Quantification of two-dimensional NOE spectra via a combined linear and nonlinear least-squares fit

Summary Determining the volumes of peaks in 2D NMR spectra can be prohibitively difficult in cases of overlapping, broad lines. Deconvolution and parameter estimation can be attempted on either the time-domain or the frequency-domain data. We present a method of estimating spectral parameters from frequency-domain data, using a combination of Lorentzian and Gaussian lineshapes for reference lines. This approach combines a previously published method of projecting the data on a linear space spanned by reference lines with a nonlinear least-squares fitting algorithm. Comparison of this method with other published methods of frequency-domain deconvolution shows that it is both more precise and more accurate when estimating 2D volumes.     

Analysis of fluorescence decay curves by means of the Laplace transformation.

A computational procedure is described for the analysis of fluorescence decay data convolved with a lamp flash of finite width. The computer program calculates the ratio of the Laplace transforms of the decay and the lamp flash for different values of s to give the transforms of the impulse response for each value of s. These are set equal to the analytical Laplace transforms of the decay law involved. Solution of the nonlinear simultaneous equations yields the desired decay parameters. The method can be modified to analyze data that contains a component due to scattered light and can also provide essential information regarding transit time changes of the photomultiplier with changes in emission wavelength. The method was tested by the analysis of real and simulated data. The accuracy of the analysis depends on the degree of correlation among the parameters.     

THE LABELLED MITOSES CURVE AND THE ESTIMATION OF THE PARAMETERS OF THE CELL CYCLE

A method is described for fitting a 'fraction labelled mitoses'curve to a set of data points and for estimating the values of the best fitting parameters of the cell cycle. Estimates of the SE of the parameters are obtained. The method depends on the fact that when gamma distributions are used to describe the durations of the phases of the cell cycle, the Laplace transform of a FLM curve can be described by simple analytic functions enabling a least squares fit to be made to a set of Laplace transforms of the experimental data. The method is easy to program and quick to execute.     

Simultaneous analysis of multiple fluorescence decay curves by Laplace transforms. Deconvolution with reference or excitation profiles

The properties and potentials of the noniterative Laplace deconvolution (LAP2) (M. Ameloot and H. Hendrickx, Biophys. J. 44 (1983) 27) are further investigated. It is shown that LAP2 is exact and that no extrapolations have to be calculated or assumed for the data measured in the actual time window if the impulse response function of the investigated system can be described by a sum of exponentials. The formulas for the LAP2 deconvolution against the measured decay of a reference compound instead of the recorded excitation profile are derived. The procedure for the simultaneous analysis of multiple fluorescence decay curves by LAP2 is described in detail. This global analysis allows one to link any decay parameter, is fast and compares favorably with the nonlinear least-squares iterative reconvolution methods. Because of its short computation time the global analysis by LAP2 provides an efficient way to analyze the fluorescence decay surface in terms of decay associated spectra.     

DeconvTest: Simulation framework for quantifying errors and selecting optimal parameters of image deconvolution

Deconvolution is an essential step of image processing that aims to compensate for the image blur caused by the microscope's point spread function. With many existing deconvolution methods, it is challenging to choose the method and its parameters most appropriate for particular image data at hand. To facilitate this task, we developed DeconvTest: an open‐source Python‐based framework for generating synthetic microscopy images, deconvolving them with different algorithms, and quantifying reconstruction errors. In contrast to existing software, DeconvTest combines all components required to analyze deconvolution performance in a systematic, high‐throughput and quantitative manner. We demonstrate the power of the framework by using it to identify the optimal deconvolution settings for synthetic and real image data. Based on this, we provide a guideline for (a) choosing optimal values of deconvolution parameters for image data at hand and (b) optimizing imaging conditions for best results in combination with subsequent image deconvolution.     

