Separation of the rotational contribution in fluorescence correlation experiments

Solution-phase sample-averaged single-particle spectroscopy of quantum emitters with femtosecond resolution

The development of many quantum optical technologies depends on the availability of single quantum emitters with near-perfect coherence. Systematic improvement is limited by a lack of understanding of the microscopic energy flow at the single-emitter level and ultrafast timescales. Here we utilize a combination of fluorescence correlation spectroscopy and ultrafast spectroscopy to capture the sample-averaged dynamics of defects with single-particle sensitivity. We employ this approach to study heterogeneous emitters in two-dimensional hexagonal boron nitride. From milliseconds to nanoseconds, the translational, shelving, rotational and antibunching features are disentangled in time, which quantifies the normalized two-photon emission quantum yield. Leveraging the femtosecond resolution of this technique, we visualize electron-phonon coupling and discover the acceleration of polaronic formation on multi-electron excitation. Corroborated with theory, this translates to the photon fidelity characterization of cascaded emission efficiency and decoherence time. Our work provides a framework for ultrafast spectroscopy in heterogeneous emitters, opening new avenues of extreme-scale characterization for quantum applications.

Rotational and translational diffusion of biomolecules in complex liquids and HeLa cells

Diffusive motion accompanies many physical and biological processes. The Stokes-Sutherland-Einstein relation for the translational diffusion coefficient, DT, agrees with experiments done in simple fluids but fails for complex fluids. Moreover, the interdependence between DT and rotational diffusion coefficient, DR, also deviates in complex fluids from the classical relation of DT/DR = 4r2/3 known in simple fluids. Makuch et al. Soft Matter, 2020, 16, 114-124 presented a generalization of the classical translational and rotational diffusion theory for complex fluids. In this work, we empirically verify this model based on simultaneous translational and rotational diffusion measurements. We use fluorescently stained cowpea chlorotic mottle virus (CCMV) particles as monodisperse probes and aqueous polyethylene glycol (PEG) solutions as a model complex fluid. The theory and experimental data obtained from fluorescence correlation spectroscopy (FCS) measurements agreed. Finally, we used the same model and analyzed the diffusion of Yo-Pro-1 stained large ribosomal subunits (LSU) in the cytoplasm and nucleus of living HeLa cells.

The Onset of Molecule-Spanning Dynamics in Heat Shock Protein Hsp90

Protein dynamics have been investigated on a wide range of time scales. Nano- and picosecond dynamics have been assigned to local fluctuations, while slower dynamics have been attributed to larger conformational changes. However, it is largely unknown how fast (local) fluctuations can lead to slow global (allosteric) changes. Here, fast molecule-spanning dynamics on the 100 to 200 ns time scale in the heat shock protein 90 (Hsp90) are shown. Global real-space movements are assigned to dynamic modes on this time scale, which is possible by a combination of single-molecule fluorescence, quasi-elastic neutron scattering and all-atom molecular dynamics (MD) simulations. The time scale of these dynamic modes depends on the conformational state of the Hsp90 dimer. In addition, the dynamic modes are affected to various degrees by Sba1, a co-chaperone of Hsp90, depending on the location within Hsp90, which is in very good agreement with MD simulations. Altogether, this data is best described by fast molecule-spanning dynamics, which precede larger conformational changes in Hsp90 and might be the molecular basis for allostery. This integrative approach provides comprehensive insights into molecule-spanning dynamics on the nanosecond time scale for a multi-domain protein.

