Additive models for dependent cell populations

We propose an additive model for cell population growth which allows for positive correlation between sister cell lifetimes but arbitrary correlations between mother and daughter cell lifetimes. In the model each cell lifetime is the sum of two independent components, one of which is shared with its sister cell and which is also a function of the components of the lifetime of their mother. Assuming that the components follow a gamma distribution, the model is fitted to cell lifetime data of EMT6 cells obtained by the method of time-lapse cinematography.     

Fluorescence lifetime: Beating the IRF and interpulse window

Fluorescence lifetime imaging captures the spatial distribution of chemical species across cellular environments employing pulsed illumination confocal setups. However, quantitative interpretation of lifetime data continues to face critical challenges. For instance, fluorescent species with known in vitro excited-state lifetimes may split into multiple species with unique lifetimes when introduced into complex living environments. What is more, mixtures of species, which may be both endogenous and introduced into the sample, may exhibit 1) very similar lifetimes as well as 2) wide ranges of lifetimes including lifetimes shorter than the instrumental response function or whose duration may be long enough to be comparable to the interpulse window. By contrast, existing methods of analysis are optimized for well-separated and intermediate lifetimes. Here, we broaden the applicability of fluorescence lifetime analysis by simultaneously treating unknown mixtures of arbitrary lifetimes—outside the intermediate, Goldilocks, zone—for data drawn from a single confocal spot leveraging the tools of Bayesian nonparametrics (BNP). We benchmark our algorithm, termed BNP lifetime analysis, using a range of synthetic and experimental data. Moreover, we show that the BNP lifetime analysis method can distinguish and deduce lifetimes using photon counts as small as 500.     

Application of method of moments analysis to fluorescence decay lifetime distributions

In fluorescence decay work, distributions of exponential decay lifetimes are anticipated where complex systems are examined. We describe here methods of gaining information on such distributions using the method of moments analysis approach. The information obtained may be as simple as the average and deviation of the lifetime distribution, quantities which we show may be estimated directly from the results of a multiexponential analysis. An approximation to the actual distribution shape may also be obtained using a procedure we call the variable filter analysis (VFA) method without making any assumptions about the shape of the distribution. Tests of VFA using both simulated and experimental data are described. Limitations of this method and of distribution analysis methods in general are discussed. Results of analyses on experimental decays for ethidium intercalated in core particles and in free DNA are reported.     

A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation

Global fitting algorithms have been shown to improve effectively the accuracy and precision of the analysis of fluorescence lifetime imaging microscopy data. Global analysis performs better than unconstrained data fitting when prior information exists, such as the spatial invariance of the lifetimes of individual fluorescent species. The highly coupled nature of global analysis often results in a significantly slower convergence of the data fitting algorithm as compared with unconstrained analysis. Convergence speed can be greatly accelerated by providing appropriate initial guesses. Realizing that the image morphology often correlates with fluorophore distribution, a global fitting algorithm has been developed to assign initial guesses throughout an image based on a segmentation analysis. This algorithm was tested on both simulated data sets and time-domain lifetime measurements. We have successfully measured fluorophore distribution in fibroblasts stained with Hoechst and calcein. This method further allows second harmonic generation from collagen and elastin autofluorescence to be differentiated in fluorescence lifetime imaging microscopy images of ex vivo human skin. On our experimental measurement, this algorithm increased convergence speed by over two orders of magnitude and achieved significantly better fits.     