Calibration of Wide-Field Deconvolution Microscopy for Quantitative Fluorescence Imaging

Deconvolution enhances contrast in fluorescence microscopy images, especially in low-contrast, high-background wide-field microscope images, improving characterization of features within the sample. Deconvolution can also be combined with other imaging modalities, such as confocal microscopy, and most software programs seek to improve resolution as well as contrast. Quantitative image analyses require instrument calibration and with deconvolution, necessitate that this process itself preserves the relative quantitative relationships between fluorescence intensities. To ensure that the quantitative nature of the data remains unaltered, deconvolution algorithms need to be tested thoroughly. This study investigated whether the deconvolution algorithms in AutoQuant X3 preserve relative quantitative intensity data. InSpeck Green calibration microspheres were prepared for imaging, z-stacks were collected using a wide-field microscope, and the images were deconvolved using the iterative deconvolution algorithms with default settings. Afterwards, the mean intensities and volumes of microspheres in the original and the deconvolved images were measured. Deconvolved data sets showed higher average microsphere intensities and smaller volumes than the original wide-field data sets. In original and deconvolved data sets, intensity means showed linear relationships with the relative microsphere intensities given by the manufacturer. Importantly, upon normalization, the trend lines were found to have similar slopes. In original and deconvolved images, the volumes of the microspheres were quite uniform for all relative microsphere intensities. We were able to show that AutoQuant X3 deconvolution software data are quantitative. In general, the protocol presented can be used to calibrate any fluorescence microscope or image processing and analysis procedure.     

From peptide libraries to optimized nonpeptide ligands in the search for S-farnesyltransferase inhibitors.

A complete 331,776-member library of tetrapeptides made of 24 amino acid building blocks was synthesized robotically on solid phase and subjected to a deconvolution based on the inhibitory potency of the sublibraries in a HPLC assay of the S-farnesyltransferase activity in vitro. One of the non-natural peptide and noncysteine-containing leads Nip-Trp-Phe-His (Nip=p-nitrophenyl-L-alanine) was optimized chemically to give a proteolytically stable pseudopeptide with a 200-fold potency compared with the original lead. The final compound was converted to the C-terminal ethyl ester: p-F-C6H4-CO(CH2)2-CO-Bta-D-Phepsi[CH2NH]His-OEt (Bta = benzothienyl-L-alanine) and shown to behave as a prodrug which was hydrolyzed back to the C-terminal acid following cell penetration. The method confirmed that several structurally original leads can be discovered in large libraries when deconvolution relies upon a highly specific assay and that these leads can be optimized by chemical modification to impart the final compound the desired pharmacological and pharmacokinetic properties.     

Iron-induced luminescence as a method for assessing lipid peroxidation of frozen-thawed goat spermatozoa

Freezing/thawing procedures induce enhanced reactive oxygen species (ROS) formation in mammalian sperm and these ROS may be a cause for the decrease in sperm function following cryopreservation. In the present study, we used a chemiluminescence method to detect ROS-induced damage in goat spermatozoa. Iron-induced luminescence of fresh and frozen/thawed sperm cells was assessed using a luminometer. It was shown that the freezing/thawing procedure had a significant effect on some luminescence parameters. Semen freezing significantly increased the values of integral, peak max, T.half (rise) and T.max (peak) parameters. A significant correlation was observed between the percentage of motile spermatozoa and integral, peak max and T.half (rise) parameters. In conclusion, the results of the present study indicate that measurement of induced luminescence can be an alternative, sensitive and relatively simple method for assessing the effect of cryopreservation on oxidative damage to spermatozoa.     

Determination of the volumetric mass transfer coefficient (k(L)a) using the dynamic "gas out-gas in" method: Analysis of errors caused by dissolved oxygen probes

There are many dynamic methods for measuring the volumetric mass transfer coefficient. The "gas out-gas in" method can directly determine the volumetric mass transfer coefficient in a bioreactor system and provide estimates of the volumetric microbial oxygen uptake rate and the average oxygen saturation concentration at the gas-liquid interface. The errors on these parameters are large if the dissolved oxygen probe response time is not considered. For reliable measurements, deconvolution of the oxygen probe measurements must be made. (c) 1995 John Wiley & Sons, Inc.     

