Rapid Global Fitting of Large Fluorescence Lifetime Imaging Microscopy Datasets

Fluorescence lifetime imaging (FLIM) is widely applied to obtain quantitative information from fluorescence signals, particularly using Förster Resonant Energy Transfer (FRET) measurements to map, for example, protein-protein interactions. Extracting FRET efficiencies or population fractions typically entails fitting data to complex fluorescence decay models but such experiments are frequently photon constrained, particularly for live cell or in vivo imaging, and this leads to unacceptable errors when analysing data on a pixel-wise basis. Lifetimes and population fractions may, however, be more robustly extracted using global analysis to simultaneously fit the fluorescence decay data of all pixels in an image or dataset to a multi-exponential model under the assumption that the lifetime components are invariant across the image (dataset). This approach is often considered to be prohibitively slow and/or computationally expensive but we present here a computationally efficient global analysis algorithm for the analysis of time-correlated single photon counting (TCSPC) or time-gated FLIM data based on variable projection. It makes efficient use of both computer processor and memory resources, requiring less than a minute to analyse time series and multiwell plate datasets with hundreds of FLIM images on standard personal computers. This lifetime analysis takes account of repetitive excitation, including fluorescence photons excited by earlier pulses contributing to the fit, and is able to accommodate time-varying backgrounds and instrument response functions. We demonstrate that this global approach allows us to readily fit time-resolved fluorescence data to complex models including a four-exponential model of a FRET system, for which the FRET efficiencies of the two species of a bi-exponential donor are linked, and polarisation-resolved lifetime data, where a fluorescence intensity and bi-exponential anisotropy decay model is applied to the analysis of live cell homo-FRET data. A software package implementing this algorithm, FLIMfit, is available under an open source licence through the Open Microscopy Environment.     

A Multi-Variate framework to assess reliability and discrimination power of Bayesian estimation of Intravoxel Incoherent Motion parameters

PurposeTo propose a multivariate multi-step framework for a systematic assessment of the estimation reliability and discriminability of Intravoxel Incoherent Motion (IVIM) model parameters.MethodsMonte-Carlo simulations were generated on a range of SNRs and in different IVIM combinations considering: i) a dense discretization with 24 b-values; ii) a discretization with 9 b-values. A state-of-the-art Bayesian fitting method was adopted. The framework assessed: i) the best model between mono- and bi-exponential, through the BIC index; ii) the fitting accuracy; iii) the power in discriminating two different IVIM parameters distributions of estimated coefficients, using a multivariate test. Exemplificative oncologic cases were also presented.ResultsThe bi-exponential fitting was reliable for perfusion fraction higher than 5%, with high accuracy in D estimation, acceptable error for f, but high uncertainty in D*. The discrimination of two distributions is generally feasible if differences in D values (at least 0.3 x10^-3 mm²/s) are present; in the case of similar D values, a minimal difference of 5% in f can be discriminated just in case of balanced sample size and dense b-values discretization, whereas the impact of D* is quite negligible. These results were also supported by clinical examples.ConclusionsIVIM model is generally accurate in estimating diffusion, but uncertainties related to perfusion estimation are not negligible and compromise the discrimination power when different populations should be differentiated. The proposed framework should be adopted as interpretative guidelines to better understand when IVIM model applied on real data can provide reliable findings.     

Protein fluorescence decay: discrete components or distribution of lifetimes? Really no way out of the dilemma?

A new methodology of fluorescence decay analysis by iterative reconvolution is presented. It is based on the recent finding that the statistics of single-photon time-correlated data are best described by a compound Poisson law and requires the recording of a sample of at least 20 decays. Application of multivariate statistical methods to the analysis of the recovered decay parameters results in improved accuracy and better estimation of the uncertainties of mono- and multiexponential decays. If it is, of course, not possible to distinguish unambiguously between discrete components and a continuous distribution of lifetimes, it is, however, possible to determine a higher limit of the width of such a distribution should it be present. With our methodology, the presence of a distribution of lifetimes with a width of approximately 20% of its center value inevitably leads to a failure in the deconvolution procedure, a fact of crucial importance in protein conformational studies, for example.     

Megavariate data analysis of mass spectrometric proteomics data using latent variable projection method

There are many data mining techniques for processing and general learning of multivariate data. However, we believe the wavelet transformation and latent variable projection method are particularly useful for spectroscopic and chromatographic data. Projection based methods are designed to handle hugely multivariate nature of such data effectively. For the actual analysis of the data we have used latent variable projection methods such as principal component analysis (PCA) and partial least squares projection to latent structures based discriminant analysis (PLS-DA) to analyze the raw data presented to the participants of the First Duke Proteomics Data Mining Conference. PCA was used to solve problem #1 (clustering problem) and the PLS-DA was used to solve problem #2 (classification problem). The idea of internal and external cross-validation was used to validate the model obtained from the classification analysis. The simple two-component PLS-DA model obtained from the analysis performed well. The model has completely separated the two groups from all the data. The same model applied on two-thirds of the data showed good performance by external validation with independent test set of remaining 13 specimens obtained by setting aside the spectra of every third specimen (accuracy of 85%).     