Are fluctuating asymmetry studies adequately sampled? Implications of a new model for size distribution

Previous work on fluctuating asymmetry (FA) has highlighted its controversial relationship with environmental stress and genetic architecture. While size-based measures of FA have been assumed to have half-normal distributions within populations, studies of model developmental mechanisms have suggested other plausible distributions for FA. We investigated the distribution of FA in large empirical data sets of wing shape and wing size asymmetry from three species of insects (cotton aphid Aphis gossipyii Glover, honeybee Apis mellifera, and long-legged fly Chrysosoma crinitus). Regardless of measurement method, FA was best described by a double Pareto-lognormal (DPLN) distribution or one of its limiting functional forms. To investigate convergence of mean sample FA to the population mean at various sample sizes, we sampled repeatedly under a DPLN distribution using parameter values that best fitted our data. Sample variances are much larger, and hence, convergence is slowed considerably with univariate or multivariate size-based measures of FA in contrast to a multivariate shape-based measure of FA. We suggest that much of the past work on FA may be undersampled, and we recommend using multivariate shape-based approaches or collecting larger data sets in future studies. We also discuss the implications of the DPLN distribution for understanding the developmental mechanisms underlying FA.     

Persistence of cell cycle times over many generations as determined by heritability of colony sizes of ras oncogene-transformed and non-transformed cells

Abstract. The persistence of cell lifetimes during about 10 successive cell generations was investigated by comparing the number of cells in primary colonies and in secondary colonies derived from primary colonies. Primary colonies were grown from single cells for 3 or 4 days (a time equivalent to an average of five cell generations) and the number of cells in each primary colony determined. Cells in each primary colony were dispersed to initiate secondary colonies, grown for the same time, and the number of cells in secondary colonies determined. Several criteria were used to compare primary and related secondary colonies, the most informative was found to be regression and correlation coefficients between number of cells in primary colonies and mean numbers of cells in related secondary colonies. For two non-transformed mouse fibroblast cell lines, NIH 3T3 and BALB 3T3, the regression and correlation coefficients of cell number in primary and secondary colonies were positive. This suggests inheritance of cell lifetimes over many cell generations. After the addition of an activated ras oncogene (human cellular Harvey ras , or viral Kirsten ras ) some regression and correlation coefficients changed in magnitude but all remained positive. Comparison of experimental data and the results of computer simulations suggest that several models of inheritance of cell lifetimes are not adequate to explain the results, including a model of independence between lifetimes of mother and daughter cells and the common model that describes daughter cells as inheriting the lifetime of their mother with deviation. Simulations do suggest that cell lifetimes are inherited within clones as deviation from the lifetime of the initial cell, and that the ras oncogene does not destroy persistence within clones but does increase heterogeneity of cell lifetimes.     

Application of the stretched exponential function to fluorescence lifetime imaging

Conventional analyses of fluorescence lifetime measurements resolve the fluorescence decay profile in terms of discrete exponential components with distinct lifetimes. In complex, heterogeneous biological samples such as tissue, multi-exponential decay functions can appear to provide a better fit to fluorescence decay data than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is essentially arbitrary and is often erroneous. Moreover, interactions, both between fluorophores and with their environment, can result in complex fluorescence decay profiles that represent a continuous distribution of lifetimes. Such continuous distributions have been reported for tryptophan, which is one of the main fluorophores in tissue. This situation is better represented by the stretched-exponential function (StrEF). In this work, we have applied, for the first time to our knowledge, the StrEF to time-domain whole-field fluorescence lifetime imaging (FLIM), yielding both excellent tissue contrast and goodness of fit using data from rat tissue. We note that for many biological samples for which there is no a priori knowledge of multiple discrete exponential fluorescence decay profiles, the StrEF is likely to provide a truer representation of the underlying fluorescence dynamics. Furthermore, fitting to a StrEF significantly decreases the required processing time, compared with a multi-exponential component fit and typically provides improved contrast and signal/noise in the resulting FLIM images. In addition, the stretched-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the resulting heterogeneity map can reveal subtle tissue differences that other models fail to show.     