A comparison of deconvolution techniques for stress relaxation

Stress relaxation (or equivalently creep) allows a large range of the relaxation (retardation) spectrum of materials to be examined, particularly at lower frequencies. However, higher frequency components of the relaxation curves (typically of the order of Hertz) are attenuated due to the finite time taken to strain the specimen. This higher frequency information can be recovered by deconvolution of the stress and strain during the loading period. This paper examines the use of three separate deconvolution techniques: numerical (Fourier) deconvolution, semi-analytical deconvolution using a theoretical form of the strain, and deconvolution by a linear approximation method. Both theoretical data (where the exact form of the relaxation function is known) and experimental data were used to assess the accuracy and applicability of the deconvolution methods. All of the deconvolution techniques produced a consistent improvement in the higher frequency data up to the frequencies of the order of Hertz, with the linear approximation method showing better resolution in high-frequency analysis of the theoretical data. When the different deconvolution techniques were applied to experimental data, similar results were found for all three deconvolution techniques. Deconvolution of the stress and strain during loading is a simple and practical method for the recovery of higher frequency data from stress-relaxation experiments.     

Use of mixture distributions to deconvolute the behavior of "hits" and controls in high-throughput screening data

The stochastic nature of high-throughput screening (HTS) data indicates that information may be gleaned by applying statistical methods to HTS data. A foundation of parametric statistics is the study and elucidation of population distributions, which can be modeled using modern spreadsheet software. The methods and results described here use fundamental concepts of statistical population distributions analyzed using a spreadsheet to provide tools in a developing armamentarium for extracting information from HTS data. Specific examples using two HTS kinase assays are analyzed. The analyses use normal and gamma distributions, which combine to form mixture distributions. HTS data were found to be described well using such mixture distributions, and deconvolution of the mixtures to the constituent gamma and normal parts provided insight into how the assays performed. In particular, the proportion of hits confirmed was predicted from the original HTS data and used to assess screening assay performance. The analyses also provide a method for determining how hit thresholds--values used to separate active from inactive compounds--affect the proportion of compounds verified as active and how the threshold can be chosen to optimize the selection process.     

Thermally stimulated luminescence glow curve structure of β‐irradiated CaB4O7:Dy

Thermally stimulated luminescence glow curves of CaB₄O₇:Dy samples after β‐irradiation showed glow peaks at ~335, 530 and 675 K, with a heating rate of 2 K/s. The main peak at 530 K was analyzed using the T_max–T_stop method and was found to be composed of at least five overlapping glow peaks. A curve‐fitting program was used to perform computerized glow curve deconvolution (CGCD) analysis of the complex peak of the dosimetric material of interest. The kinetic parameters, namely activation energy (E) and frequency factor (s), associated with the main glow peak of CaB₄O₇:Dy at 520 K were evaluated using peak shape (PS) and isothermal luminescence decay (ILD) methods. In addition, the kinetics was determined to be first order (b =1) by applying the additive dose method. The activation energies and frequency factors obtained using PS and ILD methods are calculated to be 0.72 and 0.72 eV and 8.76 × 10⁵ and 1.44 × 10⁶/s, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

An iterative method for the deconvolution of microcalorimeter thermograms

An iterative method for the deconvolution of microcalorimetry thermograms suitable for small digital computers is presented. The method employs a measured impulse response function directly as the deconvolution kernel, thus explicit system simulation is not required. Data are presented showing the performance of the method and the exchange of signal-to-noise ratio for time resolution that is made when deconvolution techniques are employed. An improvement in the system time resolution of fifty times is demonstrated with measured data.     

Computer simulation for deconvolution of a heat conduction batch microcalorimeter by the D-B finite element technique

The method described here is a generla numerical analysis procedure which has been applied to a heat conduction Batch calorimeter for the deconvolution of its thermograms, and is based on a computer simulations of the heat conduction behavior of the instrument with time. We show by means of test signals that the method can deconvolute the signal with a resolving time that is about two orders of magnitude smaller than the time constant of the calorimeter itself. The method can be applied to time signals generally, provided that the instrument producing them can be stimulated.     

