Resolving heterogeneity on the single molecular level with the photon-counting histogram

The diffusion of fluorescent particles through a small, illuminated observation volume gives rise to intensity fluctuations caused by particle number fluctuations in the open observation volume and the inhomogeneous excitation-beam profile. The intensity distribution of these fluorescence fluctuations is experimentally captured by the photon-counting histogram (PCH). We recently introduced the theory of the PCH for diffusing particles (Chen et al., Biophys. J., 77:553-567), where we showed that we can uniquely describe the distribution of photon counts with only two parameters for each species: the molecular brightness of the particle and the average number of particles within the observation volume. The PCH is sensitive to the molecular brightness and thus offers the possibility to separate a mixture of fluorescent species into its constituents, based on a difference in their molecular brightness alone. This analysis is complementary to the autocorrelation function, traditionally used in fluorescence fluctuation spectroscopy, which separates a mixture of species by a difference in their diffusion coefficient. The PCH of each individual species is convoluted successively to yield the PCH of the mixture. Successful resolution of the histogram into its components is largely a matter of the signal statistics. Here, we discuss the case of two species in detail and show that a concentration for each species exists, where the signal statistics is optimal. We also discuss the influence of the absolute molecular brightness and the brightness contrast between two species on the resolvability of two species. A binary dye mixture serves as a model system to demonstrate that the molecular brightness and the concentration of each species can be resolved experimentally from a single or from several histograms. We extend our study to biomolecules, where we label proteins with a fluorescent dye and show that a brightness ratio of two can be resolved. The ability to resolve a brightness ratio of two is very important for biological applications.     

The photon counting histogram in fluorescence fluctuation spectroscopy.

Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a super-Poissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel's formula. Based on this equation and considering the fluorescence intensity distribution in the two-photon excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time epsilon. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation profile upon the photon counting statistics for two relevant point spread functions (PSFs), the three-dimensional Gaussian PSF conventionally employed in confocal detection and the square of the Gaussian-Lorentzian PSF for two photon excitation, is explicitly treated. Measured photon counting distributions obtained with a two-photon excitation source agree, within experimental error with the theoretical PCHs calculated for the square of a Gaussian-Lorentzian beam profile. We demonstrate and discuss the influence of the average number of particles within the observation volume and the detected photon counts per molecule per sampling interval upon the super-Poissonian character of the photon counting distribution.     

Molecular Brightness Characterization of EGFP In Vivo by Fluorescence Fluctuation Spectroscopy

We characterize the molecular properties of autofluorescence and transiently expressed EGFP in the nucleus and in the cytoplasm of HeLa cells by fluorescence correlation spectroscopy (FCS) and by photon counting histogram (PCH) analysis. PCH has been characterized and applied in vitro, but its potential for in vivo studies needs to be explored. Thus, this study mainly focuses on the characterization of PCH analysis in vivo. The strength of PCH lies in its ability to distinguish biomolecules by their molecular brightness value. Because the concept of molecular brightness is crucial for PCH analysis, we study the molecular brightness of EGFP and determine the statistical accuracy of its measurement under in vivo conditions. We started by characterizing the influence of autofluorescence on EGFP measurements. We found a molecular brightness of EGFP that is a factor of 10 higher than the brightness of the autofluorescence. Moment analysis demonstrates that the contribution of autofluorescence to fluorescence fluctuation experiments is negligible at EGFP concentrations of one protein per excitation volume. The molecular brightness of EGFP measured in the nucleus, the cytoplasm, and in vitro are identical and our study demonstrates that molecular brightness is a very stable and predictable quantity for cellular measurements. In addition to PCH, we also analyzed the autocorrelation function of EGFP. The diffusion coefficient of EGFP is a factor of 3 lower in vivo than compared to in vitro, and a simple diffusion process describes the autocorrelation function. We found that in the nucleus the fluorescence intensity is stable as a function of time, while measurements in the cytoplasm display fluorescence intensity drifts that complicate the data analysis. We introduce and discuss an analysis method that minimizes the influence of the intensity drifts on PCH analysis. This method allows us to recover the correct molecular brightness of EGFP even in the presence of drifts of the fluorescence intensity signal. We found the molecular brightness of EGFP to be a very robust parameter, and anticipate the use of PCH analysis for the study of oligomerization processes in vivo.     