Interpretation of fluorescence decays using a power-like model

A power-like decay function, characterized by the mean excited-state lifetime and relative variance of lifetime fluctuation around the mean value, was applied in analysis of fluorescence decays measured with the aid of time-correlated single photon counting. We have examined the fluorescence decay, in neutral aqueous medium, of tyrosine (L-tyrosine and N-acetyl-L-tyrosinamide), and of the tyrosine residues in a tryptophan-free protein, the enzyme purine nucleoside phosphorylase from Escherichia coli in a complex with formycin A (an inhibitor), and orthophosphate (a co-substrate). Tryptophan fluorescence decay was examined in neutral aqueous medium for L-tryptophan, N-acetyl-L-tryptophanamide, and for two tryptophan residues in horse liver alcohol dehydrogenase. To detect solvent effect, fluorescence decay of Nz-acetyl-L-tryptophanamide in aqueous medium was compared with that in dioxan. Hitherto, complex fluorescence decays have usually been analyzed with the aid of a multiexponential model, but interpretation of the individual exponential terms (i.e., pre-exponential amplitudes and fluorescence lifetimes), has not been adequately characterized. In such cases the intensity decays were also analyzed in terms of the lifetime distribution as a consequence of an interaction of fluorophore with environment. We show that the power-like decay function, which can be directly obtained from the gamma distribution of fluorescence lifetimes, is simpler and provides good fits to highly complex fluorescence decays as well as to a purely single-exponential decay. Possible interpretation of the power-like model is discussed.     

Fluorescence lifetime distributions of diphenylhexatriene-labeled phosphatidylcholine as a tool for the study of phospholipid-cholesterol interactions.

Fluorescence lifetimes of 1-palmitoyl-2-diphenylhexatrienylpro-pionyl-phosphatidylc hol ine in vesicles of palmitoyloleoyl phosphatidylcholine (POPC) (1:300, mol/mol) in the liquid crystalline state were determined by multifrequency phase fluorometry. On the basis of statistic criteria (chi 2red) the measured phase angles and demodulation factors were equally well fitted to unimodal Lorentzian, Gaussian, or uniform lifetime distributions. No improvement in chi 2red could be observed if the experimental data were fitted to bimodal Lorentzian distributions or a double exponential decay. The unimodal Lorentzian lifetime distribution was characterized by a lifetime center of 6.87 ns and a full width at half maximum of 0.57 ns. Increasing amounts of cholesterol in the phospholipid vesicles (0-50 mol% relative to POPC) led to a slight increase of the lifetime center (7.58 ns at 50 mol% sterol) and reduced significantly the distributional width (0.14 ns at 50 mol% sterol). Lifetime distributions of POPC-cholesterol mixtures containing greater than 20 mol% sterol were within the resolution limit and could not be distinguished from monoexponential decays on the basis of chi 2red. Cholesterol stabilizes and rigidifies phospholipid bilayers in the fluid state. Considering its effect on lifetime distributions of fluorescent phospholipids it may also act as a membrane homogenizer.     

Lateral Microheterogeneity of Diphenylhexatriene-Labeled Choline Phospholipids in the Erythrocyte Ghost Membrane as Determined by Time-Resolved Fluorescence Spectroscopy

Choline phospholipids are the major constituents of the outer layer of the erythrocyte membrane. To investigate their lateral membrane organization we determined the fluorescence lifetime properties of diphenylhexatriene analogues of phosphatidylcholine, choline plasmalogen, (the respective enolether derivative), and sphingomyelin inserted into the outer layer of hemoglobin-free ghosts. Fluorescence lifetimes were recorded by time-resolved phase and modulation fluorometry and analyzed in terms of Continuous Lorentzian distributions. To assess the influence of membrane proteins on the fluorescence lifetime of the labeled lipids in the biomembrane, lipid vesicles were used as controls. In general, the lifetime distributions in the ghost membranes are broad compared to vesicles. Phosphatidylcholine and sphingomyelin exhibit very similar lifetime distributions in contrast to an increased plasmalogen lifetime heterogeneity in both systems. Orientational effects of side chain mobilities on the observed lifetimes can be excluded. Fluorescence anisotropies revealed identical values for all three labeled phospholipids in the biomembrane. Received: 22 July 1999/Revised: 6 January 2000     

Conformational heterogeneity of creatine kinase determined from phase resolved fluorometry.

