An Experimental Comparison of the Maximum Likelihood Estimation and Nonlinear Least-Squares Fluorescence Lifetime Analysis of Single Molecules

Tuned lifetime, at the ensemble and single molecule level, of a xanthenic fluorescent dye by means of a buffer-mediated excited-state proton exchange reaction

The photophysical behaviour of the new fluorescein derivative 9-[1-(2-methyl-4-methoxyphenyl)]-6-hydroxy-3H-xanthen-3-one has been explored by using absorption, and steady-state, time-resolved and single-molecule fluorescence measurements. The apparent ground-state acidity constant of the dye determined by both the absorbance and steady-state fluorescence is almost independent of the added buffer and salt concentrations. The excited-state proton exchange reaction around the physiological pH becomes reversible upon addition of phosphate buffer, inducing a pH-dependent change of the steady-state fluorescence and decay times. Fluorescence decay traces, collected as a function of total buffer concentration and pH, were analyzed by global compartmental analysis (GCA) to elucidate the values of the excited-state rate constants. The features of this system make the fluorescence decays monoexponential at pH values and phosphate buffer concentrations higher than 6.10 and 0.2 M respectively, with the possibility of tuning the fluorescence lifetime value by changing pH or buffer concentrations. The tuned lifetimes obtained by means of phosphate concentration at constant pH have also been recovered at the single-molecule level.

Multiparameter fluorescence image spectroscopy to study molecular interactions

Multiparameter Fluorescence Image Spectroscopy (MFIS) is used to monitor simultaneously a variety of fluorescence parameters in confocal fluorescence microscopy. As the photons are registered one by one, MFIS allows for fully parallel recording of Fluorescence Correlation/Cross Correlation Spectroscopy (FCS/FCCS), fluorescence lifetime and pixel/image information over time periods of hours with picosecond accuracy. The analysis of the pixel fluorescence information in higher-dimensional histograms maximizes the selectivity of fluorescence microscopic methods. Moreover it facilitates a statistically-relevant data analysis of the pixel information which makes an efficient detection of heterogeneities possible. The reliability of MFIS has been demonstrated for molecular interaction studies in different complex environments: (I) detecting the heterogeneity of diffusion properties of the dye Rhodamine 110 in a sepharose bead, (II) Förster Resonance Energy Transfer (FRET) studies in mammalian HEK293 cells, and (III) FRET study of the homodimerisation of the transcription factor BIM1 in plant cells. The multidimensional analysis of correlated changes of several parameters measured by FRET, FCS, fluorescence lifetime and anisotropy increases the robustness of the analysis significantly. The economic use of photon information allows one to keep the expression levels of fluorescent protein-fusion proteins as low as possible (down to the single-molecule level).

Manipulation of the local density of photonic states to elucidate fluorescent protein emission rates

We present experiments to determine the quantum efficiency and emission oscillator strength of exclusively the emitting states of the widely used enhanced green fluorescent protein (EGFP). We positioned the emitters at precisely defined distances from a mirror to control the local density of optical states, resulting in characteristic changes in the fluorescence decay rate that we monitored by fluorescence lifetime microscopy. To the best of our knowledge, this is the first emission lifetime control of a biological emitter. From the oscillation of the observed emission lifetimes as a function of the emitter to mirror distance, we determined the radiative and nonradiative decay rates of the fluorophore. Since only the emitting species contribute to the change in emission lifetimes, the rates determined characterize specifically the quantum efficiency and oscillator strength of the on-states of the emitter, in contrast to other methods that do not differentiate between emitting and dark states. The method reported is especially interesting for photophysically complex systems like fluorescent proteins, where a range of emitting and dark forms has been observed. We have validated the analysis method using Rhodamine 6G dye, obtaining results in very good agreement with the literature. For EGFP we determine the quantum efficiency of the on-states to be 72%. As expected for this complex system, our value is higher than that determined by methods that average over on- and off-states.