Fluorescence fluctuation spectroscopy in the presence of immobile fluorophores

Fluorescence contributions from immobile sources present a challenge for fluorescence fluctuation spectroscopy (FFS) because the absence of signal fluctuations from stationary fluorophores leads to a biased analysis. This is especially of concern for cellular FFS studies on proteins that interact with immobile structures. Here we present a method that correctly analyzes FFS experiments in the presence of immobile sources by exploiting selective photobleaching of immobile fluorophores. The fluorescence decay due to photobleaching of the immobile species is modeled taking into account the nonuniform illumination volume. The experimentally observed decay curve serves to separate the mobile and immobile fluorescence contribution, which is used to calculate the molecular brightness from the FFS data. We experimentally verify this approach in vitro using the fluorescent protein EGFP as our immobilized species and a diffusing dye of a different color as the mobile one. For this special case, we also use an alternative method of determining the brightness by spectrally resolving the two species. By conducting a dilution study, we show that the correct parameters are obtained using either technique for a wide range of mobile fractions. To demonstrate the application of our technique in living cells, we perform experiments using the histone core protein H2B fused with EGFP expressed in COS-1 cells. We successfully recovered the brightness of the mobile fraction of H2B-EGFP.     

Near-infrared spectral imaging for quality assurance of pharmaceutical products: analysis of tablets to assess powder blend homogeneity

The objective of this study was to evaluate near-infrared (NIR) spectroscopic imaging as a tool to assess a pharmaceutical quality assurance problem—blend uniformity in the final dosage product. A system based on array detector technology was used to rapidly collect high-contrast NIR images of furosemide tablets. By varying the mixing, 5 grades of experimental tablets containing the same amount of furosemide and microcrystalline cellulose were produced, ranging from well blended to unblended. For comparison, these tablets were also analyzed by traditional NIR spectroscopy, and both approaches were used to evaluate drug product homogeneity. NIR spectral imaging was capable of clearly differentiating between each grade of blending, both qualitatively and quantitatively. The spatial distribution of the components was based on the variation or contrast in pixel intensity, which is due to the NIR spectral contribution to each pixel. The chemical nature of each pixel could be identified by the localized spectrum associated with each pixel. Both univariate and partial least squares (PLS) images were evaluated. In the suboptimal blends, the regions of heterogeneity were obvious by visual inspection of the images. A quantitative measure of blending was determined by calculating the standard deviation of the distribution of pixel intensities in the PLS score images. The percent standard deviation increased progressively from 11% to 240% from well blended to unblended tablets. The NIR spectral imaging system provides a rapid approach for acquiring spatial and spectral information on pharmaceuticals. The technique has potential for a variety of applications in product quality assurance and could affect the control of manufacturing processes.     

Effect of microsome-liposome fusion on the rotational mobility of cytochrome P450IIB4 in rabbit liver microsomes

Membrane fusion of microsomes with soybean phospholipid vesicles was performed at pH 6.5 to investigate the effect of lipid-enrichment in the membrane on the rotational mobility of cytochrome P450. Rotational diffusion of cytochrome P450 in the microsomal membrane of phenobarbital-induced rabbit liver was measured by detecting the decay of absorption anisotropy after photolysis of the heme CO complex by a vertically polarized laser flash. The fusion procedures yielded three separate fractions upon sucrose density gradient centrifugation with lipid-to-protein ratio in weight (L/P) as follows: 1.5 in the bottom fraction, 2.2 in the middle fraction, and 3.9 in the top fraction. In each fraction, co-existence of mobile and immobile cytochrome P450 was observed. The percentage of rotationally mobile P450 (with the mean rotational relaxation time of phi=505-828 micros) in each of the different bands was found to be 59% in the bottom fraction, 61% in the middle fraction, and 68% in the top fraction. This increase in mobile population of P450 due to lipid-enrichment indicates that aggregated proteins in microsomal membranes dissociate with increasing L/P which is inversely proportional to the protein concentration in the membrane. With freeze-fracture electron microscopy, it was shown that the average distance increased between intramembrane particles by lipid-enrichment. Thus, the significant immobile population (32%) of P450 in microsomal membranes can be explained by nonspecific protein aggregation which is a consequence of the low L/P of 0.8. The decrease in the mobile population in the bottom fraction compared with intact microsomes was shown to be due to the pH 6.5 incubation used for fusion.     