A systems-theory approach to the analysis of multiexponential fluorescence decay.

A mathematical model of the fluorescence decay experiment based on linear systems theory is presented. The model suggests an experimental technique that increases the probability of correctly determining the decay constants of a multicomponent system. The use of moment methods for data analysis improves accuracy by combining information obtained from several discrete experiments. Examples are presented to show that the analysis of a three component system composed of known standards is improved as the number of experimental determinations is increased from one to four. The discrete measurements are made by changing the excitation and emission wavelengths.     

Geographical information system parallelization for spatial big data processing: a review

With the increasing interest in large-scale, high-resolution and real-time geographic information system (GIS) applications and spatial big data processing, traditional GIS is not efficient enough to handle the required loads due to limited computational capabilities.Various attempts have been made to adopt high performance computation techniques from different applications, such as designs of advanced architectures, strategies of data partition and direct parallelization method of spatial analysis algorithm, to address such challenges. This paper surveys the current state of parallel GIS with respect to parallel GIS architectures, parallel processing strategies, and relevant topics. We present the general evolution of the GIS architecture which includes main two parallel GIS architectures based on high performance computing cluster and Hadoop cluster. Then we summarize the current spatial data partition strategies, key methods to realize parallel GIS in the view of data decomposition and progress of the special parallel GIS algorithms. We use the parallel processing of GRASS as a case study. We also identify key problems and future potential research directions of parallel GIS.     

Analysing spectral data: comparison and application of two techniques

This study compares two different methods of condensing complex spectral data into interpretable indices or metrics of colour. Colour spectra were measured on standardized Munsell colour paint chips and estimates of the three fundamental components of colour (brightness, chroma and hue) were generated using principal component analysis (PCA) and segment classification (SC). We tested the accuracy of these techniques for generating colour component estimates from spectral data in four different 'colour classes' (red/orange, yellow/ green, green/blue, and blue/purple) and in an aggregate data set containing all measured spectra. We conclude that both analysis techniques will generally provide more information than more conventional colour assessment techniques. Neither technique was superior under all conditions; appropriateness of each technique depends on the system under study. Efficacy of both techniques depends on the variability present in the data set; greater variance in colour tends to reduce overall resolution. An application of tfiese techniques is also presented in which we characterize sex-specific differences in colour between different populations of the poecilliid fish, Limia perugia.     

Statistical inference from single channel records: two-state Markov model with limited time resolution

Though stochastic models are widely used to describe single ion channel behaviour, statistical inference based on them has received little consideration. This paper describes techniques of statistical inference, in particular likelihood methods, suitable for Markov models incorporating limited time resolution by means of a discrete detection limit. To simplify the analysis, attention is restricted to two-state models, although the methods have more general applicability. Non-uniqueness of the mean open-time and mean closed-time estimators obtained by moment methods based on single exponential approximations to the apparent open-time and apparent closed-time distributions has been reported. The present study clarifies and extends this previous work by proving that, for such approximations, the likelihood equations as well as the moment equations (usually) have multiple solutions. Such non-uniqueness corresponds to non-identifiability of the statistical model for the apparent quantities. By contrast, higher-order approximations yield theoretically identifiable models. Likelihood-based estimation procedures are developed for both single exponential and bi-exponential approximations. The methods and results are illustrated by numerical examples based on literature and simulated data, with consideration given to empirical distributions and model control, likelihood plots, and point estimation and confidence regions.     

A segmentation/clustering model for the analysis of array CGH data

Microarray-CGH (comparative genomic hybridization) experiments are used to detect and map chromosomal imbalances. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose representative sequences share the same relative copy number on average. Segmentation methods constitute a natural framework for the analysis, but they do not provide a biological status for the detected segments. We propose a new model for this segmentation/clustering problem, combining a segmentation model with a mixture model. We present a new hybrid algorithm called dynamic programming-expectation maximization (DP-EM) to estimate the parameters of the model by maximum likelihood. This algorithm combines DP and the EM algorithm. We also propose a model selection heuristic to select the number of clusters and the number of segments. An example of our procedure is presented, based on publicly available data sets. We compare our method to segmentation methods and to hidden Markov models, and we show that the new segmentation/clustering model is a promising alternative that can be applied in the more general context of signal processing.     