Extreme dynamics in a biomolecular condensate

Proteins and nucleic acids can phase-separate in the cell to form concentrated biomolecular condensates1-4. The functions of condensates span many length scales: they modulate interactions and chemical reactions at the molecular scale5, organize biochemical processes at the mesoscale6 and compartmentalize cells4. Understanding the underlying mechanisms of these processes will require detailed knowledge of the rich dynamics across these scales7. The mesoscopic dynamics of biomolecular condensates have been extensively characterized8, but their behaviour at the molecular scale has remained more elusive. Here, as an example of biomolecular phase separation, we study complex coacervates of two highly and oppositely charged disordered human proteins9. Their dense phase is 1,000 times more concentrated than the dilute phase, and the resulting percolated interaction network10 leads to a bulk viscosity 300 times greater than that of water. However, single-molecule spectroscopy optimized for measurements within individual droplets reveals that at the molecular scale, the disordered proteins remain exceedingly dynamic, with their chain configurations interconverting on submicrosecond timescales. Massive all-atom molecular dynamics simulations reproduce the experimental observations and explain this apparent discrepancy: the underlying interactions between individual charged side chains are short-lived and exchange on a pico- to nanosecond timescale. Our results indicate that, despite the high macroscopic viscosity of phase-separated systems, local biomolecular rearrangements required for efficient reactions at the molecular scale can remain rapid.

Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry

Motions in biomolecules are critical for biochemical reactions. In cells, many biochemical reactions are executed inside of biomolecular condensates formed by ultradynamic intrinsically disordered proteins. A deep understanding of the conformational dynamics of intrinsically disordered proteins in biomolecular condensates is therefore of utmost importance but is complicated by diverse obstacles. Here we review emerging data on the motions of intrinsically disordered proteins inside of liquidlike condensates. We discuss how liquid–liquid phase separation modulates internal motions across a wide range of time and length scales. We further highlight the importance of intermolecular interactions that not only drive liquid–liquid phase separation but appear as key determinants for changes in biomolecular motions and the aging of condensates in human diseases. The review provides a framework for future studies to reveal the conformational dynamics of intrinsically disordered proteins in the regulation of biomolecular condensate chemistry.

Advanced fluorescence correlation spectroscopy for studying biomolecular conformation

We present the recent developments and advances in fluorescence correlation spectroscopy (FCS) and their application to the investigation of biomolecular conformations. In particular, we present and discuss three techniques: multichannel nanosecond FCS, photo-induced electron transfer FCS, and fluorescence lifetime correlation spectroscopy. We briefly describe each method and discuss recent applications to diverse biophysical studies of biomolecular conformation.

Quantitative evaluation of macromolecular crowding environment based on translational and rotational diffusion using polarization dependent fluorescence correlation spectroscopy

Macromolecular crowding (MMC) in cells is a hot topic in biology; therefore, well-characterized measurement standards for the evaluation of the nano-environment in MMC solutions are necessary. We propose to use polarization-dependent fluorescence correlation spectroscopy (Pol-FCS) for evaluation of macromolecular crowding in solutions. Pol-FCS can simultaneously measure the relaxation times of rotational and translational diffusion of fluorescent molecules at the same position, even in living cells with low damage. In this report, the differences in the nano-environment among solutions of small molecules, gels, and MMC solutions were evaluated by comparing their rotational and translational diffusion using Pol-FCS. Moreover, this method could distinguish the phase shift in the polyethylene glycol solution. Finally, we separately evaluated the nano-environment in the cytosol and nucleus of living cells in different cell lines and cell cycles. We expect this evaluation method to be useful in characterizing the nano-environment in MMC studies. In addition, the proposed method may be useful for other nano-environments such as liquid-liquid phase separation.

Dye Encapsulation in Fluorescent Core-Shell Silica Nanoparticles as Probed by Fluorescence Correlation Spectroscopy

Synthetic advances in the formation of ultrasmall (<10 nm) fluorescent poly(ethylene glycol)-coated (PEGylated) core-shell silica nanoparticles (SNPs), enabling improved particle size and surface chemical property control have led to successful clinical translation of SNPs as diagnostic probes in oncology. Despite the success of such probes, details of the dye incorporation and resulting silica architecture are still poorly understood. Here, we employ afterpulse-corrected fluorescence correlation spectroscopy (FCS) to monitor fast fluorescence fluctuations (lag times <10^-5 s) of the negatively charged cyanine dye Cy5 as a probe to study such details for dye encapsulation in 5 nm silica cores of PEGylated core-shell SNPs (C dots). Upon deposition of additional silica shells over the silica core we find that the amplitude of photo-induced cis-trans isomerization decreases, suggesting that the Cy5 dyes are located near or on the surface of the original SNP cores. In combination with time correlated fluorescence decay measurements we deduce radiative and non-radiative rates of the Cy5 dye in these particles. Results demonstrate that FCS is a well-suited tool to investigate aspects of the photophysics of fluorescent nanoparticles, and that conformational changes of cyanine dyes like Cy5 are excellent indicators for the local dye environment within ultrasmall SNPs.