Using FCS to accurately measure protein concentration in the presence of noise and photobleaching

Quantitative cell biology requires precise and accurate concentration measurements, resolved both in space and time. Fluorescence correlation spectroscopy (FCS) has been held as a promising technique to perform such measurements because the fluorescence fluctuations it relies on are directly dependent on the absolute number of fluorophores in the detection volume. However, the most interesting applications are in cells, where autofluorescence and confinement result in strong background noise and important levels of photobleaching. Both noise and photobleaching introduce systematic bias in FCS concentration measurements and need to be corrected for. Here, we propose to make use of the photobleaching inevitably occurring in confined environments to perform series of FCS measurements at different fluorophore concentration, which we show allows a precise in situ measurement of both background noise and molecular brightness. Such a measurement can then be used as a calibration to transform confocal intensity images into concentration maps. The power of this approach is first illustrated with in vitro measurements using different dye solutions, then its applicability for in vivo measurements is demonstrated in Drosophila embryos for a model nuclear protein and for two morphogens, Bicoid and Capicua.     

Weber and noise adaptation in the retina of the toad Bufo marinus

Responses to flashes and steps of light were recorded intracellularly from rods and horizontal cells, and extracellularly from ganglion cells, in toad eyecups which were either dark adapted or exposed to various levels of background light. The average background intensities needed to depress the dark-adapted flash sensitivity by half in the three cell types, determined under identical conditions, were 0.9 Rh*s-1 (rods), 0.8 Rh*s-1 (horizontal cells), and 0.17 Rh*s-1 (ganglion cells), where Rh* denotes one isomerization per rod. Thus, there is a range (approximately 0.7 log units) of weak backgrounds where the sensitivity (response amplitude/Rh*) of rods is not significantly affected, but where that of ganglion cells (1/threshold) is substantially reduced, which implies that the gain of the transmission from rods to the ganglion cell output is decreased. In this range, the ganglion cell threshold rises approximately as the square root of background intensity (i.e. in proportion to the quantal noise from the background), while the maintained rate of discharge stays constant. The threshold response of the cell will then signal light deviations (from a mean level) of constant statistical significance. We propose that this type of ganglion cell desensitization under dim backgrounds is due to a post-receptoral gain control driven by quantal fluctuations, and term it noise adaptation in contrast to the Weber adaptation (desensitization proportional to the mean background intensity) of rods, horizontal cells, and ganglion cells at higher background intensities.     

Size-exclusion chromatography with evaporative light scattering detection: Method for determination of polydimethylsiloxanes. I. Testing dependence of molecular weight of polydimethylsiloxanes and injected mass upon the detector signal

In recent years the evaporative light scattering detector has become a promising device in the analysis of variable chemical compounds using liquid chromatography. Due to the detection specificity, based on the scattering of the laser light on non-volatile analyte particles, this detector is considered a most universal one. Many authors consider detector signal as a mass signal and subsequently, evaporative light scattering detector has been regarded as a mass detector. Although the scientists pinpoint to many advantages of this device, many of its drawbacks were also noticed. Due to variable examinations carried out some scientist characterised the detector response as a non-linear, seeing in fact a significant limitation of this detector for the purposes of quantitative tests. The author of the present study researched, in many ways, for the solution to this problem, by carrying out tests on polydimethylsiloxanes (PDMS) of a linear structure. The aim of this study was to test the dependence of the evaporative light scattering detector signal upon the molecular weight of PDMS of a linear structure and viscosity ranging from 10 to 60,000 cSt and the injected mass. The evaluation of function monotonicity of the detector response and determination of the function for particular analytes referred to the mass ranges of 8.9-149.0 microg. In order to find the dependence of the integrated signal value of the detector signal intensity, expressed as a surface area in mug, upon analyte mass for particular PDMS, several analytical functions and formulas were used. Parameters of regression equations were calculated for linear and non-linear functions as well as their logarithmic transformations. The aim of the research for the optimal regression equation could mean increased reliability of results obtained from analyses of PDMS.     

