Continuous Lifetime Distributions Research Articles

Analysis of Kinetics Using a Hybrid Maximum-Entropy/Nonlinear-Least-Squares Method: Application to Protein Folding

A hybrid analysis that combines the maximum entropy method (MEM) with nonlinear least squares (NLS) fitting has been developed to interpret a general time-dependent signal. Data that include processes of opposite sign and a slow baseline drift can be inverted to obtain both a continuous distribution of lifetimes and a sum of discrete exponentials. Fits by discrete exponentials are performed with initial parameters determined from the distribution of lifetimes obtained with the MEM. The regularization of the parameter space achieved by the MEM stabilizes the introduction of each successive exponential in the NLS fits. This hybrid approach is particularly useful when fitting by a large number of exponentials. Revision of the MEM “prior” based on features in the data can improve the lifetime distribution obtained. Standard errors in the mean are estimated automatically for raw data. The results presented for simulated data and for fluorescence measurements of protein folding illustrate the utility and accuracy of the hybrid algorithm. Analysis of the folding of dihydrofolate reductase reveals six kinetic processes, one more than previously reported.

Compatibilization of Metallocene Polyethylene/Polyamide Blends with Maleic Anhydride Studied by Positron Annihilation

Positron lifetime spectroscopy was used to study the compatibilization effect of maleic-anhydride (maH) grafted copolymers and its ionomers in metallocene polyethylene/poly-amide blends. The ortho-positronium (o-Ps) lifetime τ3 showed a decrease with increasing maH content from 0 to 0.5%, then remained constant. A larger decrease was observed for the Na+-neutralized ionomer containing blends. From the analysis of continuous positron lifetime distribution, we found that in the blend with no or smaller maH content, the o-Ps lifetime distribution was composed of two peaks, which can be attributed to the phase separation in these blends. When the maH content was equal to or higher than 0.5%, the phase separation disappeared, which is due to the decrease of dispersed polyethylene (PE) phase size. In the blends with ionomer, the phase separation disappeared at a lower content of maH. These results proved that the maH grafted copolymer and ionomer can be very good compatibilizers for the PE/PA blends.

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.

Asymmetrical Distribution of Intrinsic Fluorescence Lifetimes in Proteins

Dynamic fluorescence measurements of proteins in solution are often interpreted in terms of continuous distributions of lifetimes, which reflect the intrinsic structural heterogeneity of these systems. In several cases a single Gaussian or Lorentzian symmetric distribution has been used to fit the data. In this paper we describe a new nonsymmetric Lorentzian function which contains three free parameters (the center, the left, and the right widths) like the double-discrete exponential model (the two lifetimes and one preexponential factor). Simulated data in the frequency domain have been used to compare the fits obtained with these different approaches, introducing a new parameter, ρ, which quantitatively measures the asymmetry of the distribution or the ratio of the two preexponential factors, in the continuous and discrete models, respectively. Real measurements of a mixture of independent fluorophores, as well as of protein fluorescence decays, have also been performed and analyzed in terms of the new asymmetric function. The data have also been fitted with traditional discrete methods (such as the two- and the three-exponential decay) and with another asymmetric function, namely, the skewed Gaussian distribution.

Discrimination of defects in III–V semiconductors by positron lifetime distribution

In this paper, the numerical Laplace inversion technique and maximum entropy method are utilized to extract continuous positron lifetime distribution in semiconductors. The result is used to discriminate the native vacancy-type defects in as-grown GaAs and InP with different conduction type. Direct evidence of shallow positron traps were also observed in ion-implanted p-InP. It is demonstrated that the lifetime distribution can give us more detailed information on the native defects.