Measuring the Hydrodynamic Size of Nanoparticles Using Fluctuation Correlation Spectroscopy

Fluctuation correlation spectroscopy (FCS) is a well-established analytical technique traditionally used to monitor molecular diffusion in dilute solutions, the dynamics of chemical reactions, and molecular processes inside living cells. In this review, we present the recent use of FCS for measuring the size of colloidal nanoparticles in solution. We review the theoretical basis and experimental implementation of this technique and its advantages and limitations. In particular, we show examples of the use of FCS to measure the size of gold nanoparticles, monitor the rotational dynamics of gold nanorods, and investigate the formation of protein coronas on nanoparticles.

Quantitative FRET studies and integrative modeling unravel the structure and dynamics of biomolecular systems

Förster Resonance Energy Transfer (FRET) combined with single-molecule spectroscopy probes macromolecular structure and dynamics and identifies coexisting conformational states. We review recent methodological developments in integrative structural modeling by satisfying spatial restraints on networks of FRET pairs (hybrid-FRET). We discuss procedures to incorporate prior structural knowledge and to obtain optimal distance networks. Finally, a workflow for hybrid-FRET is presented that automates integrative structural modeling and experiment planning to put hybrid-FRET on rails. To test this workflow, we simulate realistic single-molecule experiments and resolve three protein conformers, exchanging at 30μs and 10ms, with accuracies of 1-3Å RMSD versus the target structure. Incorporation of data from other spectroscopies and imaging is also discussed.

Rotational diffusion measurements using polarization-dependent fluorescence correlation spectroscopy based on superconducting nanowire single-photon detector

Conventional polarization-dependent fluorescence correlation spectroscopy (pol-FCS) requires two sets of photon detectors to eliminate after-pulse noises (dual-channel pol-FCS; DC-pol-FCS) in the sub-microsecond range. In this study, we successfully realized pol-FCS using a visible-wavelength superconductive nanowire single-photon detector (single-channel pol-FCS; SC-pol-FCS). The detector used is free of after-pulse noises and thus eliminates the need for dual channels in pol-FCS. Further, the optics in the SC-pol-FCS system are easier to adjust than those in the conventional system. Consequently, we obtained higher signal-to-noise ratios compared with conventional DC-pol-FCS systems. Thus, SC-pol-FCS is a potentially useful system for obtaining pol-FCS measurements, and can facilitate improved rotational diffusion studies.

Excited-state annihilation reduces power dependence of single-molecule FRET experiments

Singlet–singlet annihilation between FRET dyes is evident in nanosecond fluorescence cross-correlation measurements.

Analysis of quantum rod diffusion by polarized fluorescence correlation spectroscopy

To measure the polarization dependence of fluorescent probes, a confocal-microscope-based polarized fluorescence correlation spectroscopy system was developed, and the polarization dependence on the rotational diffusion of well-defined quantum rods (Qrods) was investigated and characterized. The rotational diffusion region of the Qrods was observed over a time range of less than 10(-5) s in a water solution, and the rotational diffusion parameters were extracted using a rotational diffusion model in which the viscosity of the solution media was varied. Our work demonstrated that polarized fluorescence correlation spectroscopy (FCS) is useful for investigating both the rotational and translational diffusion of fluorescent probes.