Nanopatterned monolayers of an adsorbed chromophore

A simple lift-off process was developed to rapidly fabricate nanopatterned photofunctional surfaces. Dye molecules of a perylene derivative (PDID) were adsorbed irreversibly on clean silicon through the holes of an electron-beam lithographied polymer mask. The subsequent removal of the mask in a proper solvent results in PDID nanosized regions of width as small as 30 nm for stripes and of diameter as small as 120 nm for dots. Numerical analyses of atomic force microscopy and laser-scanning confocal microscopy images show that the dye molecules are confined to the regions defined by the lithographic process, with the integrated fluorescence intensity being essentially proportional to the size of the nanofeatures. This demonstrates that a simple organic lift-off process compatible with clean-room technology, and not involving any chemical step, is able to produce photofunctional nanopatterned surfaces, even though the dye is not chemically bonded to the silicon surface.

Fluorescence lifetime imaging of mixing dynamics in continuous-flow microdroplet reactors

Water-in-oil microdroplets within fluidic channels have the potential to serve as isolated reaction compartments for monitoring real-time dynamics with high efficiency and repeatability. Droplets, usually generated from aqueous and oil solutions using standard microfluidic formats, can be produced at frequencies in excess of 1 kHz. Although mixing within such microdroplets is normally enhanced by chaotic advection, the mixing pattern from droplet to droplet is almost identical and reproducible in form. Herein, we demonstrate that fluorescence lifetime imaging can be used to reconstruct mixing patterns within a droplet with a time resolution of 5 micros.

On-chip, time-correlated, fluorescence lifetime extraction algorithms and error analysis

A new, simple, and hardware-only fluorescence-lifetime-imaging microscopy (FLIM) is proposed to implement on-chip lifetime extractions, and their signal-to-noise-ratio based on statistics theory is also deduced. The results are compared with Monte Carlo simulations, giving good agreement. Compared with the commonly used iterative least-squares method or the maximum-likelihood-estimation- (MLE-) based, general purpose FLIM analysis software, our algorithm offers direct calculation of fluorescence lifetime based on the collected photon counts stored in on-chip counters and therefore delivers faster analysis for real-time applications, such as clinical diagnosis. Error analysis considering timing jitter based on statistics theory is carried out for the proposed algorithms and is also compared with MLE to obtain optimized channel width or measurement window and bit resolution of the time-to-digital converters for a given accuracy. A multi-exponential, pipelined fluorescence lifetime method based on the proposed algorithms is also introduced. The performance of the proposed methods has been tested on mono-exponential and four-exponential decay experimental data.

Visualization of membrane rafts using a perylene monoimide derivative and fluorescence lifetime imaging

A new membrane probe, based on the perylene imide chromophore, with excellent photophysical properties (high absorption coefficient, quantum yield (QY) approximately 1, high photostability) and excited in the visible domain is proposed for the study of membrane rafts. Visualization of separation between the liquid-ordered (Lo) and the liquid-disordered (Ld) phases can be achieved in artificial membranes by fluorescence lifetime imaging due to the different decay times of the membrane probe in the two phases. Rafts on micrometer-scale in cell membranes due to cellular activation can also be observed by this method. The decay time of the dye in the Lo phase is higher than in organic solvents where its QY is 1. This allows proposing a (possible general) mechanism for the decay time increase in the Lo phase, based on the local field effects of the surrounding molecules. For other fluorophores with QY<1, the suggested mechanism could also contribute, in addition to effects reducing the nonradiative decay pathways, to an increase of the fluorescence decay time in the Lo phase.

Fluorescence lifetime fluctuations of single molecules probe the local environment of oligomers around the glass transition temperature

Single molecule fluorescence experiments have been performed on a BODIPY-based dye embedded in oligo(styrene) matrices to probe the density fluctuations and the relaxation dynamics of chain segments surrounding the dye molecules. The time-dependent fluorescence lifetime of the BODIPY probe was recorded as an observable for the local density fluctuations. At room temperature, the mean fraction of holes surrounding the probes is shown to be unaffected by the molecular weight in the glassy state. In contrast, the free volume increases significantly in the supercooled regime. These observations are discussed in the framework of the entropic theories of the glass transition.