Modeling the Genetic Control of HIV-1 Dynamics After Highly Active Antiretroviral Therapy

The progression of HIV disease has been markedly slowed by the use of highly active antiretroviral therapy (HAART). However, substantial genetic variation was observed to occur among different people in the decay rate of viral loads caused by HAART. The characterization of specific genes involved in HIV dynamics is central to design personalized drugs for the prevention of this disease, but usually cannot be addressed by experimental methods alone rather than require the help of mathematical and statistical methods. A novel statistical model has been recently developed to detect genetic variants that are responsible for the shape of HAART-induced viral decay curves. This model was employed to an HIV/AIDS trial, which led to the identification of a major genetic determinant that triggers an effect on HIV dynamics. This detected major genetic determinant also affects several clinically important parameters, such as half-lives of infected cells and HIV eradication times.Key Words: Hardy-weinberg equilibrium, bi-exponential function, quantitative trait loci, HIV dynamics, functional mapping.     

Constrained analysis of fluorescence anisotropy decay:application to experimental protein dynamics

Hydrodynamic properties as well as structural dynamics of proteins can be investigated by the well-established experimental method of fluorescence anisotropy decay. Successful use of this method depends on determination of the correct kinetic model, the extent of cross-correlation between parameters in the fitting function, and differences between the timescales of the depolarizing motions and the fluorophore's fluorescence lifetime. We have tested the utility of an independently measured steady-state anisotropy value as a constraint during data analysis to reduce parameter cross correlation and to increase the timescales over which anisotropy decay parameters can be recovered accurately for two calcium-binding proteins. Mutant rat F102W parvalbumin was used as a model system because its single tryptophan residue exhibits monoexponential fluorescence intensity and anisotropy decay kinetics. Cod parvalbumin, a protein with a single tryptophan residue that exhibits multiexponential fluorescence decay kinetics, was also examined as a more complex model. Anisotropy decays were measured for both proteins as a function of solution viscosity to vary hydrodynamic parameters. The use of the steady-state anisotropy as a constraint significantly improved the precision and accuracy of recovered parameters for both proteins, particularly for viscosities at which the protein's rotational correlation time was much longer than the fluorescence lifetime. Thus, basic hydrodynamic properties of larger biomolecules can now be determined with more precision and accuracy by fluorescence anisotropy decay.     

On the analysis of fluorescence decay kinetics by the method of least-squares

Analysis of fluorescence decay kinetics aims at the determination of the analytic expression and the numerical values of the pertinent parameters which describe the decay process. In the well-known method of least-squares, one assumes a plausible functional form for the decay data and adjusts the values of the parameters until the statistically best fit is obtained between the data and the calculated decay function, i.e., until the sum of the weighted squares of the residuals is at a minimum. It is shown that proper weighting of the squares of the residuals may markedly improve the quality of the analysis. Such weighting requires information about the character of the experimental noise, which is often available, e.g., when the noise is due to counting error in photon-counting techniques. Furthermore, dramatic improvements in the accuracy of the analysis may often be achieved by use of auxiliary information available about the system studied. For example, the preexponents in a multiexponential fluorescence decay of a mixture of chromophores (such as tryptophan residues in a protein molecule) may sometimes be estimated independently; much higher accuracy can then be attained for the decay lifetimes by analysis of the decay kinetics. It is proposed that the shape of the autocorrelation function of the weighted residuals may serve as a convenient criterion for the quality of fit between the experimental data and the decay function obtained by analysis. The above conclusions were reached by analysis of computer-simulated experiments, and the usefulness of this approach is illustrated. The importance of stating the uncertainties in the estimated parameters inherent in the analysis of decay kinetics is stressed.     

Drug metabolite profiling and identification by high-resolution mass spectrometry

Mass spectrometry plays a key role in drug metabolite identification, an integral part of drug discovery and development. The development of high-resolution (HR) MS instrumentation with improved accuracy and stability, along with new data processing techniques, has improved the quality and productivity of metabolite identification processes. In this minireview, HR-MS-based targeted and non-targeted acquisition methods and data mining techniques (e.g. mass defect, product ion, and isotope pattern filters and background subtraction) that facilitate metabolite identification are examined. Methods are presented that enable multiple metabolite identification tasks with a single LC/HR-MS platform and/or analysis. Also, application of HR-MS-based strategies to key metabolite identification activities and future developments in the field are discussed.     

Analysis of the Inheritance, Selection and Evolution of Growth Trajectories

We present methods for estimating the parameters of inheritance and selection that appear in a quantitative genetic model for the evolution growth trajectories and other "infinite-dimensional" traits that we recently introduced. Two methods for estimating the additive genetic covariance function are developed, a "full" model that fully fits the data and a "reduced" model that generates a smoothed estimate consistent with the sampling errors in the data. By decomposing the covariance function into its eigenvalues and eigenfunctions, it is possible to identify potential evolutionary changes in the population's mean growth trajectory for which there is (and those for which there is not) genetic variation. Algorithms for estimating these quantities, their confidence intervals, and for testing hypotheses about them are developed. These techniques are illustrated by an analysis of early growth in mice. Compatible methods for estimating the selection gradient function acting on growth trajectories in natural or domesticated populations are presented. We show how the estimates for the additive genetic covariance function and the selection gradient function can be used to predict the evolutionary change in a population's mean growth trajectory.     

