectric techniques for studying nerve axons.