Fluorescence correlation spectroscopy in biology, chemistry, and medicine

This review describes the method of fluorescence correlation spectroscopy (FCS) and its applications. FCS is used for investigating processes associated with changes in the mobility of molecules and complexes and allows researchers to study aggregation of particles, binding of fluorescent molecules with supramolecular complexes, lipid vesicles, etc. The size of objects under study varies from a few angstroms for dye molecules to hundreds of nanometers for nanoparticles. The described applications of FCS comprise various fields from simple chemical systems of solution/micelle to sophisticated regulations on the level of living cells. Both the methodical bases and the theoretical principles of FCS are simple and available. The present review is concentrated preferentially on FCS applications for studies on artificial and natural membranes. At present, in contrast to the related approach of dynamic light scattering, FCS is poorly known in Russia, although it is widely employed in laboratories of other countries. The goal of this review is to promote the development of FCS in Russia so that this technique could occupy the position it deserves in modern Russian science.

FRET and FCS--friends or foes?

Fluorescence correlation spectroscopy (FCS) and Förster resonance energy transfer (FRET) are both scientific concepts that are frequently discussed in the context of single-molecule fluorescence techniques. In contrast to FCS, FRET is strictly not a technique but a photophysical phenomenon, which can be employed in combination with any method that probes fluorescence intensity or lifetime. Thus, the combination of FCS with FRET is possible and—although these concepts are quite often treated as alternative approaches, particularly for the analysis of biological systems—also quite attractive. However, under certain circumstances, for example, for applications of fluorescence cross-correlation spectroscopy, FRET effects can cause significant complications for quantitative data analysis, and careful calibration has to be carried out to avoid FRET-induced artifacts. This can be most elegantly done if alternating excitation schemes such as PIE (pulsed interleaved excitation) are employed. In this minireview, we discuss the potential and the caveats of FCS combined with FRET and give a short record on successful and promising applications.

Scalable time-correlated photon counting system with multiple independent input channels

Time-correlated single photon counting continues to gain importance in a wide range of applications. Most prominently, it is used for time-resolved fluorescence measurements with sensitivity down to the single molecule level. While the primary goal of the method used to be the determination of fluorescence lifetimes upon optical excitation by short light pulses, recent modifications and refinements of instrumentation and methodology allow for the recovery of much more information from the detected photons, and enable entirely new applications. This is achieved most successfully by continuously recording individually detected photons with their arrival time and detection channel information (time tagging), thus avoiding premature data reduction and concomitant loss of information. An important property of the instrumentation used is the number of detection channels and the way they interrelate. Here we present a new instrument architecture that allows scalability in terms of the number of input channels while all channels are synchronized to picoseconds of relative timing and yet operate independent of each other. This is achieved by means of a modular design with independent crystal-locked time digitizers and a central processing unit for sorting and processing of the timing data. The modules communicate through high speed serial links supporting the full throughput rate of the time digitizers. Event processing is implemented in programmable logic, permitting classical histogramming, as well as time tagging of individual photons and their temporally ordered streaming to the host computer. Based on the time-ordered event data, any algorithms and methods for the analysis of fluorescence dynamics can be implemented not only in postprocessing but also in real time. Results from recently emerging single molecule applications are presented to demonstrate the capabilities of the instrument.

Structural changes of yellow Cameleon domains observed by quantitative FRET analysis and polarized fluorescence correlation spectroscopy

Förster resonance energy transfer (FRET) is a widely used method for monitoring interactions between or within biological macromolecules conjugated with suitable donor-acceptor pairs. Donor fluorescence lifetimes in absence and presence of acceptor molecules are often measured for the observation of FRET. However, these lifetimes may originate from interacting and noninteracting molecules, which hampers quantitative interpretation of FRET data. We describe a methodology for the detection of FRET that monitors the rise time of acceptor fluorescence on donor excitation thereby detecting only those molecules undergoing FRET. The large advantage of this method, as compared to donor fluorescence quenching method used more commonly, is that the transfer rate of FRET can be determined accurately even in cases where the FRET efficiencies approach 100% yielding highly quenched donor fluorescence. Subsequently, the relative orientation between donor and acceptor chromophores is obtained from time-dependent fluorescence anisotropy measurements carried out under identical conditions of donor excitation and acceptor detection. The FRET based calcium sensor Yellow Cameleon 3.60 (YC3.60) was used because it changes its conformation on calcium binding, thereby increasing the FRET efficiency. After mapping distances and orientation angles between the FRET moieties in YC3.60, cartoon models of this FRET sensor with and without calcium could be created. Independent support for these representations came from experiments where the hydrodynamic properties of YC3.60 under ensemble and single-molecule conditions on selective excitation of the acceptor were determined. From rotational diffusion times as found by fluorescence correlation spectroscopy and consistently by fluorescence anisotropy decay analysis it could be concluded that the open structure (without calcium) is flexible as opposed to the rather rigid closed conformation. The combination of two independent methods gives consistent results and presents a rapid and specific methodology to analyze structural and dynamical changes in a protein on ligand binding.