Fluorescence lifetimes of dimeric rabbit muscle creatine kinase specifically dansylated at both active sites and the homologous monomeric lobster muscle arginine kinase singly dansylated were determined using phase-modulation methods with global analysis of overdetermined data sets. For both proteins, the data is adequately described by three discrete exponential decays or a Lorentzian double distributed decay. Analogue phase resolved spectroscopy also reveals the presence of at least two distinct fluorophore domains for the dansyl moieties of creatine kinase. The model fluorophore, dansyllysine, exhibits a monoexponential decay with a value that is highly solvent dependent. Because the monomeric arginine kinase exhibits essentially the same decay law as doubly derivatized dimeric creatine kinase, it is proposed that the multiple lifetimes of creatine kinase reflect two or more isomeric dimeric states and not subunit asymmetry within a conformationally homogeneous dimeric population. Exposure of arginine kinase to 6 M guanidinium chloride results in a shift to shorter lifetimes and narrowing of the lifetime distributions. Creatine kinase displays a small narrowing of the distribution, but little change in fractional populations or lifetimes. These results suggest the presence of structural elements resistant to denaturation. The longest lifetime component in the triexponential discrete decay law of doubly dansylated creatine kinase is totally unquenched by acrylamide, whereas the two shorter lifetime components exhibit limited dynamic quenching. Steady-state quenching by acrylamide is significant and reveals a sharp distinction between accessible and nonaccessible dansyl groups. The major mechanism for interaction between the dansyl moieties and acrylamide is, atypically, static quenching.(ABSTRACT TRUNCATED AT 250 WORDS)     

Tryptophanyl fluorescence lifetime distribution of hyperthermophilic beta-glycosidase from molecular dynamics simulation: a comparison with the experimental data

A molecular dynamics simulation approach has been utilized to understand the unusual fluorescence emission decay observed for beta-glycosidase from the hyperthermophilic bacterium Solfolobus sulfotaricus (Sbeta gly), a tetrameric enzyme containing 17 tryptophanyl residues for each subunit. The tryptophanyl emission decay of Sbeta gly results from a bimodal distribution of fluorescence lifetimes with a short-lived component centered at 2.5 ns and a long-lived one at 7.4 ns (Bismuto E, Nucci R, Rossi M, Irace G, 1999, Proteins 27:71-79). From the examination of the trajectories of the side chains capable of causing intramolecular quenching for each tryptophan microenvironment and using a modified Stern-Volmer model for the emission quenching processes, we calculated the fluorescence lifetime for each tryptophanyl residue of Sbeta gly at two different temperatures, i.e., 300 and 365 K. The highest temperature was chosen because in this condition Sbeta gly evidences a maximum in its catalytic activity and is stable for a very long time. The calculated lifetime distributions overlap those experimentally determined. Moreover, the majority of trytptophanyl residues having longer lifetimes correspond to those originally identified by inspection of the crystallographic structure. The tryptophanyl lifetimes appear to be a complex function of several variables, such as microenvironment viscosity, solvent accessibility, the chemical structure of quencher side chains, and side-chain dynamics. The lifetime calculation by MD simulation can be used to validate a predicted structure by comparing the theoretical data with the experimental fluorescence decay results.     

