The application of fluorescence lifetime readouts in high-throughput screening

Measurement of fluorescence lifetime is a well-established technique, which has recently been introduced into the portfolio of assay formats used in high-throughput screening (HTS). This investigation establishes appropriate conditions for using lifetime measurements to reduce the impact of compound interference effects during large-scale HTS of corporate screening files. Experimental data on mixtures of standard fluorophores and interfering compounds (from 5 HTS campaigns) have been combined with a theoretical model to identify the minimum data quality required, defined by the photon count in the peak channel, for discrimination of biological activity. Single-component fluorophore lifetimes can be recovered with an error of 1%, with a peak photon count of 10(2), but the same accuracy with a 2-component decay requires a peak photon count of 10(3). When a 3rd component is introduced, the minimum peak count increases to 10(4). The influence of scattered light on lifetime determination was investigated using an emulsion (diameters 25-675 nm). The measured decays of interfering compounds, identified as autofluorescent, show that the vast majority have a very short lifetime that can readily be resolved from the reporter fluorophore, using appropriate data-fitting methods.     

Studying polyglutamine aggregation in Caenorhabditis elegans using an analytical ultracentrifuge equipped with fluorescence detection

This work explores the heterogeneity of aggregation of polyglutamine fusion constructs in crude extracts of transgenic Caenorhabditis elegans animals. The work takes advantage of the recent technical advances in fluorescence detection for the analytical ultracentrifuge. Further, new sedimentation velocity methods, such as the multi‐speed method for data capture and wide distribution analysis for data analysis, are applied to improve the resolution of the measures of heterogeneity over a wide range of sizes. The focus here is to test the ability to measure sedimentation of polyglutamine aggregates in complex mixtures as a prelude to future studies that will explore the effects of genetic manipulation and environment on aggregation and toxicity. Using sedimentation velocity methods, we can detect a wide range of aggregates, ranging from robust analysis of the monomer species through an intermediate and quite heterogeneous population of oligomeric species, and all the way up to detecting species that likely represent intact inclusion bodies based on comparison to an analysis of fluorescent puncta in living worms by confocal microscopy. Our results support the hypothesis that misfolding of expanded polyglutamine tracts into insoluble aggregates involves transitions through a number of stable intermediate structures, a model that accounts for how an aggregation pathway can lead to intermediates that can have varying toxic or protective attributes. An understanding of the details of intermediate and large‐scale aggregation for polyglutamine sequences, as found in neurodegenerative diseases such as Huntington's Disease, will help to more precisely identify which aggregated species may be involved in toxicity and disease.     

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.     

Analysis of multi-component fluorescence emission by phase-sensitive detection using one modulation frequency

We describe the use of phase-sensitive detection of fluorescence to resolve the lifetimes and fractional intensities from multi-component fluorescence samples, using data obtained at a single modulation frequency. Phase-sensitive spectra of the mixture are recorded at arbitrarily chosen detector phase angles. The steady-state spectrum of each component must be known. The phase-sensitive spectra are fitted, using a nonlinear least-squares algorithm, to obtain the lifetimes and fractional intensities of each fluorophore in the mixture. Simulations for two- and three-component mixtures are presented to illustrate how the resolution is affected by spectral overlap and lifetime separation. Experimentally, we resolved two- and three-component mixtures of protein-like fluorophores (N-acetyl-L-tyrosinamide, N-acetyl- L-tryptophanamide, indole and 2,3-dimethylindole) using data collected at 30 MHz. These fluorophores have closely spaced lifetimes of 1.5, 2.9, 4.5 and 4.3 ns, respectively, and display extensive spectral overlap. These results demonstrate that phase-sensitive spectra, recorded at only one modulation frequency with a standard phase fluorometer, can be used to resolve multi-component emissions.     