Optimal maintenance decisions on the basis of uncertain failure probabilities

Due to a lack of data, many maintenance optimisation models have to be initialised on the basis of expert judgment. Rather than eliciting the parameters of a continuous lifetime distribution, experts give more reliable answers when assessing a discrete lifetime distribution. If the prior uncertainty in the probabilities of failure per unit time is expressed in terms of a Dirichlet distribution, Bayes estimates can be obtained of three cost‐based criteria to compare maintenance decisions over unbounded time‐horizons: first, the expected average costs per unit time; second, the expected discounted costs over an unbounded horizon; and third, the expected equivalent average costs per unit time. Illustrates the maintenance model by determining optimal age replacement and lifecycle costing policies, which optimally balance both the failure cost against the preventive repair cost, and the initial cost against the future cost.

Application of positron lifetime distribution to the discrimination of defects in semiconductors

In this paper, two methods of extracting continuous positron lifetime distribution are utilized, one is the numerical Laplace inversion, another is the maximum entropy method. The result of continuous lifetime distribution is used to discriminate the native vacancy-type defects in GaAs and InP with different conduction type. It is demonstrated that the lifetime distribution can give us more detailed information on the native defects. In particular, the direct evidence of positron trapping by vacancies is observed both in semi-insulating GaAs and in p-type InP, of which the identification of defects is still a question in debate.

Analysis of Phosphorescence Decay in Heterogeneous Systems: Consequences of Finite Excitation Flash Duration

Analysis of phosphorescence lifetimes using the Stern-Volmer equation is a reliable means of determining quencher concentration for a uniform sample. Methods of analysis for heterogeneous systems are based on the assumption that the excitation is produced by a momentary flash. This condition is an idealization because a real flash has a finite duration and a complex time profile. In the case of a heterogeneous quencher concentration, an excitation flash produces different initial intensities and different times of peak intensity from compartments having different concentrations of quencher. We formulated a model to explore the effects of flash duration on the shape of the emission curve obtained from systems in which the heterogeneity is continuous. We developed mathematical models that can be used to recover fitting parameters of continuous distributions of reciprocal lifetimes approximated as rectangular or Gaussian distributions, or an arbitrary histogram. We also formulated a procedure to convert the distribution of reciprocal lifetimes into a volume distribution of quencher concentration. We found that (1) the Stern-Volmer ratio of phosphorescence intensities cannot be employed for interpretation of pulse phosphorometric data in terms of a volume distribution of quencher; (2) shortening the flash duration decreases the difference of initial intensities between compartments having high and low quencher concentration; (3) the parameters of the volume distribution of quencher concentration can be recovered correctly only after taking account of the difference in initial intensities; and (4) calibration of the initial intensities for a given fitting delay and flash function is necessary.

Structural and dynamic aspects of ?-glycosidase from mesophilic and thermophilic bacteria by multitryptophanyl emission decay studies

The tryptophanyl emission decay of beta-glycosidase from the extremophilic archaeon Sulfolobus solfataricus (Sbetagly) has been investigated by frequency domain fluorometry. The data were analyzed in terms of sum of discrete lifetimes as well as in terms of quasi- continuous lifetime distributions of different shape. At neutral pH the emission decay is characterized by two components: a long-lived component, centered at 7.4 ns, and a short one at 2.7 ns, irrespective of the decay scheme used for the interpretation of the experimental results. The effects of an irreversible inhibitor, that is, cyclophellitol, and that of a powerful denaturant such as guanidinium hydrochloride on the dynamics of Sbetagly has been investigated by observing the changes induced in the two components of the tryptophanyl emission decay. The addition of cyclophellitol to native Sbetagly reduces the contribution of the short-lived component but does not affect the long-lived one. Increasing concentrations of guanidinium hydrochloride differently affect the contributions of the two emission components. Higher concentrations were required to unfold the molecular regions containing the long-lived indolic fluorophores. These results indicate that the long-lived contribution arises from tryptophanyl residues deeply clustered in the interior of the protein matrix, whereas the short-lived one includes residues located in less rigid and more solvent accessible regions, some of which might be located in functionally important parts of protein. The knowledge of the crystallographic structure of Sbetagly allowed us to evaluate some average parameters for each tryptophanyl microenvironment in the Sbetagly such as hydrophobicity, structural flexibility, and ability of side chains to act as fluorescence quenchers. These results permitted to divide the tryptophanyl fluorescence of Sbetagly in the contribution of two emitting groups: one consisting of eight closely clustered tryptophans, that is, Trp 33, 36, 60, 84, 151 174, 425, and 433, responsible for the long-lived emission component and the other one, composed of nine tryptophans nearer to the subunit surface, that is, Trp 12, 156, 192, 287, 288, 316, 361, 376, 455, associable to the short-lived emission component. Finally, the examination of the tryptophanyl emission decay of the mesophilic beta-galactosidase from Escherichia coli (Cbetagal) and the Arrhenius analysis of its dependence on temperature indicated that the tryptophanyl environments of the mesophilic enzyme are rather homogeneous in consequence of a larger protein dynamics.