Global analysis of fluorescence lifetime imaging microscopy data

Global analysis techniques are described for frequency domain fluorescence lifetime imaging microscopy (FLIM) data. These algorithms exploit the prior knowledge that only a limited number of fluorescent molecule species whose lifetimes do not vary spatially are present in the sample. Two approaches to implementing the lifetime invariance constraint are described. In the lifetime invariant fit method, each image in the lifetime image sequence is spatially averaged to obtain an improved signal-to-noise ratio. The lifetime estimations from these averaged data are used to recover the fractional contribution to the steady-state fluorescence on a pixel-by-pixel basis for each species. The second, superior, approach uses a global analysis technique that simultaneously fits the fractional contributions in all pixels and the spatially invariant lifetimes. In frequency domain FLIM the maximum number of lifetimes that can be fit with the global analysis method is twice the number of lifetimes that can be fit with conventional approaches. As a result, it is possible to discern two lifetimes with a single-frequency FLIM setup. The algorithms were tested on simulated data and then applied to separate the cellular distributions of coexpressed green fluorescent proteins in living cells.     

Growth of cell populations with arbitrarily distributed cycle durations. I. basic model

A discrete model is proposed describing the growth of cell populations with arbitrary frequency distributions of cycle durations. The model assumes that each cell divides into two cells at the end of its cycle, and that each new cell is assigned an individual cycle duration according to a probability distribution that can be arbitrarily defined. The increase in the cell number is calculated, either from the numbers of cells at earlier time points or from the initial conditions of the population, by a recurrence formula; it is also approximated by the optimal exponential function, whose parameters are determined by the initial conditions. The appropriate average cycle duration is shown not to be the arithmetic or geometric mean, but rather the solution to a more complex equation. Age distributions are calculated and compared with those found in the literature. The results of the model calculations are compared with computer simulations and with observed data on populations of the ciliate Tetrahymena geleii.     

Similarity of fluorescence lifetime distributions for single tryptophan proteins in the random coil state.

The picosecond time-resolved fluorescence decay data of nine single-tryptophan (trp) proteins and two multi-trp proteins in their native and denatured states were analyzed by the maximum entropy method (MEM). In the denatured state (6 M guanidine hydrochloride) a majority of the single-trp proteins show bimodal (at 25 degrees C) and trimodal (at 85 degrees C) distributions with similar patterns and similar values for average lifetimes. In the native state of the proteins the lifetime distributions were bimodal or trimodal. These results (multimodal distributions) are contradictory to the unimodal Lorentzian distribution of lifetimes reported for some proteins in the native and denatured states. MEM analysis gives a unimodal distribution of lifetimes only when the signal-to-noise ratio is poor in the time-resolved fluorescence decay data. The unimodal distribution model is therefore not realistic for proteins in the native and denatured states. The fluorescence decay components of the bi- or trimodal distribution are associated with the rotamer structures of the indole moiety when the protein is in the random coil state.     

Molecular dynamics of the salt dependence of a cold-adapted enzyme: endonuclease I

The effects of salt on the stability of globular proteins have been known for a long time. In the present investigations, we shall focus on the effect of the salt ions upon the structure and the activity of the endonuclease I enzyme. In the present work, we shall focus on the relationship between ion position and the structural features of the Vibrio salmonicida (VsEndA) enzyme. We will concentrate on major questions such as: how can salt ions affect the molecular structure? What is the activity of the enzyme and which specific regions are directly involved? For that purpose, we will study the behaviour of the VsEndA over different salt concentrations using molecular dynamics (MD) simulations. We report the results of MD simulations of the endonuclease I enzyme at five different salt concentrations. Analysis of trajectories in terms of the root mean square fluctuation (RMSF), radial distribution function, contact numbers and hydrogen bonding lifetimes, indicate distinct differences when changing the concentration of NaCl. Results are found to be in good agreement with experimental data, where we have noted an optimum salt concentration for activity equal to 425 mM. Under this salt concentration, the VsEndA exhibits two more flexible loop regions, compared to the other salt concentrations. When analysing the RMSF of these two specific regions, three residues were selected for their higher mobility. We find a correlation between the structural properties studied here such as the radial distribution function, the contact numbers and the hydrogen bonding lifetimes, and the structural flexibility of only two polar residues. Finally, in the light of the present work, the molecular basis of the salt adaptation of VsEndA enzyme has been explored by mean of explicit solvent and salt treatment. Our results reveal that modulation of the sodium/chloride ions interaction with some specific loop regions of the protein is the strategy followed by this type of psychrophilic enzyme to enhance catalytic activity at the physiological conditions.     