Discrimination between single Escherichia coli cells using time-resolved confocal spectroscopy

We describe a technique for rapidly discriminating between single-cell populations within a flowing microfluidic stream. Single-cell time-correlated single-photon counting (scTCSPC) as well as photon burst spectroscopy are used to characterize individual Escherichia coli cells expressed with either green, cyano, or yellow fluorescent protein. The approach utilizes standard confocal fluorescence microscopy incorporating femtoliter detection volumes. The measured burst width characteristics are predominately governed by the fluorescence quantum yield and absorption cross section of the proteins used. It is these characteristics which were used to distinguish between cells with high precision. By utilizing scTCSPC individual fluorescence lifetimes originating from single cells could also be determined. Average fluorescence lifetimes are determined using standard deconvolution procedures. The simplicity of the approach for obtaining well-defined burst width distributions is expected to be extremely valuable for single-cell sorting experiments.

Single molecule fluorescence spectroscopy of pH sensitive oligonucleotide switches

Several authors demonstrated that an oligonucleotide based pH-sensitive construct can act as a switch between an open and a closed state by changing the pH. To validate this process, specially designed fluorescence dye-quencher substituted oligonucleotide constructs were developed to probe the switching between these two states. This paper reports on bulk and single molecule fluorescence investigations of a duplex-triplex pH sensitive oligonucleotide switch. On the bulk level, only a partial quenching of the fluorescence is observed, similarly to what is observed for other published switches and is supposed to be due to intermolecular interactions between oligonucleotide strands. On the single molecule level, each DNA-based nanometric construct shows a complete switching. These observations suggest the tendency of the DNA construct to associate at high concentration.

Non-conjugated, phenyl assisted coupling in through bond electron transfer in a perylenemonoimide–triphenylamine system

Two donor-bridge-acceptor compounds containing triphenylamine (TPA) donors and perylenemonoimide (PMI) acceptors have been studied by spectroscopic techniques and quantum chemical computation. Both systems have been observed to emit prompt and delayed fluorescence under certain conditions indicating that forward and reverse electron transfer (ET) processes can occur between the locally excited and the charge separated states. The experimental and computational results show that the TPA and PMI chromophores are better coupled by almost 50% in the meta isomers which undergo ET more readily than the para isomers. Quantum chemical calculations indicate that this unexpected situation is the result of a phenyl group on the side of the bridge being advantageously positioned in the meta isomers. This leads to more extensive delocalisation of the TPA HOMO into the bridge enhancing the total through bond electronic coupling between the TPA and PMI chromophores. The calculations also indicate a strong angle dependence of the total coupling in both isomers. The experimental results are discussed in the context of the high temperature limit of Marcus's theory of non-adiabatic ET.

Monitoring dynamic systems with multiparameter fluorescence imaging

A new general strategy based on the use of multiparameter fluorescence detection (MFD) to register and quantitatively analyse fluorescence images is introduced. Multiparameter fluorescence imaging (MFDi) uses pulsed excitation, time-correlated single-photon counting and a special pixel clock to simultaneously monitor the changes in the eight-dimensional fluorescence information (fundamental anisotropy, fluorescence lifetime, fluorescence intensity, time, excitation spectrum, fluorescence spectrum, fluorescence quantum yield, distance between fluorophores) in real time. The three spatial coordinates are also stored. The most statistically efficient techniques known from single-molecule spectroscopy are used to estimate fluorescence parameters of interest for all pixels, not just for the regions of interest. Their statistical significance is judged from a stack of two-dimensional histograms. In this way, specific pixels can be selected for subsequent pixel-based subensemble analysis in order to improve the statistical accuracy of the parameters estimated. MFDi avoids the need for sequential measurements, because the registered data allow one to perform many analysis techniques, such as fluorescence-intensity distribution analysis (FIDA) and fluorescence correlation spectroscopy (FCS), in an off-line mode. The limitations of FCS for counting molecules and monitoring dynamics are discussed. To demonstrate the ability of our technique, we analysed two systems: (i) interactions of the fluorescent dye Rhodamine 110 inside and outside of a glutathione sepharose bead, and (ii) microtubule dynamics in live yeast cells of Schizosaccharomyces pombe using a fusion protein of Green Fluorescent Protein (GFP) with Minichromosome Altered Loss Protein 3 (Mal3), which is involved in the dynamic cycle of polymerising and depolymerising microtubules.