Review fluorescence correlation spectroscopy for probing the kinetics and mechanisms of DNA hairpin formation

This article reviews the application of fluorescence correlation spectroscopy (FCS) and related techniques to the study of nucleic acid hairpin conformational fluctuations in free aqueous solutions. Complimentary results obtained using laser-induced temperature jump spectroscopy, single-molecule fluorescence spectroscopy, optical trapping, and biophysical theory are also discussed. The studies cited reveal that DNA and RNA hairpin folding occurs by way of a complicated reaction mechanism involving long- and short-lived reaction intermediates. Reactions occurring on the subnanoseconds to seconds time scale have been observed, pointing out the need for experimental techniques capable of probing a broad range of reaction times in the study of such complex, multistate reactions.

Recent Advances in Fluorescence Cross-correlation Spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS) is a method that measures the temporal fluorescence fluctuations coming from two differently labeled molecules diffusing through a small sample volume. Cross-correlation analysis of the fluorescence signals from separate detection channels extracts information of the dynamics of the dual-labeled molecules. FCCS has become an essential tool for the characterization of diffusion coefficients, binding constants, kinetic rates of binding, and determining molecular interactions in solutions and cells. By cross-correlating between two focal spots, flow properties could also be measured. Recent developments in FCCS have been targeted at using different experimental schemes to improve on the sensitivity and address their limitations such as cross-talk and alignment issues. This review presents an overview of the different excitation and detection methodologies used in FCCS and their biological applications. This is followed by a description of the fluorescent probes currently available for the different methods. This will introduce biological readers to FCCS and its related techniques and provide a starting point to selecting which experimental scheme is suitable for their type of biological study.

Multifunctional fluorescence correlation microscope for intracellular and microfluidic measurements

A modified fluorescence correlation microscope (FCM) was built on a commercial confocal laser scanning microscope (CLSM) by adding two sensitive detectors to perform fluorescence correlation spectroscopy (FCS). A single pinhole for both imaging and spectroscopy and a simple slider switch between the two modes thus facilitate the accurate positioning of the FCS observation volume after the confocal image acquisition. Due to the use of a single pinhole for CLSM and FCS the identity of imaged and spectroscopically observed positions is guaranteed. The presented FCM system has the capability to position the FCS observation volume at any point within the inner 30% of the field of view without loss in performance and in the inner 60% of the field of view with changes of FCS parameters of less than 10%. A single pinhole scheme for spatial fluorescence cross correlation spectroscopy performed on the FCM system is proposed to determine microfluidic flow angles. To show the applicability and versatility of the system, we measured the translational diffusion coefficients on the upper and lower membranes of Chinese hamster ovary cells. Two-photon excitation FCS was also realized by coupling a pulsed Ti: sapphire laser into the microscope and used for flow direction characterization in microchannels.