Resolvability of fluorescence lifetime distributions using phase fluorometry.

The analysis of the fluorescence decay using discrete exponential components assumes that a small number of species is present. In the absence of a definite kinetic model or when a large number of species is present, the exponential analysis underestimates the uncertainty of the recovered lifetime values. A different approach to determine the lifetime of a population of molecules is the use of probability density functions and lifetime distributions. Fluorescence decay data from continuous distributions of exponentially decaying components were generated. Different magnitudes of error were added to the data to simulate experimental conditions. The resolvability of the distributional model was studied by fitting the simulated data to one and two exponentials. The maximum width of symmetric distributions (uniform, gaussian, and lorentzian), which cannot be distinguished from single and double exponential fits for statistical errors of 1 and 0.1%, were determined. The width limits are determined by the statistical error of the data. It is also shown that, in the frequency domain, the discrete exponential analysis does not uniformly weights all the components of a distribution. This systematic error is less important when probability and distribution functions are used to recover the decay. Finally, it is shown that real lifetime distributions can be proved using multimodal probability density functions. In the companion paper that follows we propose a physical approach, which provides lifetime distribution functions for the tryptophan decay in proteins. In the third companion paper (Alcala, J.R., E. Gratton, and F.J. Prendergast, 1987, Biophys. J., in press) we use the distribution functions obtained to fit data from the fluorescence decay of single tryptophan proteins.     

Mixture and nonmixture cure fraction models assuming discrete lifetimes: Application to a pelvic sarcoma dataset

Different cure fraction models have been used in the analysis of lifetime data in presence of cured patients. This paper considers mixture and nonmixture models based on discrete Weibull distribution to model recurrent event data in presence of a cure fraction. The novelty of this study is the use of a discrete lifetime distribution in place of usual existing continuous lifetime distributions for lifetime data in presence of cured fraction, censored data, and covariates. In the verification of the fit of the proposed model it is proposed the use of randomized quantile residuals. An extensive simulation study is considered to evaluate the properties of the estimates of the parameters related to the proposed model. As an illustration of the proposed methodology, it is considered an application considering a medical dataset related to lifetimes in a retrospective cohort study conducted by Puchner et al. (2017) that consists of 147 consecutive cases with surgical treatment of a sarcoma of the pelvis between the years of 1980 and 2012.     

Texture analysis of fluorescence lifetime images of nuclear DNA with effect of fluorescence resonance energy transfer

BACKGROUND: Fluorescence lifetime imaging microscopy (FLIM) is becoming an important tool in cellular imaging. In FLIM, the image contrast is concentration insensitive, whereas it is sensitive to the local environment and interactions of fluorophores such as fluorescence resonance energy transfer (RET). METHODS: Fluorescence microscopy, lifetime imaging, and texture analysis were used to study the spatial distribution of fluorophores bound to nuclear DNA. 3T3-Swiss albino mice fibroblast nuclei were labeled with Hoechst 33258 (Ho), an AT-specific dye, and 7-aminoactinomycin D (7-AAD), a GC-specific dye. Ho is a RET donor to the 7-AAD acceptor. RESULTS: Texture analysis of 50 alcohol-fixed nuclei quantitatively showed changes of spatial distribution of apparent donor lifetimes. RET increased the spatial heterogeneity in the phase and modulation lifetime images. In most of the doubly stained cells (about 80%), the phase and modulation lifetime distributions were spatially homogeneous. In about 20% of the cells, we noticed that lower phase and modulation lifetimes caused by RET were correlated with regions of high Ho intensity in the nuclei. CONCLUSIONS: The spatial lifetime heterogeneity of Ho in presence of 7-AAD seems to be caused by RET between closely spaced strands in the three dimensionally condensed regions of DNA.