Pulsed Interleaved Excitation Fluctuation Imaging

Fluorescence fluctuation imaging is a powerful means to investigate dynamics, interactions, and stoichiometry of proteins inside living cells. Pulsed interleaved excitation (PIE) is the method of nanosecond alternating excitation with time-resolved detection and allows accurate, independent, and quasi-simultaneous determination of fluorescence intensities and lifetimes of different fluorophores. In this work, we combine pulsed interleaved excitation with fluctuation imaging methods (PIE-FI) such as raster image correlation spectroscopy (RICS) or number and brightness analysis (N&B). More specifically, we show that quantitative measurements of diffusion and molecular brightness of Venus fluorescent protein (FP) can be performed in solution with PIE-RICS and compare PIE-RICS with single-point PIE-FCS measurements. We discuss the advantages of cross-talk free dual-color PIE-RICS and illustrate its proficiency by quantitatively comparing two commonly used FP pairs for dual-color microscopy, eGFP/mCherry and mVenus/mCherry. For N&B analysis, we implement dead-time correction to the PIE-FI data analysis to allow accurate molecular brightness determination with PIE-NB. We then use PIE-NB to investigate the effect of eGFP tandem oligomerization on the intracellular maturation efficiency of the fluorophore. Finally, we explore the possibilities of using the available fluorescence lifetime information in PIE-FI experiments. We perform lifetime-based weighting of confocal images, allowing us to quantitatively determine molecular concentrations from 100 nM down to <30 pM with PIE-raster lifetime image correlation spectroscopy (RLICS). We use the fluorescence lifetime information to perform a robust dual-color lifetime-based FRET analysis of tandem fluorescent protein dimers. Lastly, we investigate the use of dual-color RLICS to resolve codiffusing FRET species from non-FRET species in cells. The enhanced capabilities and quantitative results provided by PIE-FI make it a powerful method that is broadly applicable to a large number of interesting biophysical studies.     

Pulsed Interleaved Excitation Fluctuation Imaging

Fluorescence fluctuation imaging is a powerful means to investigate dynamics, interactions, and stoichiometry of proteins inside living cells. Pulsed interleaved excitation (PIE) is the method of nanosecond alternating excitation with time-resolved detection and allows accurate, independent, and quasi-simultaneous determination of fluorescence intensities and lifetimes of different fluorophores. In this work, we combine pulsed interleaved excitation with fluctuation imaging methods (PIE-FI) such as raster image correlation spectroscopy (RICS) or number and brightness analysis (N&B). More specifically, we show that quantitative measurements of diffusion and molecular brightness of Venus fluorescent protein (FP) can be performed in solution with PIE-RICS and compare PIE-RICS with single-point PIE-FCS measurements. We discuss the advantages of cross-talk free dual-color PIE-RICS and illustrate its proficiency by quantitatively comparing two commonly used FP pairs for dual-color microscopy, eGFP/mCherry and mVenus/mCherry. For N&B analysis, we implement dead-time correction to the PIE-FI data analysis to allow accurate molecular brightness determination with PIE-NB. We then use PIE-NB to investigate the effect of eGFP tandem oligomerization on the intracellular maturation efficiency of the fluorophore. Finally, we explore the possibilities of using the available fluorescence lifetime information in PIE-FI experiments. We perform lifetime-based weighting of confocal images, allowing us to quantitatively determine molecular concentrations from 100 nM down to <30 pM with PIE-raster lifetime image correlation spectroscopy (RLICS). We use the fluorescence lifetime information to perform a robust dual-color lifetime-based FRET analysis of tandem fluorescent protein dimers. Lastly, we investigate the use of dual-color RLICS to resolve codiffusing FRET species from non-FRET species in cells. The enhanced capabilities and quantitative results provided by PIE-FI make it a powerful method that is broadly applicable to a large number of interesting biophysical studies.     

Characterization of probe binding and comparison of its influence on fluorescence lifetime of two pH-sensitive benzo[c]xanthene dyes using intensity-modulated multiple-wavelength scanning technique

Quantitative pH imaging using the carboxy seminaphthofluorescein dyes SNAFL-1 and SNAFL-2 can be performed by measurement of intensity ratios or fluorescence lifetimes. However, there is a controversy as to whether the latter method has the practical advantage of a straightforward pH calibration in buffers compared to a cumbersome and time-consuming procedure in cells. In this study we have undertaken a systematic study of the potential factors influencing the fluorescence lifetime of the probes at different pH using confocal microscopy. In vitro results demonstrate that factors such as lipid and protein concentrations have a substantial influence on pH measurements based on fluorescence lifetime. The pH could be overestimated by more than 2 pH units. Studies in permeabilized COS-7 cells demonstrate the same trends as observed in the in vitro studies.     