Estimation and Prediction for Cancer Screening Models Using Deconvolution and Smoothing

The model that specifies that cancer incidence, I, is the convolution of the preclinical incidence, g, and the density of time in the preclinical phase, f, has frequently been utilized to model data from cancer screening trials and to estimate such quantities as sojourn time, lead time, and sensitivity. When this model is fit to the above data, the parameters of f as well as the parameter(s) governing screening sensitivity must be estimated. Previously, g was either assumed to be equal to clinical incidence or assumed to be a constant or exponential function that also had to be estimated. Here we assume that the underlying incidence, I, in the study population (in the absence of screening) is known. With I known, g then becomes a function of f, which can be solved for using (numerical) deconvolution, thus eliminating the need to estimate g or make assumptions about it. Since numerical deconvolution procedures may be highly unstable, however, we incorporate a smoothing procedure that produces a realistic g function while still closely reproducing the original incidence function I upon convolution with f. We have also added the concept of competing mortality to the convolution model. This, along with the realistic preclinical incidence function described above, results in more accurate estimates of sojourn time and lead time and allows for estimation of quantities related to overdiagnosis, which we define here.     

Structure determination of lipid bilayers

A method of determining the phases of X-ray reflections from oriented model membrane systems at low resolution is described. The method involves deconvolution and requires that d less than or equal to 2v where v is the width of the head group region within the bilayer and d is the thickness of the bilayer. The method can be used with a single set of X-ray data and applies to lipid bilayers which have a relatively constant density in the hydrocarbon region. Phases for the first five or six orders of phosphatidylethanolamine and lecithin are derived. A refined analysis based upon deconvolution but using information inherent in the Fourier profile is also described.     

Three-dimensional imaging by deconvolution microscopy

Deconvolution is a computational method used to reduce out-of-focus fluorescence in three-dimensional (3D) microscope images. It can be applied in principle to any type of microscope image but has most often been used to improve images from conventional fluorescence microscopes. Compared to other forms of 3D light microscopy, like confocal microscopy, the advantage of deconvolution microscopy is that it can be accomplished at very low light levels, thus enabling multiple focal-plane imaging of light-sensitive living specimens over long time periods. Here we discuss the principles of deconvolution microscopy, describe different computational approaches for deconvolution, and discuss interpretation of deconvolved images with a particular emphasis on what artifacts may arise.     

Padé-Laplace method for analysis of fluorescence intensity decay.

This novel approach to the analysis of multiexponential functions is based on the combined use of the Laplace transform and Padé approximants (Yeramian, E., and P. Claverie. 1987. Nature (Lond.). 326:169-174). It is similar in principle to the well-known Isenberg method of moments (Isenberg, I. 1983. Biophys. J. 43:141-148) traditionally applied to the analysis of fluorescence decay. The advantage of the Padé-Laplace method lies in its ability to detect the number of components in a multiexponential function as well as their parameters. In this paper we modified the original method so that it can be applied to the analysis of multifrequency phase/modulation measurements of fluorescence decay. The method was tested first on simulated data. It afforded recovery up to four distinct lifetime components (and their fractional contributions). In the case of simulated data corresponding to continuous lifetime distributions (nonexponential decay), the results of the analysis by the Padé-Laplace method indicated the absence of discrete exponential components. The method was also applied to real phase/modulation data gathered on known fluorophores and their mixtures and on tryptophan fluorescence in phospholipase A2. The lifetime and fraction recoveries were consistent with those obtained from standard methods involving nonlinear least-square fitting.     

Effect of IRSL-BLSL-TSL reading modes combination on thermoluminescence (TL) response of BeO dosimeter

The ultimate goal of this work is the study of the effect of luminescence stimulations and signals reading modes combinations on the thermoluminescence intensity and glow curve behaviour for the same X-ray irradiation dose. Three interesting stimulating and reading modes are considered, namely, infrared stimulated luminescence (IRSL), blue light-emitting diode stimulated luminescence (BLSL) and thermally stimulated luminescence (TSL). The studied stimulation and reading modes combination protocols are (Protocol 1) IRSL-TSL, (Protocol 2) IRSL-BLSL-TSL and (Protocol 3) BLSL-IRSL-TSL. Experiments are performed on beryllium oxide (BeO) dosimeter. Results demonstrate well that the combination of reading modes have direct impact on the TL signal in terms of intensity and glow curve shape. It was also found that when reading modes are correctly combined, particularly when IRSL is applied first, then BLSL and TL, it is possible to collect two or more exploitable signals of different stimulation types for the same irradiation that can be used for different purposes and final applications.