Accurate and unbiased estimation of power-law exponents from single-emitter blinking data

Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching.

Statistical evaluation of single nano-object fluorescence

Single nano-objects display strong fluctuations of their fluorescence signals. These random and irreproducible variations must be subject to statistical analysis to provide microscopic information. We review the main evaluation methods used so far by experimentalists in the field of single-molecule spectroscopy: time traces, correlation functions, distributions of "on" and "off" times, higher-order correlations. We compare their advantages and weaknesses from a theoretical point of view, illustrating our main conclusions with simple numerical simulations. We then review experiments on different types of single nano-objects, the phenomena which are observed and the statistical analyses applied to them.

Quantitative two-photon Ca2+ imaging via fluorescence lifetime analysis

Two-photon microscopy (TPM) revolutionized Ca2+ imaging by allowing recordings in the depth of intact tissue and live organisms. A serious limitation in TPM, however, is the lack of an accurate and straightforward approach for the quantification of Ca2+ signals, an ability that became an invaluable tool in fluorescence microscopy. Here, we present time-correlated fluorescence lifetime imaging (tcFLIM) as a ratiometric method for the quantification of Ca2+ signals in TPM. The fluorescence lifetime of the Ca2+-indicator dye Oregon Green BAPTA-1 (OGB-1) can be recorded using the approximately 80 MHz excitation pulses utilized in TPM. It shows a Ca2+ dependence that can be explained by the Ca2+-affinity, spectral properties and purity of the dye. Pixel-wise lifetime recordings, controlled by a laser-scanning microscope, allowed quantitative Ca2+ imaging in full-frame and linescan mode. Although we focused on the high-affinity Ca2+ indicator OGB-1, our tcFLIM-based quantification is applicable to other Ca2+ dyes and to fluorescence indicators in general.

Single Molecule Spectroscopy as a Probe for Dye−Polymer Interactions

Experimental (Single Molecule Spectroscopy) and theoretical (quantum-chemical calculations and Monte Carlo and molecular dynamics simulations) techniques are combined to investigate the behavior and dynamics of a polymer-dye molecule system. It is shown that the dye molecule of interest (1,1'-dioctadecyl-3,3,3',3'-tetramethylindo-dicarbocyanine) adopts two classes of conformations, namely planar and nonplanar ones, when embedded in a poly(styrene) matrix. From an in-depth analysis of the fluorescence lifetime trajectories, the planar conformers can be further classified according to the way their alkyl side chains interact with the surrounding poly(styrene) chains.

Branching Out of Single‐Molecule Fluorescence Spectroscopy: Challenges for Chemistry and Influence on Biology

In the last decade emerging single-molecule fluorescence-spectroscopy tools have been developed and adapted to analyze individual molecules under various conditions. Single-molecule-sensitive optical techniques are now well established and help to increase our understanding of complex problems in different disciplines ranging from materials science to cell biology. Previous dreams, such as the monitoring of the motility and structural changes of single motor proteins in living cells or the detection of single-copy genes and the determination of their distance from polymerase molecules in transcription factories in the nucleus of a living cell, no longer constitute unsolvable problems. In this Review we demonstrate that single-molecule fluorescence spectroscopy has become an independent discipline capable of solving problems in molecular biology. We outline the challenges and future prospects for optical single-molecule techniques which can be used in combination with smart labeling strategies to yield quantitative three-dimensional information about the dynamic organization of living cells.

