A Comparison between Photon Counting Histogram and Fluorescence Intensity Distribution Analysis

Fluorescence Correlation Spectroscopy and Photon Counting Histograms in Finite, Bounded Domains

Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of a broad range of molecular kinetic processes. Two key mathematical frameworks that have enabled these quantifications are fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis. Although these frameworks are effective and accurate when the focused laser beam is well approximated by an infinite Gaussian beam with a waist that is small compared to the size of the region over which the fluorescent particles can diffuse, they cannot be applied to situations in which this region is bounded at the nanoscale. We therefore derived general forms of the FCS and PCH frameworks for bounded systems. The finite-domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case when the system is much larger than the Gaussian beam and can be considered to be infinite. We also derived the PCH form for the bounded systems. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time, to our knowledge. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible.

Resolving fluorescent species by their brightness and diffusion using correlated photon-counting histograms

Fluorescence fluctuation spectroscopy (FFS) refers to techniques that analyze fluctuations in the fluorescence emitted by fluorophores diffusing in a small volume and can be used to distinguish between populations of molecules that exhibit differences in brightness or diffusion. For example, fluorescence correlation spectroscopy (FCS) resolves species through their diffusion by analyzing correlations in the fluorescence over time; photon counting histograms (PCH) and related methods based on moment analysis resolve species through their brightness by analyzing fluctuations in the photon counts. Here we introduce correlated photon counting histograms (cPCH), which uses both types of information to simultaneously resolve fluorescent species by their brightness and diffusion. We define the cPCH distribution by the probability to detect both a particular number of photons at the current time and another number at a later time. FCS and moment analysis are special cases of the moments of the cPCH distribution, and PCH is obtained by summing over the photon counts in either channel. cPCH is inherently a dual channel technique, and the expressions we develop apply to the dual colour case. Using simulations, we demonstrate that two species differing in both their diffusion and brightness can be better resolved with cPCH than with either FCS or PCH. Further, we show that cPCH can be extended both to longer dwell times to improve the signal-to-noise and to the analysis of images. By better exploiting the information available in fluorescence fluctuation spectroscopy, cPCH will be an enabling methodology for quantitative biology.

Two-Color Spatial Cumulant Analysis Detects Heteromeric Interactions between Membrane Proteins

Fluorescence fluctuation spectroscopy can be used to measure the aggregation of fluorescently labeled molecules and is typically performed using time series data. Spatial intensity distribution analysis and fluorescence moment image analysis are established tools for measuring molecular brightnesses from single-color images collected with laser scanning microscopes. We have extended these tools for analysis of two-color images to resolve heteromeric interactions between molecules labeled with spectrally distinct chromophores. We call these new methods two-color spatial intensity distribution analysis and two-color spatial cumulant analysis (2c-SpCA). To implement these techniques on a hyperspectral imaging system, we developed a spectral shift filtering technique to remove artifacts due to intrinsic cross talk between detector bins. We determined that 2c-SpCA provides better resolution from samples containing multiple fluorescent species; hence, this technique was carried forward to study images of living cells. We used fluorescent heterodimers labeled with enhanced green fluorescent protein and mApple to quantify the effects of resonance energy transfer and incomplete maturation of mApple on brightness measurements. We show that 2c-SpCA can detect the interaction between two components of trimeric G-protein complexes. Thus, 2c-SpCA presents a robust and computationally expedient means of measuring heteromeric interactions in cellular environments.

Fluorescence cumulants analysis with non-ideal observation profiles

One of the challenges of fluorescence fluctuation fpectroscopy (FFS) is an adequate approximation of a brightness profile. The key feature of fluorescence intensity distribution analysis (FIDA) is a polynomial approximation of a brightness profile. A broad range of brightness profile shapes can be well described by this approximation. A different approach consisting of the introduction of additional fitting parameters, defined as a relative difference between integrals of the actual brightness profile and its Gaussian approximation, is used in photon counting histogram (PCH) analysis. It is sufficient to introduce only one additional fitting parameter (first-order correction) to get an adequate fit to the experimental data in many practical applications. In the current study, we apply these approaches to the theory of time integrated fluorescence cumulants analysis. We demonstrate that developed corrections improve results of FFS analysis applied to simulated and experimental data. The use of different brightness profile approximations and normalizations in PCH and FIDA leads to different estimates of brightness and the number of molecules, even though they represent the same physical quantities. Based on the developed theory, we derive equations that relate brightness and the number of molecules in PCH and FIDA.