Use of fluorescence lifetime technology to provide efficient protection from false hits in screening applications

This article describes novel data analysis of fluorescence lifetime-based protein kinase assays to identify and correct for compound interference in several practical cases. This ability, together with inherent advantages of fluorescence lifetime technology (FLT) as a homogeneous, antibody-free format independent of sample concentration, volume, excitation intensity, and geometry, makes fluorescence lifetime a practical alternative to the established “gold standards” of radiometric and mobility shift (Caliper) assays. The analysis is based on a photochemical model that sets constraints on the values of fluorescence lifetimes in the time responses of the assay. The addition of an exponential component with free floating lifetime to the constrained model, in which the lifetimes are constants predetermined from control measurements and the preexponential coefficients are “floating” parameters, allows the relative concentration of phosphorylated and nonphosphorylated substrates to be calculated even in the presence of compound fluorescence. The method is exemplified using both simulated data and experimental results measured from mixtures of dye-labeled phosphorylated and nonphosphorylated kinase substrates. A change of the fluorescence lifetime is achieved by the phosphorylated substrate-specific interaction with a bifunctional ligand, where one binding site interacts with the phosphate group and the other interacts with the dye.     

Lifetime of Organic Photovoltaics: Status and Predictions

The results of a meta‐analysis conducted on organic photovoltaics (OPV) lifetime data reported in the literature is presented through the compilation of an extensive OPV lifetime database based on a large number of articles, followed by analysis of the large body of data. We fully reveal the progress of reported OPV lifetimes. Furthermore, a generic lifetime marker has been defined, which helps with gauging and comparing the performance of different architectures and materials from the perspective of device stability. Based on the analysis, conclusions are drawn on the bottlenecks for stability of device configurations and packaging techniques, as well as the current level of OPV lifetimes reported under different aging conditions. The work is summarized by discussing the development of a tool for OPV lifetime prediction and the development of more stable technologies. An online platform is introduced that will aid the process of generating statistical data on OPV lifetimes and further refinement of the lifetime prediction tool.     

Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy

We show that fluorescence lifetime imaging microscopy (FLIM) of green fluorescent protein (GFP) molecules in cells can be used to report on the local refractive index of intracellular GFP. We expressed GFP fusion constructs of Rac2 and gp91^phox, which are both subunits of the phagocyte NADPH oxidase enzyme, in human myeloid PLB-985 cells and showed by high-resolution confocal fluorescence microscopy that GFP-Rac2 and GFP-gp91^phox are targeted to the cytosol and to membranes, respectively. Frequency-domain FLIM experiments on these PLB-985 cells resulted in average fluorescence lifetimes of 2.70 ns for cytosolic GFP-Rac2 and 2.31 ns for membrane-bound GFP-gp91^phox. By comparing these lifetimes with a calibration curve obtained by measuring GFP lifetimes in PBS/glycerol mixtures of known refractive index, we found that the local refractive indices of cytosolic GFP-Rac2 and membrane-targeted GFP-gp91^phox are ∼1.38 and ∼1.46, respectively, which is in good correspondence with reported values for the cytosol and plasma membrane measured by other techniques. The ability to measure the local refractive index of proteins in living cells by FLIM may be important in revealing intracellular spatial heterogeneities within organelles such as the plasma and phagosomal membrane.     

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.     

Liquid-ordered microdomains in lipid rafts and plasma membrane of U-87 MG cells: a time-resolved fluorescence study