Electron Transfer at the Single-Molecule Level in a Triphenylamine-Perylene Imide Molecule

Photoinduced electron transfer (ET) processes in a donor-acceptor system based on triphenylamine and perylene imide have been studied at the single-molecule (SM) and ensemble levels. The system exists as two isomers, one of which undergoes forward and reverse ET in toluene with decay constants of 3.0 and 2.2x10(9) s(-1), respectively, resulting in the dual emission of quenched and delayed fluorescence while the other isomer remains ET-inactive. The fluorescence of both isomers is heavily quenched in the more polar solvent, diethyl ether, by ET. A broad range of ET dynamics is seen at the SM level in polystryene with the two isomers nonresolvable indicating that the local nanoenvironment of the SMs varies considerably throughout the polymer matrix. Both the electronic coupling and the driving force for ET are shown to influence the ET dynamics. Many fluorescence trajectories of SMs show long periods (tens of milliseconds to seconds) where the count rate is attenuated either partly (a "dim" state) or to the background level (an "off-time"). During these periods, the reduction or interruption of emission is attributed to cycles of rapid charge separation followed by charge recombination to the ground state reducing the fluorescence quantum yield of the SM.

Near-infrared time-resolved fluorescence lifetime determinations in poly(methylmethacrylate) microchip electrophoresis devices

High aspect-ratio microstructures were hot-embossed in polymer substrates with a molding tool fabricated using lithography/electroplating/forming (LIGA). The resulting devices were used for the electrophoretic separation of oligonucleotides labeled with near-infrared (near-IR) dyes. Near-IR time-resolved fluorescence was used as an identification method for the labeling dyes. The detection apparatus consisted of a pulsed laser diode operating at 680 nm, a single-photon avalanche diode, an integrated microscope, and a PC-board incorporating time-correlated single photon counting electronics. Investigation of the optical quality and amount of autofluorescence generated from different polymer substrates was carried out in the near-IR region for determining compatibility with time-resolved fluorescence. Our results revealed that of several poly(methylmethacrylate)(PMMA) substrates, brand Plexiglas offered minimal replication errors in the embossed features using appropriate embossing conditions with low background fluorescence contributions to the observed decay. Near-IR dye-labeled oligonucleotides were separated to determine the applicability of fluorescence lifetime discrimination between Cy5.5 (tauf = 930 ps) and IRD700 (tauf = 851 ps) labeling dyes during the microchip separation. These dyes were used to label T-fragments (thymine) of an M13mp18 ssDNA template. The DNA ladders were electrophoresed at 130 V/cm in a 4% linear polyacrylamide gel (LPA) gel matrix in a 9.5 cm long serpentine channel heated to 50 degrees C. The electropherogram revealed that the lifetimes could be accurately read well beyond 450 bases, although single-base pair resolution in the electropherogram was difficult to achieve due to potential solute-wall interactions in the polymer microdevice or the electroosmotic flow (EOF) properties of the device. The relative standard deviations secured for individual bands in the electropherogram were similar to those obtained using capillary gel electrophoresis, in spite of the lower load volume.