Mean residual life of lifetime distributions

This paper characterizes the general behaviors of the MRL (mean residual lives) for both continuous and discrete lifetime distributions, with respect to their failure rates. For the continuous lifetime distribution with failure rates with only one or two change-points, the characteristic of the MRL depends only on its mean and failure rate at time zero. For failure rates with "roller coaster" behavior, the subsequent behavior of the MRL depends on its MRL and failure-rates at the change points. Using the characterization, their behaviors for the: Weibull; lognormal; Birnbaum-Saunders; inverse Gaussian; and bathtub failure rate distributions are tabulated in terms of their shape parameters. For discrete lifetime distributions, for upside-down bathtub failure rate with only one change point, the characteristic of the MRL depends only on its mean and the probability mass function at time zero.

Reasons for the deviation of I1/ I3 and τ1 from the expected lifetime parameters of positronium annihilation in polymers

High quality positron lifetime spectra were taken for several amorphous polymers. The spectra were analysed using the routine MELT which assumes continuous lifetime distributions, as well as the discrete-term analysis routine LIFSPECFIT. Disagreements between the analysed lifetime parameters and theoretical expectations, I 1 /I 3 > I p- Ps/ I o- Ps=1/3 and τ 1 > τ p- Ps, which are well known, also appear in our results. The disagreements are distinctly larger using a discrete-term routine than when applying MELT (or CONTIN). From the analysis of computer-generated spectra, we found that these disagreements may be well understood by assuming a distribution of e + lifetimes in addition to an o-Ps lifetime distribution, both of which can occur as consequence of size and shape distributions of free-volume holes in amorphous polymers (or of bubbles in molecular liquids). The disagreements appear to be due to the inability of the routines correctly to mirror very broad lifetime distributions. For broad distributions, MELT (and also CONTIN) delivers, as an artefact of the spectrum analysis, a distribution consisting of two narrow subpeaks instead of a single broad one. The lower subpeak of the e + lifetime distribution may mix with the p-Ps lifetime component resulting in artificially large values for τ 1 and I 1. That is the reason for the unphysical increase of τ 1 and I 1 with decreasing I 3 observed in the analysed parameters of simulated as well as experimental spectra.

Resolution of the heterogeneous fluorescence in multi-tryptophan proteins: ascorbate oxidase.

Ascorbate oxidase is a copper-containing enzyme which catalyzes a redox reaction between vitamin C and molecular oxygen. The protein, which shows a complex tertiary structure, is an homodimer of monomers, each containing three domains and 14 tryptophan residues. Recently, we have demonstrated by spectroscopic and ultracentrifugation techniques the existence of a stable dimeric intermediate along the unfolding pathway of this enzyme [Mei, G., Di Venere, A., Buganza, M., Vecchini, P., Rosato, N. & Finazzi Agrò, A. (1997) Biochemistry 36, 10917-10922]. In this study, the steady-state and dynamic fluorescence features of ascorbate oxidase have been exploited in order to find a way of monitoring the individual subsystems of the protein. The fluorescence intensity and anisotropy upon excitation at 295 nm are extremely sensitive functions of the emission wavelength, indicating a great heterogeneity of the system. The emission decay collected through a cut-off filter can be analyzed in terms of two continuous distributions of lifetimes. Using a monochromator in emission or an optical multichannel analyzer, the two distributions may be attributed to distinct components of the fluorescence spectrum. Differential quenching by cesium chloride also confirmed that the several tryptophan residues present in the protein structure may be grouped into two main classes, each with a different environment. Once the complex fluorescence decay of ascorbate oxidase was analyzed and resolved, a comparison with the crystallographic data allowed a first, approximate attribution of the protein spectroscopic properties to some of the tryptophan residues. This might provide a powerful tool of investigation about the role of definite segments of the protein in its three-dimensional structure and catalytic activity. Furthermore, the methodology set up for ascorbate oxidase can be usefully extended to other multitryptophan proteins.