Circumvention of fluorophore photobleaching in fluorescence fluctuation experiments: a beam scanning approach

Photobleaching is a fluorophore-damaging process that commonly afflicts single-molecule fluorescence studies. It becomes an especially severe problem in fluorescence fluctuation experiments when studying slowly diffusing particles. One way to circumvent this problem is to use beam scanning to decrease the residence time of the fluorophores in the excitation volume. We report a systematic study of the effects of circular beam scanning on the photobleaching of fluorescent particles as observed in single-photon excitation fluorescence fluctuation experiments. We start by deriving a simple expression relating the average detected fluorescence to the photobleaching cross section of the fluorophores. We then perform numerical calculations of the spatial distribution of fluorescent particles in order to understand under which conditions beam scanning can prevent the formation of a photobleaching hole. To support these predictions, we show experimental results obtained for large unilamellar vesicles containing a small amount of the fluorescent lipophilic tracer DiD. We establish the required scanning radius and frequency range in order to obtain sufficient reduction of the photobleaching effect for that system. From the detected increase in fluorescence upon increase in scanning speed, we estimate the photobleaching cross section of DiD.

Rotational and translational diffusion of peptide-coated CdSe/CdS/ZnS nanorods studied by fluorescence correlation spectroscopy

CdSe/CdS/ZnS nanorods (NRs) of three aspect ratios were coated with phytochelatin-related peptides and studied using fluorescence correlation spectroscopy (FCS). Theoretical predictions of the NRs' rotational diffusion contribution to the correlation curves were experimentally confirmed. We monitored rotational and translational diffusion of NRs and extracted hydrodynamic radii from the extracted diffusion constants. Translational and rotational diffusion constants (D(trans) and D(rot)) for NRs were in good agreement with Tirado and Garcia de la Torre's as well as with Broersma's theories when accounting for the ligand dimensions. NRs fall in the size range where rotational diffusion can be monitored with higher sensitivity than translational diffusion due to a steeper length dependence, D(rot) approximately L(-)(3) versus D(trans) approximately L(-)(1). By titrating peptide-coated NRs with bovine serum albumin, we monitored (nonspecific) binding through rotational diffusion and showed that D(rot) is an advantageous observable for monitoring binding. Monitoring rotational diffusion of bioconjugated NRs using FCS might prove to be useful for observing binding and conformational dynamics in biological systems.

Pulsed interleaved excitation

In this article, we demonstrate the new method of pulsed interleaved excitation (PIE), which can be used to extend the capabilities of multiple-color fluorescence imaging, fluorescence cross-correlation spectroscopy (FCCS), and single-pair fluorescence resonance energy transfer (spFRET) measurements. In PIE, multiple excitation sources are interleaved such that the fluorescence emission generated from one pulse is complete before the next excitation pulse arrives. Hence, the excitation source for each detected photon is known. Typical repetition rates used for PIE are between approximately 1 and 50 MHz. PIE has many applications in various fluorescence methods. Using PIE, dual-color measurements can be performed with a single detector. In fluorescence imaging with multicolor detection, spectral cross talk can be removed, improving the contrast of the image. Using PIE with FCCS, we can eliminate spectral cross talk, making the method sensitive to weaker interactions. FCCS measurements with complexes that undergo FRET can be analyzed quantitatively. Under specific conditions, the FRET efficiency can be determined directly from the amplitude of the measured correlation functions without any calibration factors. We also show the application of PIE to spFRET measurements, where complexes that have low FRET efficiency can be distinguished from those that do not have an active acceptor.

Polarized fluorescence correlation spectroscopy of DNA-DAPI complexes

We discuss the use of fluorescence correlation spectroscopy for the measurement of relatively slow rotations of large macromolecules in solution or attached to other macromolecular structures. We present simulations and experimental results to illustrate the range of rotational correlation times and diffusion times that the technique can analyze. In particular, we examine various methods to analyze the polarization fluctuation data. We have found that by first constructing the polarization function and then calculating the autocorrelation function, we can obtain the rotational motion of the molecule with very little interference from the lateral diffusion of the macromolecule, as long as the rotational diffusion is significantly faster than the lateral diffusion. Surprisingly, for common fluorophores the autocorrelation of the polarization function is relatively unaffected by the photon statistics. In our instrument, two-photon excitation is used to define a small volume of illumination where a few molecules are present at any instant of time. The measurements of long DNA molecules labeled with the fluorescent probe DAPI show local rotational motions of the polymers in addition to translation motions of the entire polymer. For smaller molecules such as EGFP, the viscosity of the solution must be increased to bring the relaxation due to rotational motion into the measurable range. Overall, our results show that polarized fluorescence correlation spectroscopy can be used to detect fast and slow rotational motion in the time scale from microsecond to second, a range that cannot be easily reached by conventional fluorescence anisotropy decay methods.