Lipid rafts, the functional microdomains in the cell membrane, are believed to exist as liquid-ordered (Lo) phase domains along with the liquid-disordered (Ld) phase of the bulk of the cell membranes. We have examined the lipid order in model and natural membranes by time-resolved fluorescence of trimethylammonium-1,6-diphenylhexatriene incorporated into the membranes. The lipid phases were discerned by the limiting anisotropy, rotational diffusion rate and distribution of the fluorescence lifetime. In dipalmitoylphosphatidylcholine (DPPC)-cholesterol mixtures the gel phase exhibited higher anisotropy and a two-fold slower rotational diffusion rate of the probe as compared to the Ld phase. On the other hand, the Lo phase exhibited higher limiting anisotropy but a rotational diffusion rate comparable to the Ld phase. The Ld and Lo phases elicited unimodal distribution of lifetimes with distinct mean values and their co-existence in phospholipid-cholesterol mixtures was reflected as a biphasic change in the width of the lifetime distribution. Global analysis of the lifetimes yielded a best fit with two lifetimes which were identical to those observed in single Lo or Ld phases, but their fractional contribution varied with cholesterol concentration. Attributing the shorter and longer lifetime components to the Ld and Lo phases, respectively, the extent of the Lo/Ld phase domains in the membranes was estimated by their fractional contribution to the fluorescence decay. In ternary mixtures of egg PC-gangliosides-cholesterol, the gangliosides induced heterogeneity in the membrane but the Ld phase prevailed. The Lo phase properties were observed only in the presence of cholesterol. Results obtained in the plasma membrane and detergent-resistant membrane fractions (DRMs) isolated from U-87 MG cells revealed that DRMs mainly possess the Lo phase; however, a substantially large proportion of plasma membrane also exists in the Lo phase. Our data show that, besides cholesterol, the membrane proteins play a significant role in the organization of lipid rafts and, furthermore, a considerable amount of heterogeneity is present among the lipid rafts.     

Combination of a spinning disc confocal unit with frequency-domain fluorescence lifetime imaging microscopy.

BACKGROUND: Wide-field frequency-domain fluorescence lifetime imaging microscopy (FLIM) is an established technique to determine fluorescence lifetimes. Disadvantage of wide-field imaging is that measurements are compromised by out-of-focus blur. Conventional scanning confocal typically means long acquisition times and more photo bleaching. An alternative is spinning-disc confocal whereby samples are scanned simultaneously by thousands of pinholes, resulting in a virtually instantaneous image with more than tenfold reduced photo bleaching. METHODS: A spinning disc unit was integrated into an existing FLIM system. Measurements were made of fluorescent beads with a lifetime of 2.2 ns against a 5.3 ns fluorescent background outside the focal plane. In addition, living HeLa cells were imaged with different lifetimes in the cytosol and the plasma membrane. RESULTS: In spinning-disc mode, a lifetime of the beads of 2.8 ns was measured, whereas in wide field a lifetime of 4.1 ns was measured. Lifetime contrast within living HeLa cells could be resolved with the spinning-disc unit, where this was impossible in wide field. CONCLUSIONS: Integration of a spinning-disc unit into a frequency-domain FLIM instrument considerably reduces artifacts, while maintaining the advantages of wide field. For FLIM on objects with 3D lifetime structure, spinning-disc is by far preferable over wide-field measurements.     

Water molecule binding and lifetimes on the DNA duplex d(CGCGAATTCGCG)2

Summary Measurements of the water proton spin-lattice relaxation rate for aqueous solutions of the palindromic dodecamer, d(CGCGAATTCGCG)₂, are reported as a function of the magnetic field strength. The magnitude of the relaxation rates at low magnetic field strengths and the shape of the relaxation dispersion curve permit assessment of the number of water molecules which may be considered bound to the DNA for a time equal to or longer than the rotational correlation time of the duplex. The data are examined using limiting models that arbitrarily use the measured rotational correlation time of the polynucleotide complex as a reference point for the water molecule lifetime. If it is assumed that water molecules are bound at DNA sites for times as long as or longer than the rotational correlation time of the duplex, then the magnitude of the relaxation rates at low field require that there may be only two or three such water sites. However, if the lifetime constraints is relaxed, and we assume that the number of water molecules bound to the DNA is more nearly the number identified in the X-ray structures, then the average water molecule lifetime is on the order of 1 ns. Measurements of ¹H NOESY spectra demonstrate that some water molecules must have lifetimes sufficiently long that negative Overhauser effects are observed. Taken together, these results suggest a distribution of water molecule lifetimes in which most of the DNA-bound water molecule lifetimes are shorter than the rotational correlation time of the duplex, but where some have lifetimes of at least 1 ns under these concentrated conditions.Abbreviations DNA deoxyribonucleic acid - NOE nuclear Overhauser enhancement - NOESY nuclear Overhauser enhancement spectroscopy     

Development and characterization of green fluorescent protein mutants with altered lifetimes