Dual-color time-integrated fluorescence cumulant analysis

We introduce dual-color time-integrated fluorescence cumulant analysis (TIFCA) to analyze fluorescence fluctuation spectroscopy data. Dual-color TIFCA utilizes the bivariate cumulants of the integrated fluorescent intensity from two detection channels to extract the brightness in each channel, the occupation number, and the diffusion time of fluorophores simultaneously. Detecting the fluorescence in two detector channels introduces the possibility of differentiating fluorophores based on their fluorescence spectrum. We derive an analytical expression for the bivariate factorial cumulants of photon counts for arbitrary sampling times. The statistical accuracy of each cumulant is described by its variance, which we calculate by the moments-of-moments technique. A method that takes nonideal detector effects such as dead-time and afterpulsing into account is developed and experimentally verified. We perform dual-color TIFCA analysis on simple dye solutions and a mixture of dyes to characterize the performance and accuracy of our theory. We demonstrate the robustness of dual-color TIFCA by measuring fluorescent proteins over a wide concentration range inside cells. Finally we demonstrate the sensitivity of dual-color TIFCA by resolving EGFP/EYFP binary mixtures in living cells with a single measurement.     

Theory and Measurement of the buffer value of bicarbonate in saliva

All known sensory systems have at least two components, which will tend to counteract and compensate for each other. For light, the sensitivity of the eye is some function of the area of the pupil (aperture of the iris diaphragm) and the relative amount of unbleached pigment (visual purple or rhodopsin). An intermittent light will result in a constriction of the pupil and a bleaching of the pigment. The interaction between these two processes results in a total response with components of both a logarithmic and an arithmetic function of the light intensity and duration. The sensitivity of the eye is a linear function of the logarithm of the intensity of incident light (Weber's and Fechner's laws, Fig. 6), yet a rapidly oscillating light causes approximately the same sensitivity as a steady light of the same intensity as the arithmetic average of the fluctuating light (Talbot's and Bloch's laws, Fig. 9c).     

Light scattering and fluorescence by small particles having internal structure.

We consider two related, yet distinct queries: 1. How does the internal morphology of a small particle affect the elastic light scattering signals? We have devised an algorithm, presently accurate for particles comparable only to small biological spheres (diameter less than 1 micron), which suggests that light scattering is sensitive to internal morphology only in the backward directions. Accordingly, observations should be obtained in these directions when probing for internal morphology. 2. How are fluorescent signals affected when the active molecules are variously distributed within small particles? One cannot assume that the fluorescent signals are simply proportional to the number of active molecules contained in the particle because there may also be a dependence upon the geometrical and optical properties of the particle and upon the particular spatial distribution of these molecules within the particle. Indeed, even the measured emission spectrum may be affected by such morphological features. Here, too, these calculations are mainly restricted to small particles (diameter less than 1 micron) in which the fluorescent molecules are isotropic and immobile. Under these conditions the effects are quite dramatic. These effects should be considered in quantitative procedures which utilize fluorescence for determining the concentration of specific molecules in small particles such as biological cells. They may provide a clue for discriminating among cells which differ morphologically or in which the spatial distribution of the fluorescent moiety differs. These effects may be minimized by utilizing a light source which is polarized perpendicularly to the scattering plane.     

Single-molecule detection technologies in miniaturized high-throughput screening: fluorescence intensity distribution analysis

Single-molecule detection technologies are becoming a powerful readout format to support ultra-high-throughput screening. These methods are based on the analysis of fluorescence intensity fluctuations detected from a small confocal volume element. The fluctuating signal contains information about the mass and brightness of the different species in a mixture. The authors demonstrate a number of applications of fluorescence intensity distribution analysis (FIDA), which discriminates molecules by their specific brightness. Examples for assays based on brightness changes induced by quenching/dequenching of fluorescence, fluorescence energy transfer, and multiple-binding stoichiometry are given for important drug targets such as kinases and proteases. FIDA also provides a powerful method to extract correct biological data in the presence of compound fluorescence.     