Folding and Unfolding Kinetics of DNA Hairpins in Flowing Solution by Multiparameter Fluorescence Correlation Spectroscopy

Dynamic equilibrium between the folded and unfolded conformations of single stranded DNA hairpin molecules containing polythymine hairpin loops was investigated using simultaneous two-beam fluorescence cross-correlation spectroscopy and single beam autocorrelation spectroscopy. The hairpins were end-labeled with a fluorescent dye and a quencher, such that folding and unfolding of the DNA hairpin primary structure caused the dye fluorescence to fluctuate on the same characteristic time scale as the folding and unfolding reaction. These fluctuations were observed as the molecules flowed sequentially between two spatially offset, microscopic detection volumes. Cross-correlation analysis of fluorescence from the two detection volumes revealed the translational diffusion and flow properties of the hairpins, as well as the average molecular occupancy of the two volumes. Autocorrelation analysis of the fluorescence from the individual detection volumes revealed the kinetics of hairpin folding and unfolding, with the parameters relating to diffusion, flow, and molecular occupancy constrained to the values determined from the cross-correlation analysis. This allowed unambiguous characterization of the folding and unfolding kinetics, without the need to determine the hydrodynamic properties by analyzing a separate control sample. The analysis revealed nonexponential relaxation kinetics and DNA size-dependent folding times characteristic of dynamic heterogeneity in the DNA hairpin-forming mechanism.

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.

Dynamics of ANS binding to tuna apomyoglobin measured with fluorescence correlation spectroscopy

The dynamics of the binding reaction of ANS to native and partly folded (molten globule) tuna and horse apomyoglobins has been investigated by fluorescence correlation spectroscopy and frequency domain fluorometry. The reaction rate has been measured as a function of apomyoglobin and ANS concentrations, pH, and temperature. Examination of the autocorrelation functions shows that the reaction rate is fast enough to be observed in tuna apomyoglobin, whereas the reaction rate in horse apomyoglobin is on the same time scale as diffusion through the volume or longer. Specifically, for tuna apomyoglobin at pH 7 and room temperature the on rate is 2200 microM(-1) s(-1) and the off rate is 5900 s(-1), in comparison with k(on) = 640 microM(-1) s(-1) and k(off) = 560 s(-1) for horse myoglobin as measured previously. The independence of the reaction rate from the ANS concentration indicates that the reaction rate is dominated by the off rate. The temperature dependence of the on-rate shows that this rate is diffusion limited. The temperature dependence of the off rates analyzed by Arrhenius and Ferry models indicates that the off rate depends on the dynamics of the protein. The differences between horse and tuna apomyoglobins in the ANS binding rate can be explained in terms of the three-dimensional apoprotein structures obtained by energy minimization after heme removal starting from crystallographic coordinates. The comparison of the calculated apomyoglobin surfaces shows a 15% smaller cavity for tuna apomyoglobin. Furthermore, a negative charge (D44) is present in the heme cavity of tuna apomyoglobin that could decrease the strength of ANS binding. At pH 5 the fluorescence lifetime distribution of ANS-apomyoglobin is bimodal, suggesting the presence of an additional binding site in the protein. The binding rates determined by FCS under these conditions show that the protein is either in the open configuration or is more flexible, making it much easier to bind. At pH 3, the protein is in a partially denatured state with multiple potential binding sites for ANS molecule, and the interpretation of the autocorrelation function is not possible by simple models. This conclusion is consistent with the broad distribution of ANS fluorescence lifetimes observed in frequency domain measurements.