Optical Characteristics of Atomic Force Microscopy Tips for Single-Molecule Fluorescence Applications

Knowledge of the optical properties of atomic force microscopy (AFM) tips is relevant for the combination of optical and force spectroscopy. The luminescence properties of five commercial AFM tips were characterized using a combination of multiparameter fluorescence detection (MFD) and scanning confocal techniques. These include three Si3N4 tips, one silicon tip, and one high-density carbon (HDC) tip grown on top of a silicon tip. Time-decay histograms of the signal were analyzed to determine the strength of scatter, constant background, and fluorescence in the observed signal. Intensity and anisotropy images with optical resolution down to the diffraction limit were generated. The optical signal recorded from the apex of the Si3N4 tips ranged from 0.7 to 1.9 times the count rates from single Rhodamine 110 molecules under similar illumination conditions. The signal is predominantly composed of scatter and background (>85%), plus a small fluorescence component with lifetimes between 1 and 3 ns. The intensity of the recorded signal fell with increasing distance from the apex, and by 300 nm the signals fell below single-molecule levels for all Si3N4 cantilevers. Silicon cantilevers demonstrated very low count rates relative to single-molecule measurements under all conditions, and virtually no fluorescence. The high-density carbon tips also demonstrated low count rates, but the signal contained a short lifetime fluorescence component (0.7 ns). The intensity of the signals from each of the tips was geometry dependent, demonstrating the highest intensities at the edges and corners. Likewise, the anisotropy of all tip signals was observed to be geometry dependent, with the dependence varying on a case-by-case basis. The implications for using confocal illumination instead of total internal reflection are discussed.

Single-molecule spectroscopy selectively probes donor and acceptor chromophores in the phycobiliprotein allophycocyanin

We report on single-molecule fluorescence measurements performed on the phycobiliprotein allophycocyanin (APC). Our data support the presence of a unidirectional Förster-type energy transfer process involving spectrally different chromophores, alpha84 (donor) and beta84 (acceptor), as well as of energy hopping amongst beta84 chromophores. Single-molecule fluorescence spectra recorded from individual immobilized APC proteins indicate the presence of a red-emitting chromophore with emission peaking at 660 nm, which we connect with beta84, and a species with the emission peak blue shifted at 630 nm, which we attribute to alpha84. Polarization data from single APC trimers point to the presence of three consecutive red emitters, suggesting energy hopping amongst beta84 chromophores. Based on the single-molecule fluorescence spectra and assuming that emission at the ensemble level in solution comes mainly from the acceptor chromophore, we were able to resolve the individual absorption and emission spectra of the alpha84 and beta84 chromophores in APC.

Artefacts in the analysis of temporal response functions measured by photon counting

The least-squares (LS) method in fluorescence decay analyses and in time-domain analyses of the diffuse scattering light for data measured by the time-correlated single photon counting (TCSPC) technique is experimentally evaluated, and the artefact in LS analysis for data with different counting statistics is discussed. In single exponential decay analysis, the error of the decay parameter by the LS method is smaller than 10% of the expected true value when the average number of counts per bin (N/k) is more than 1, and the fitting region covers a period on the order of the decay time. In multi-exponential analysis, the decay parameters are sensitively dependent on the counting statistics. In contrast, the fitting by the maximum likelihood estimation (MLE), assuming Poissonian statistics, greatly reduces such dependence of parameters on the counting statistics. In another application, time-domain diffuse scattering measurements, the LS method is only accurate at N/k > 50 (10% error in the absorption coefficient). In particular, the absorption coefficient is largely dependent on the count. In both examples, the problem of stability in the fitting process by MLE still remains: the convergence of the fitting is critically dependent on the selection of initial guesses of the parameters in contrast to the convergence in the LS method. Thus, a hybrid method using the LS method for the determination of the initial guesses is a practical solution to this problem.

Statistics of single-molecule measurements: applications in flow-cytometry sizing of DNA fragments

BACKGROUND

The measurement of physical properties from single molecules has been demonstrated. However, the majority of single-molecule studies report values based on relatively large data sets (e.g., N > 50). While there are studies that report physical quantities based on small sample sets, there has not been a detailed statistical analysis relating sample size to the reliability of derived parameters.

METHODS

Monte Carlo simulations and multinomial analysis, dependent on quantifiable experimental parameters, were used to determine the minimum number of single-molecule measurements required to produce an accurate estimate of a population mean. Simulation results were applied to the fluorescence-based sizing of DNA fragments by ultrasensitive flow cytometry (FCM).