Growth kinetics of the photosynthetic bacterium Chlorobium thiosulfatophilum in a fed-batch reactor

Hydrogen sulfide dissolved in water can be converted to elementary sulfur or sulfate by the photosynthetic bacterium Chlorobium thiosulfatophilum. Substrate inhibition occurred at sulfide concentrations above 5.7 mM. Light inhibition was found at average light intensities of 40,000 lux in a sulfide concentration of 5 mM, where no substrate inhibition occurred. Light intensity, the most important growth parameter, was attenuated through both scattering by sulfur particles and absorption by the cells. Average cell and sulfur particle sizes were 1.1 and 9.4 mum, respectively. Cells contributed 10 times as much to the turbidity as sulfur particles of the same weight concentration. The light attenuation factor was mathematically modeled, considering both the absorption and scattering effects based on the Beer-Lambert law and the Rayleigh theory, which were introduced to the cell growth model. Optimal operational conditions relating feed rate vs. light intensity were obtained to suppress the accumulation of sulfate and sulfide and save light energy for 2- and 4-L fed-batch reactors. Light intensity should be greater for the same performance (H(2)S removal rate/unit cell concentration) in larger reactors due to the scaleup effect on light transmission. Knowledge of appropriate growth kinetics in photosynthetic fed-batch reactors was essential to increase feed rate and light intensity and therefore cell growth. A mathematical model was developed that describes the cell growth by considering the light attenuation factor due to scattering and absorption and the crowding effect of the cells. This model was in good agreement with the experimental results. (c) 1992 John Wiley & Sons, Inc.     

Development of a quantitative diagnostic method of estrogen receptor expression levels by immunohistochemistry using organic fluorescent material-assembled nanoparticles

The detection of estrogen receptors (ERs) by immunohistochemistry (IHC) using 3,3′-diaminobenzidine (DAB) is slightly weak as a prognostic marker, but it is essential to the application of endocrine therapy, such as antiestrogen tamoxifen-based therapy. IHC using DAB is a poor quantitative method because horseradish peroxidase (HRP) activity depends on reaction time, temperature and substrate concentration. However, IHC using fluorescent material provides an effective method to quantitatively use IHC because the signal intensity is proportional to the intensity of the photon excitation energy. However, the high level of autofluorescence has impeded the development of quantitative IHC using fluorescence. We developed organic fluorescent material (tetramethylrhodamine)-assembled nanoparticles for IHC. Tissue autofluorescence is comparable to the fluorescence intensity of quantum dots, which are the most representative fluorescent nanoparticles. The fluorescent intensity of our novel nanoparticles was 10.2-fold greater than quantum dots, and they did not bind non-specifically to breast cancer tissues due to the polyethylene glycol chain that coated their surfaces. Therefore, the fluorescent intensity of our nanoparticles significantly exceeded autofluorescence, which produced a significantly higher signal-to-noise ratio on IHC-imaged cancer tissues than previous methods. Moreover, immunostaining data from our nanoparticle fluorescent IHC and IHC with DAB were compared in the same region of adjacent tissues sections to quantitatively examine the two methods. The results demonstrated that our nanoparticle staining analyzed a wide range of ER expression levels with higher accuracy and quantitative sensitivity than DAB staining. This enhancement in the diagnostic accuracy and sensitivity for ERs using our immunostaining method will improve the prediction of responses to therapies that target ERs and progesterone receptors that are induced by a downstream ER signal.     