Global analysis of autocorrelation functions and photon counting distributions in fluorescence fluctuation spectroscopy

In fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis, the same experimental fluorescence intensity fluctuations are used, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding molecular diffusion coefficients and triplet-state parameters such as fraction and decay time. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding the molecular brightness. Both FCS and PCH give information about the molecular concentration. Here we describe a global analysis protocol that simultaneously recovers relevant and common parameters in model functions of FCS and PCH from a single fluorescence fluctuation trace. Application of a global analysis approach allows increasing the information content available from a single measurement that results in more accurate values of molecular diffusion coefficients and triplet-state parameters and also in robust, time-independent estimates of molecular brightness and number of molecules.

Confidence intervals for concentration and brightness from fluorescence fluctuation measurements

The theory of photon count histogram (PCH) analysis describes the distribution of fluorescence fluctuation amplitudes due to populations of fluorophores diffusing through a focused laser beam and provides a rigorous framework through which the brightnesses and concentrations of the fluorophores can be determined. In practice, however, the brightnesses and concentrations of only a few components can be identified. Brightnesses and concentrations are determined by a nonlinear least-squares fit of a theoretical model to the experimental PCH derived from a record of fluorescence intensity fluctuations. The χ(2) hypersurface in the neighborhood of the optimum parameter set can have varying degrees of curvature, due to the intrinsic curvature of the model, the specific parameter values of the system under study, and the relative noise in the data. Because of this varying curvature, parameters estimated from the least-squares analysis have varying degrees of uncertainty associated with them. There are several methods for assigning confidence intervals to the parameters, but these methods have different efficacies for PCH data. Here, we evaluate several approaches to confidence interval estimation for PCH data, including asymptotic standard error, likelihood joint-confidence region, likelihood confidence intervals, skew-corrected and accelerated bootstrap (BCa), and Monte Carlo residual resampling methods. We study these with a model two-dimensional membrane system for simplicity, but the principles are applicable as well to fluorophores diffusing in three-dimensional solution. Using simulated fluorescence fluctuation data, we find the BCa method to be particularly well-suited for estimating confidence intervals in PCH analysis, and several other methods to be less so. Using the BCa method and additional simulated fluctuation data, we find that confidence intervals can be reduced dramatically for a specific non-Gaussian beam profile.

Simultaneous diffusion and brightness measurements and brightness profile visualization from single fluorescence fluctuation traces of GFP in living cells

Fluorescence correlation spectroscopy (FCS) and photon-counting histogram (PCH) analysis use the same experimental fluorescence intensity fluctuations, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding, for instance, molecular diffusion coefficients. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding information about the molecular brightness of fluorescent species. Analysis of both FCS and PCH results in the molecular concentration of the sample. Using a previously described global analysis procedure we report here precise, simultaneous measurements of diffusion constants and brightness values from single fluorescence fluctuation traces of green-fluorescent protein (GFP, S65T) in the cytoplasm of Dictyostelium cells. The use of a polynomial profile in PCH analysis, describing the detected three-dimensional shape of the confocal volume, enabled us to obtain well fitting results for GFP in cells. We could visualize the polynomial profile and show its deviation from a Gaussian profile.

X-ray Fluorescence Emission Tomography (XFET) with Novel Imaging Geometries - A Monte Carlo Study

This paper presents a feasibility study for using two new imaging geometries for synchrotron X-ray fluorescence emission tomography (XFET) applications. In the proposed approaches, the object is illuminated with synchrotron X-ray beams of various cross-sectional dimensions. The resultant fluorescence photons are detected by high-resolution imaging-spectrometers coupled to collimation apertures. To verify the performance benefits of the proposed methods over the conventional line-by-line scanning approach, we have used both Monte Carlo simulations and an analytical system performance index to compare several different imaging geometries. This study has demonstrated that the proposed XFET approach could lead to a greatly improved imaging speed, which is critical for making XFET a practical imaging modality for a wide range of applications.

Fluorescence fluctuation spectroscopy and imaging methods for examination of dynamic protein interactions in yeast

Protein interactions are inherently dynamic. In no system is this more true and important than in signaling pathways, where spatial and temporal control of specific protein interactions is key to signaling specificity and timing. While genetic and biochemical interactions form a necessary and important starting point for deciphering interactions among signaling components, they struggle to provide precise information of where and when interactions occur in a live cell setting. In contrast, live cell fluorescence studies such as those outlined below are able to provide quantitative information on the strength, nature, timing, and location of homotypic and heterotypic protein interactions.