Luminescence and luminescence kinetics of chromium doped gahnite glass ceramics

The fluorescence decay kinetics of Cr 3+ impurity ions in a gahnite glass ceramic are analysed using a technique used previously in molecular spectroscopy that produces a continuous distribution of lifetimes rather than a number of discrete contributions. The results are shown to be consistent with Cr 3+ ions occupying three different phases within the host material. These phases are identified and shown to make different contributions to the fluorescence spectra of the material. Examples are given for different combinations of excitation and fluorescence detection wavelengths and for different sample temperatures.

Do the CONTIN or the MELT programs accurately reveal the o-Ps lifetime distribution in polymers? Analysis of experimental lifetime spectra of amorphous polymers

High quality positron lifetime spectra (total count of 70 million) were taken for polycarbonate (PC) and polystyrene (PS Hoechst). The spectra were analysed employing the routines CONTIN and MELT which both assume continuous lifetime distributions, as well as the discrete-term analysis routine LIFSPECFIT. The lifetime distributions consist of three peaks, of these, the long-lived one, corresponding to the o-Ps lifetime distribution, splits for low regularization into two sub peaks. No way was found to decide whether these sub peaks, or the smoothed o-Ps lifetime distribution obtained for higher regularization, were due to two (discrete) close neighbour lifetimes, or came from a single, broad o-Ps lifetime distribution. Assuming discrete lifetimes, values of approximately 1700 ps and 2350 ps were estimated for PS (1750 and 2400 ps for PC). Assuming a single but broad o-Ps lifetime distribution, the mass centre τ 3 of that in PS was estimated to 1985 ps (2020 ps in PC). The same analysis was carried out with distributions from simulated lifetime spectra for comparison with experimental data. From this comparison the full width at half maximum (FWHM) of the o-Ps lifetime distribution was estimated to 800–950 ps for both PS and PC. The o-Ps lifetime results may be attributed to two different Ps states or, alternatively, to hole size distributions ranging approximately from r=0.24–0.32 nm ( v=0.06–0.14 nm 3). Furthermore, short comments on how to estimate a reliable width for the o-Ps lifetime distribution and on the handling and resolving power of CONTIN and MELT are given.

Fluorescence of organic dyes in lipid membranes: Site of solubilization and effects of viscosity and refractive index on lifetimes

The fluorescence decay of several organic dye molecules intercalated in egg phosphatidylcholine lipid membrane vesicles is consistent with the existence of two or three prominent lifetime components rather than a single continuous distribution of lifetimes. The major lifetime components are identified with different sites of solubilization in the membrane. The variation of the lifetime of the membrane-bound dye was studied as a function of the sucrose concentration, which varied the viscosity and refractive index of the aqueous solution. The combined effect of viscosity and refractive index on the lifetime of the dye was used to identify the site of solubilization of the dye in the membrane. The study was useful to identify dye molecules on the surface which are exposed to the aqueous phase, for which the fluorescence lifetime increased systematically with sucrose (viscosity effect). More importantly, it was possible in a few cases to identify the dye molecules which are oriented in the membrane phase, and the fluorescence lifetime decreased systematically with sucrose (refractive index effect). Anomalous values of order parameters determined from the refractive index effect are explained in terms of an orientational distribution of the linear dye molecule weighted in favor of mutually orthogonal orientations.