Relationship of turbidity to the stages of platelet aggregation

The process of platelet aggregation as detected by turbidity changes in the platelet aggregometer was studied relative to light scattering by large particles. For latex beads a plot of light scattering intensity/unit mass versus particle size gave increased light scattering intensity for small particle sizes but decreased scattering at large particle size. This behavior is predicted by Rayleigh-Gans theory. These results were related to the platelet aggregometer, an optical instrument used to measure the association of small particles (monomeric platelets) to large particles (platelet aggregates). Formalin-fixed platelets do not show changes in light transmission due to energy-requiring processes, such as shape change, so that turbidity changes in the presence of aggregating agents could be attributed to a change in platelet aggregation state. Small platelet aggregates showed increased turbidity compared to a similar mass of monomeric platelets. In fact, very large platelet aggregates that were visible to the unaided eye were needed to produce a decrease in light scattering intensity. Thus, turbidity can either increase or decrease with platelet aggregation depending on the size of the aggregates. Studies of platelet aggregation that show no initial increase in turbidity must be characterized by dominance of large platelet aggregates and monomeric platelets.     

Method for Assessing the Reliability of Molecular Diagnostics Based on Multiplexed SERS-Coded Nanoparticles

Surface-enhanced Raman scattering (SERS) nanoparticles have been engineered to generate unique fingerprint spectra and are potentially useful as bright contrast agents for molecular diagnostics. One promising strategy for biomedical diagnostics and imaging is to functionalize various particle types (“flavors”), each emitting a unique spectral signature, to target a large multiplexed panel of molecular biomarkers. While SERS particles emit narrow spectral features that allow them to be easily separable under ideal conditions, the presence of competing noise sources and background signals such as detector noise, laser background, and autofluorescence confounds the reliability of demultiplexing algorithms. Results obtained during time-constrained in vivo imaging experiments may not be reproducible or accurate. Therefore, our goal is to provide experimentalists with a metric that may be monitored to enforce a desired bound on accuracy within a user-defined confidence level. We have defined a spectral reliability index (SRI), based on the output of a direct classical least-squares (DCLS) demultiplexing routine, which provides a measure of the reliability of the computed nanoparticle concentrations and ratios. We present simulations and experiments to demonstrate the feasibility of this strategy, which can potentially be utilized for a range of instruments and biomedical applications involving multiplexed SERS nanoparticles.     

Dynamic light scattering microscopy. A novel optical technique to image submicroscopic motions. I: theory

The theoretical basis of an optical microscope technique to image dynamically scattered light fluctuation decay rates (dynamic light scattering microscopy) is developed. It is shown that relative motions between scattering centers even smaller than the optical resolution of the microscope are sufficient to produce significant phase variations resulting in interference intensity fluctuations in the image plane. The timescale and time dependence for the temporal autocorrelation function of these intensity fluctuations is derived. The spatial correlation distance, which reports the average distance between constructive and destructive interference in the image plane, is calculated and compared with the pixel size, and the distance dependence of the spatial correlation function is derived. The accompanying article in this issue describes an experimental implementation of dynamic light scattering microscopy.     

The use and development of the dynamic light-scattering method to investigate supramolecular structures in aqueous solutions of bacterial lipopolysaccharides

The temperature dependence of the scattering intensity, average size, and size distribution for supramolecular particles in aqueous solutions of lipopolysaccharides from Azospirillum bacteria was investigated by dynamic light scattering. Relationships were obtained that made it possible to comparatively estimate the mass–volume concentration of the biopolymeric substance in suspensions and the number concentration of supramolecular particles with their size and degree of polydispersity taken into account. In the range from 0 to 60°C, two types of the temperature dependence of scattering intensity were found: (a) with an irregular spasmodic change in scattering intensity and with considerable heterogeneity of the systems with respect to particle size and (b) with a smoother character of this dependence with considerably decreased heterogeneity of the suspensions. In the ranges of the latter type, whose location depended on what strain was used to isolate lipopolysaccharides, it proved to be possible to correctly determine the parameters of the supramolecular particles (of the supposedly formed micellar phase) by dynamic light scattering. The revealed statistically significant differences in the size and the concentration of the micellar particles are explained by their dependence on the peculiarities of the chemical structure of lipopolysaccharides. Atomic-force microscopy was used for an independent morphological estimation of the preparations, yielding good agreement with the dynamic light-scattering results.