Multiple-probe fluorescence imaging applications demand an ever-increasing number of resolvable probes, and the use of fluorophores with resolvable fluorescence lifetimes can help meet this demand. Green fluorescent protein (GFP) and its variants have been widely used in spectrally resolved multiprobe imaging, but as yet, there has not been a systematic set of mutants generated with resolvable lifetimes. Therefore, to generate such mutants, we have utilized error-prone PCR and fluorescence lifetime imaging to screen for mutants of UV-excited green fluorescent protein (GFPuv) that exhibit altered fluorescence decay lifetimes. This has resulted in the isolation of GFPuv mutants displaying at least three distinctly different lifetimes in the range of 1.9-2.8 ns. Mutation of Y145 to either histidine or cysteine was found to shift the fluorescence lifetime of GFPuv from 3.03 +/- 0.03 to 2.78 +/- 0.05 ns for the Y145H mutant and to 2.74 +/- 0.05 ns for Y145C. Some of the shorter-lifetime mutants exhibited excitation peaks that were red-shifted relative to their maximal absorption, indicating that the mutations allowed the adoption of additional conformations relative to wtGFPuv. The utility of these mutants for applications in simultaneous imaging and quantification is shown by the ability to quantify the composition of binary mixtures in time-resolved images using a single detector channel. The application of the screening method for generating lifetime mutants of other fluorescent proteins is also discussed.     

Fluorescence lifetime imaging.

We describe a new fluorescence imaging methodology in which the image contrast is derived from the fluorescence lifetime at each point in a two-dimensional image and not the local concentration and/or intensity of the fluorophore. In the present apparatus, lifetime images are created from a series of images obtained with a gain-modulated image intensifier. The frequency of gain modulation is at the light-modulation frequency (or a harmonic thereof), resulting in homodyne phase-sensitive images. These stationary phase-sensitive images are collected using a slow-scan CCD camera. A series of such images, obtained with various phase shifts of the gain-modulation signal, is used to determine the phase angle and/or modulation of the emission at each pixel, which is in essence the phase or modulation lifetime image. An advantage of this method is that pixel-to-pixel scanning is not required to obtain the images, as the information from all pixels is obtained at the same time. The method has been experimentally verified by creating lifetime images of standard fluorophores with known lifetimes, ranging from 1 to 10 ns. As an example of biochemical imaging we created life-time images of Yt-base when quenched by acrylamide, as a model for a fluorophore in distinct environments that affect its decay time. Additionally, we describe a faster imaging procedure that allows images in which a specific decay time is suppressed to be calculated, allowing rapid visualization of unique features and/or regions with distinct decay times. The concepts and methodologies of fluorescence lifetime imaging (FLIM) have numerous potential applications in the biosciences. Fluorescence lifetimes are known to be sensitive to numerous chemical and physical factors such as pH, oxygen, temperature, cations, polarity, and binding to macromolecules. Hence the FLIM method allows chemical or physical imaging of macroscopic and microscopic samples.     

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.     

Competition and succession among coral endosymbionts

Host species often support a genetically diverse guild of symbionts, the identity and performance of which can determine holobiont fitness under particular environmental conditions. These symbiont communities are structured by a complex set of potential interactions, both positive and negative, between the host and symbionts and among symbionts. In reef‐building corals, stable associations with specific symbiont species are common, and we hypothesize that this is partly due to ecological mechanisms, such as succession and competition, which drive patterns of symbiont winnowing in the initial colonization of new generations of coral recruits. We tested this hypothesis using the experimental framework of the de Wit replacement series and found that competitive interactions occurred among symbionts which were characterized by unique ecological strategies. Aposymbiotic octocoral recruits within high‐ and low‐light environments were inoculated with one of three Symbiodiniaceae species as monocultures or with cross‐paired mixtures, and we tracked symbiont uptake using quantitative genetic assays. Priority effects, in which early colonizers excluded competitive dominants, were evidenced under low light, but these early opportunistic species were later succeeded by competitive dominants. Under high light, a more consistent competitive hierarchy was established in which competitive dominants outgrew and limited the abundance of others. These findings provide insight into mechanisms of microbial community organization and symbiosis breakdown and recovery. Furthermore, transitions in competitive outcomes across spatial and temporal environmental variation may improve lifetime host fitness.     

Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks

Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.