Short range ordering in the melt and its manifestation in glassy Fe-Co-B Investigation by positron annihilation lifetime

Six sets of ribbons of Fe 64Co 21B 15 metallic glass obtained by rapid quenching of the melt having different temperature and time history, selected with respect to the temperature-time evolution of melt viscosity, have been investigated by positron annihilation spectroscopy. The interest has been focused on the correlation between the expected melt precursor structure and the presence of ordered units (clusters, associations) in the amorphous matrix. Ribbons have been annealed for suitable times at temperatures below and above the crystallization temperature. Such selective thermal treatment of the samples has enabled to accentuate or anneal-out the effects of the presence of small ordered structural units as reflected by the positron annihilation lifetimes and positron affinities and by changes of electron structure obtained from electrical resistivity measurements. Fine structure of the amorphous matrix has been determined by analyzing the positron annihilation lifetime spectra with the use of a numerical Laplace transform method which provides continuous distributions of the position annihilation lifetimes. Differences in local ordering have been found for samples from master alloys with different melt histories.

Structural Complexity and Fluorescence Heterogeneous Decays in Proteins

Optical spectroscopy is a suitable technique to study the functional and structural properties of large biomolecules in solution without damaging the samples. In particular, measurements of time-resolved fluorescence may give important information on the tertiary structure of proteins. Furthermore, the study of fluorescence depolarization as a function of time is a very common method to follow the dynamics of the local domains and subunits which form the quaternary structure of oligomeric enzyme. The analysis of fluorescence decays in terms of continuous distribution of lifetimes seems to be an appropriate approach to describe the dynamics of proteins which ranges over an enormous time scale (from 10 ps to 10 ns). The results obtained for several proteins are reported and discussed. The data provide further confirmation of the correlation which exist between heterogeneous fluorescence decays and a hierarchy of many conformational substates in proteins.

Physicochemical Characterization of Plasma Membranes from Density-Separated Trout Erythrocytes

Erythrocytes ofSalmo irideustrout were separated in the range from 45 to 65% Percoll, yelding three well-separated different fractions. Steady-state fluorescence of probes embedded in erythrocyte membranes and/or in liposomes from extracted lipids was used to characterize their physicochemical properties. Furthermore, the fluorescence decay of 1,6-diphenyl-1,3,5-hexatriene (DPH), embedded in the same liposomes, was measured by a frequency decay fluorometer. DPH decay was analyzed on the assumption of continuous distribution of lifetimes, for evaluating modifications of membrane microheterogeneity. Significant differences were observed in the parameters measured for the three erythrocyte fractions, possibly connected with the specific lipid composition of the samples.

Fluorescence quenching of the tryptophan emission from the F- and G-forms of actin

The parameters characterizing the quenching of fluorescence emitted by the four tryptophans of actin were measured by time resolved techniques in the monomeric (G) and the polymerized (F) forms of the protein. Acrylamide as a neutral and cesium ions as positively charged quenchers were used to characterize the subdomain 1, which contains all the four tryptophan residues. Use of acrylamide did not reveal any difference between the G- and F-forms, cesium, however, did so. The value of the quenching rate constant, k +, is significantly higher for the F-form than that for the G-form. This difference is present independently of the model (discrete or continuous lifetime distribution) used to process the data. These results are compatible with the conclusion that the charge distribution of the microenvironment around at least one of the four tryptophans is changed. This means that this region becomes more attracted to the cesium ion as a result of transition from the G- to the F-form.

Characterization of bivariate mean residual-life function

This paper gives a counter example to invalidate a claim of Nair and Nair (1989) regarding a characterization of bivariate mean residual-life function (BMRLF). The authors characterize BMRLF of an absolutely continuous life-time distribution and, based on the form of the BMRLF, introduce probability models for bivariate life-time data.