Data-independent acquisition proteomics methods for analyzing post-translational modifications

Protein post-translational modifications (PTMs) increase the functional diversity of the cellular proteome. Accurate and high throughput identification and quantification of protein PTMs is a key task in proteomics research. Recent advancements in data-independent acquisition (DIA) mass spectrometry (MS) technology have achieved deep coverage and accurate quantification of proteins and PTMs. This review provides an overview of DIA data processing methods that cover three aspects of PTMs analysis, that is, detection of PTMs, site localization, and characterization of complex modification moieties, such as glycosylation. In addition, a survey of deep learning methods that boost DIA-based PTMs analysis is presented, including in silico spectral library generation, as well as feature scoring and error rate control. The limitations and future directions of DIA methods for PTMs analysis are also discussed. Novel data analysis methods will take advantage of advanced MS instrumentation techniques to empower DIA MS for in-depth and accurate PTMs measurements.     

Magnetic particle motions within living cells. Measurement of cytoplasmic viscosity and motile activity.

Submicrometer magnetic particles, ingested by cells and monitored via the magnetic fields they generate, provide an alternative to optical microscopy for probing movement and viscosity of living cytoplasm, and can be used for cells both in vitro and in vivo. We present methods for preparing lung macrophages tagged with magnetic particles for magnetometric study. Interpretation of the data involves fitting experimental remanent-field decay curves to nonlinear mechanistic models of intracellular particle motion. The model parameters are sensitive to mobility and apparent cytoplasmic viscosity experienced by particle-containing organelles. We present results of parameter estimation for intracellular particle behavior both within control cells and after (a) variable magnetization duration, (b) incubation with cytochalasin D, and (c) particle twisting by external fields. Magnetometric analysis showed cytoplasmic elasticity, dose-dependent motion inhibition by cytochalasin D, and a shear-thinning apparent viscosity.     

The validity of different methods of analysis of 133Xe washout curves for the determination of lung function

The influence of different mathematical methods on the analysis of ¹³³Xe washout data, used in the assessment of lung function in the pig, were investigated. When the data were fitted using a bi-exponential or a bi-exponential plus a constant type equation, neither the two clearance rate constants nor the overall 50% clearance time were found totally appropriate for the study of lung function. A new two compartmental model for the in vivo clearance of ¹³³Xe is proposed. The model assumes the whole blood as one compartment and the lung, including the pulmonary blood, as the second compartment. This suggests that the curvature of the xenon clearance curve is the result of recording the summation of the activities from the alveoli and the pulmonary blood and not, as previously described, due to the existence of two different sub-populations of alveoli.     

Two-site exchange revisited: a new method for extracting exchange parameters in biological systems.

A new analysis is presented which links real volume fractions, relaxation rates, and intracompartmental exchange rates directly with apparent volume fractions and relaxation rates obtained from biexponential fits of transverse magnetization decay curves. The analysis differs from previous methods in that measurements from two paramagnetic doping levels are used to close the two-site exchange equations. Both the new method and one previously described by Herbst and Goldstein (HG) have been applied to paramagnetically doped whole-blood data sets. Significant differences in the calculated exchange parameters are found between the two methods. A small dependence of the intracellular relaxation rate on extracellular paramagnetic agent concentration, assumed nonexistent with the HG method, is inferred from the new analysis. The analysis was also applied to published data on perfused rat hearts, and we obtained a limited assessment of two-site exchange in this system.     

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves

The usefulness of fluorescence techniques for the study of macromolecular structure and dynamics depends on the accuracy and sensitivity of the methods used for data analysis. Many methods for data analysis have been proposed and used, but little attention has been paid to the maximum likelihood method, generally known as the most powerful statistical method for parameter estimation. In this paper we study the properties and behavior of maximum likelihood estimates by using simulated fluorescence intensity decay data. We show that the maximum likelihood method provides generally more accurate estimates of lifetimes and fractions than does the standard least-squares approach especially when the lifetime ratios between individual components are small. Three novelties to the field of fluorescence decay analysis are also introduced and studied in this paper: a) discretization of the convolution integral based on the generalized integral mean value theorem: b) the likelihood ratio test as a tool to determine the number of exponential decay components in a given decay profile; and c) separability and detectability indices which provide measures on how accurately, a particular decay component can be detected. Based on the experience gained from this and from our previous study of the Padé-Laplace method, we make some recommendations on how the complex problem of deconvolution and parameter estimation of multiexponential functions might be approached in an experimental setting. Offprint requests to: F. G. Prendergast