Sensitivity enhancement in fluorescence correlation spectroscopy of multiple species using time-gated detection

Fluorescence correlation spectroscopy (FCS) is a powerful technique to measure chemical reaction rates and diffusion coefficients of molecules in thermal equilibrium. The capabilities of FCS can be enhanced by measuring the energy, polarization, or delay time between absorption and emission of the collected fluorescence photons in addition to their arrival times. This information can be used to change the relative intensities of multiple fluorescent species in FCS measurements and, thus, the amplitude of the intensity autocorrelation function. Here we demonstrate this strategy using lifetime gating in FCS experiments. Using pulsed laser excitation and laser-synchronized gating in the detection channel, we suppress photons emitted within a certain time interval after excitation. Three applications of the gating technique are presented: suppression of background fluorescence, simplification of FCS reaction studies, and investigation of lifetime heterogeneity of fluorescently labeled biomolecules. The usefulness of this technique for measuring forward and backward rates of protein fluctuations in equilibrium and for distinguishing between static and dynamic heterogeneity makes it a promising tool in the investigation of chemical reactions and conformational fluctuations in biomolecules.

Two-dimensional fluorescence intensity distribution analysis: theory and applications

A method of sample analysis is presented which is based on fitting a joint distribution of photon count numbers. In experiments, fluorescence from a microscopic volume containing a fluctuating number of molecules is monitored by two detectors, using a confocal microscope. The two detectors may have different polarizational or spectral responses. Concentrations of fluorescent species together with two specific brightness values per species are determined. The two-dimensional fluorescence intensity distribution analysis (2D-FIDA), if used with a polarization cube, is a tool that is able to distinguish fluorescent species with different specific polarization ratios. As an example of polarization studies by 2D-FIDA, binding of 5'-(6-carboxytetramethylrhodamine) (TAMRA)-labeled theophylline to an anti-theophylline antibody has been studied. Alternatively, if two-color equipment is used, 2D-FIDA can determine concentrations and specific brightness values of fluorescent species corresponding to individual labels alone and their complex. As an example of two-color 2D-FIDA, binding of TAMRA-labeled somatostatin-14 to the human type-2 high-affinity somatostatin receptors present in stained vesicles has been studied. The presented method is unusually accurate among fluorescence fluctuation methods. It is well suited for monitoring a variety of molecular interactions, including receptors and ligands or antibodies and antigens.

Fluorescence fluctuation spectroscopy

The analysis of the intensity fluctuation of a fluorescence signal from a relatively small volume and from a few molecules contains information about the distribution of different species present in the solution and about kinetic parameters of the system. The same information is generally averaged out when the fluorescence experiment is performed in a much larger volume, typically a cuvette experiment. The fundamental reason for this difference is that the fluctuations of the fluorescence signal from a few molecules directly reflect the molecular nature of the matter. Only recently, with the advent of confocal microscopy and two-photon excitation, it has become practical to achieve small excitation volumes in which only a few fluorescent molecules are present. We introduce the concept of fluctuation spectroscopy and highlight some of the technical aspects. We discuss different analysis methods used in fluctuation spectroscopy and evaluate their use for studying protein-protein interactions.

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.

Resolution of fluorescence correlation measurements

The resolution limit of fluorescence correlation spectroscopy for two-component solutions is investigated theoretically and experimentally. The autocorrelation function for two different particles in solution were computed, statistical noise was added, and the resulting curve was fitted with a least squares fit. These simulations show that the ability to distinguish between two different molecular species in solution depends strongly on the number of photons detected from each particle, their difference in size, and the concentration of each component in solution. To distinguish two components, their diffusion times must differ by at least a factor of 1.6 for comparable quantum yields and a high fluorescence signal. Experiments were conducted with Rhodamine 6G and Rhodamine-labeled bovine serum albumin. The experimental results support the simulations. In addition, they show that even with a high fluorescence signal but significantly different quantum yields, the diffusion times must differ by a factor much bigger than 1.6 to distinguish the two components. Depending on the quantum yields and the difference in size, there exists a concentration threshold for the less abundant component below which it is not possible to determine with statistical means alone that two particles are in solution.