RESULTS

Our simulations show, for an analytical technique with a 10% CV, that the average of as few as five single-molecule measurements would provide a mean value within one SD of the population mean. Additional simulations determined the number of measurements required to obtain the desired number of replicates for each subpopulation within a mixture. Application of these results to flow cytometry data for lambda/HindIII and S. aureus Mu50/SmaI DNA digests produced accurate DNA fingerprints from as few as 98 single-molecule measurements.

CONCLUSIONS

A surprisingly small number of single-molecule measurements are required to obtain a mean measurement descriptive of a normally-distributed parent population.

Probing conformational dynamics in single donor-acceptor synthetic molecules by means of photoinduced reversible electron transfer

We use single-molecule fluorescence lifetimes to probe dynamics of photoinduced reversible electron transfer occurring between triphenylamine (donor) and perylenediimide (acceptor) in single molecules of a polyphenylenic rigid dendrimer embedded in polystyrene. Here, reversible electron transfer in individual donor-acceptor molecules results in delayed fluorescence that is emitted with a high photon count rate. By monitoring fluorescence decay times on a photon-by-photon basis, we find fluctuations in both forward and reverse electron transfer spanning a broad time range, from milliseconds to seconds. Fluctuations are induced by conformational changes in the dendrimer structure as well by polystyrene chain reorientation. The conformational changes are related to changes in the dihedral angle of adjacent phenyl rings located in the dendritic branch near the donor transferring the charge, a torsional motion that results in millisecond fluctuations in the "through-bond" donor-acceptor electronic coupling. Polymer chain reorientation leads to changes in the local polarity experienced by the donors and to changes in the solvation of the charge-separated state. As a result, switching between different donor moieties within the same single molecule becomes possible and induces fluctuations in decay time on a time scale of seconds.

Direct Determination of Kinetic Rates from Single-Molecule Photon Arrival Trajectories Using Hidden Markov Models

The measurement of fluorescence from single protein molecules has become an important new tool in the study of dynamic processes, allowing for the direct visualization of the motions experienced by individual proteins and macromolecular complexes. The data from such single-molecule experiments are in the form of photon trajectories, consisting of arrival times and wavelength information on individual photons. The analysis of photon trajectories can be difficult, particularly if the motions are occurring at rates comparable to the photon arrival rate or in the presence of noise. In this paper, we introduce the use of hidden Markov models (HMMs) for the analysis of photon trajectory data that operate using the photon data directly, without the need for ensemble averaging of the data as implied by correlation function analysis. Using a simple kinetic model, we examine the relationship between the uncertainty in the estimates of the motional rate and the photon detection rate. Remarkably, we obtain relative uncertainties in the rate constants of as little as 3% even when the interconversion rate is equal to the photon detection rate, and the uncertainty increases to only 10% when the interconversion rate is 10 times the photon detection rate. This suggests that useful information can be obtained for much faster kinetic regimes than have typically been studied. We also examine the impact of background photons on the determination of the rate and demonstrate that the HMM-based approach is robust, displaying small uncertainties for background photon arrival rates approaching that of the signal. These results not only are relevant in establishing the theoretical limits on precision, but are also useful in the context of experimental design. Finally, to demonstrate how the methodology can be extended to more complex kinetic models and how it can allow one to make use of the full power of statistics for purposes of model evaluation and selection, we consider a four-state kinetic model for protein conformational transitions previously studied by Schenter et al. (J. Phys. Chem. A1999, 103, 10477). We show how an HMM can be used as an alternative to higher-order correlation function analysis for the detection of "conformational memory" and apparent non-Markovian dynamics arising from such temporally inhomogeneous kinetic schemes.

Accurate Analysis of Fluorescence Decays from Single Molecules in Photon Counting Experiments

In time-resolved, single-photon counting experiments, the standard method of nonlinear least-squares curve fitting incorrectly estimates the fluorescence lifetimes. Even for single-exponential data, errors may be up to +/- 15%, and for more complex fits, may be even higher, although the fitted line appears to describe the data. The origin of this error is not a result of the Poisson distribution, as is often stated, but is entirely due to the weighting of the fit. An alternative weighting method involving a minor change in the fitting method eliminates this problem, enabling accurate fitting even in difficult cases, including the small data sets observed in single molecule experiments and with a precision similar to that of maximum likelihood methods.

Single particle confocal fluorescence spectroscopy in microchannels: dependence of burst width and burst area distributions on particle size and flow rate

This article presents a non-invasive, optical technique for measuring particulate flow within microfluidic channels. Confocal fluorescence detection is used to probe single fluorescently labeled microspheres (200-930 nm diameter) passing through a focused laser beam at a variety of flow rates (100 - 1000 nL/min). Simple statistical methods are subsequently used to investigate the resulting fluorescence bursts and generate single-particle burst width and burst area distributions. Analysis of such distributions demonstrates that the average burst width and burst area decrease as particle size increases. In addition, both burst width and burst area (for a given particle size) are observed to decrease as volumetric flow rate is increased. The dependence of such distributions on particle size is proposed as a potential route to sizing single particles and molecules in microfluidic systems.

Single-molecule fluorescence lifetime and anisotropy measurements of the red fluorescent protein, DsRed, in solution

Fluorescence lifetime and anisotropy measurements were made on the red fluorescent protein (DsRed) from tropical coral of the Discosoma genus, both at single-molecule and bulk concentrations. As expected from previous work, the fluorescence lifetime of DsRed in solution is dependent on laser power, decreasing from an average fluorescence lifetime in the beam of about 3.3 ns at low power (3.5 ns if one extrapolates to zero power) to about 2.1 ns at 28 kW/cm2. At the single-molecule level, exciting with 532 nm, 10 ps laser pulses at 80 MHz repetition rate, DsRed particles entering the laser beam initially have a lifetime of about 3.6 ns and convert to a form having a lifetime of about 3.0 ns with a quantum yield of photoconversion on the order of 10(-3) (calculated in terms of photons per DsRed tetramer). The particles then undergo additional photoconversion with a quantum yield of roughly 10(-5), generating a form with an average lifetime of 1.6 ns. These results may be explained by rapid photoconversion of one DsRed monomer in a tetramer, which acts as an energy transfer sink, resulting in a lower quantum yield for photoconversion of subsequent monomers. Multiparameter correlation and selective averaging can be used to identify DsRed in a mixture of fluorophores, in part exploiting the fact that fluorescent lifetime of DsRed changes as a function of excitation intensity.

Fluorescence intensity and lifetime distribution analysis: toward higher accuracy in fluorescence fluctuation spectroscopy

Fluorescence fluctuation methods such as fluorescence correlation spectroscopy and fluorescence intensity distribution analysis (FIDA) have proven to be versatile tools for studying molecular interactions with single molecule sensitivity. Another well-known fluorescence technique is the measurement of the fluorescence lifetime. Here, we introduce a method that combines the benefits of both FIDA and fluorescence lifetime analysis. It is based on fitting the two-dimensional histogram of the number of photons detected in counting time intervals of given width and the sum of excitation to detection delay times of these photons. Referred to as fluorescence intensity and lifetime distribution analysis (FILDA), the technique distinguishes fluorescence species on the basis of both their specific molecular brightness and the lifetime of the excited state and is also able to determine absolute fluorophore concentrations. The combined information yielded by FILDA results in significantly increased accuracy compared to that of FIDA or fluorescence lifetime analysis alone. In this paper, the theory of FILDA is elaborated and applied to both simulated and experimental data. The outstanding power of this technique in resolving different species is shown by quantifying the binding of calmodulin to a peptide ligand, thus indicating the potential for application of FILDA to similar problems in the life sciences.