Fluorescence correlation spectroscopy and Brownian rotational diffusion

A theroy relating rotational Brownian motion to the time autocorrelation function of the intensity of radiation from a fluorescent system composed of spherical rotors is presented. The calculation shows three relaxation times, two associated with the rotational diffusion, and the third associated with the natural decay of the fluorescence. The correlation function contains terms that relax independently of the fluorescence decay time, thus arbitrarily extending the time range over which rotational diffusion can be studied by fluorescence.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.     

Time-dependent rotational rates of excited fluorophores. A linkage between fluorescence depolarization and solvent relaxation

It is generally assumed that the rotational diffusion coefficients of fluorophores are independent of time subsequent to excitation, and that the rotational diffusion coefficients of the ground and the excited states are the same. We now describe a linkage between the extent of solvent relaxation and the rate of fluorescence depolarization. Specifically, if a fluorophore displays time-dependent solvent relaxation it may also show a time-dependent decrease in its rotational rate. A decreased rate of rotation could result from the increased interaction with polar solvent molecules which occurs as a result of solvent relaxation. The decays of anisotropy predicted from our model closely mimic those often observed for fluorophores which are bound to macromolecules. For example, the decays are more complex than a single exponential, and the time-resolved anisotropy can display a limiting value which does not decay to zero. The effect of solvent relaxation upon the rates of rotational diffusion is expected to be most dramatic for solvent-sensitive fluorophores in a viscous environment. These conditions are frequently encountered for fluorophore-macromolecule complexes. Consideration of the linkage between solvent relaxation and rotational diffusion leads to two unusual predictions. First even spherical fluorophores in an isotropic environment could display multi- or nonexponential decays of fluorescence anisotropy. Secondly, for the special case in which the fluorophore dipole moment decreases upon excitation, the theory predicts that the anisotropy decay rate may increase with time subsequent to pulsed excitation. The predictions of this theory are consistent with published data on the effects of red-edge excitation upon the apparent rotational rates of fluorophores in polar solvents.     

Rotational dynamics of the single tryptophan of porcine pancreatic phospholipase A2, its zymogen, and an enzyme/micelle complex. A steady-state and time-resolved anisotropy study

The rotational dynamics of the single tryptophan of porcine pancreatic phospholipase A2 and its zymogen (prophospholipase A2) have been studied by polarized fluorescence using steady-state and time-resolved single-photon counting techniques. The motion of Trp-3 in phospholipase A2 consists of a rapid subnanosecond wobble of the indole ring with an amplitude of about +/- 20 degrees accompanied by slower isotropic rotation of the entire protein. The rotational correlation times for overall particle rotational diffusion are consistent with conventional hydrodynamic theory. When phospholipase A2 binds to micelles of n-hexadecylphosphocholine, the amplitude of the fast ring rotation decreases. The whole particle rotational correlation time of the enzyme/micelle complex is smaller than the minimum value calculated from hydrodynamic theory. A similar result is obtained for the micelle itself by using the lipophilic probe transparinaric acid. These low values for the particle correlation times can be understood by postulating that an isotropic motion of the fluorophore in the small detergent particles contributes to the angular reorientation of the fluorophore. The internal reorientational motion of the tryptophan in the zymogen, prophospholipase A2, is of larger amplitude than that observed for the enzyme; specifically, the proenzyme exhibits a motion with a significant amplitude on the nanosecond time scale. This additional freedom of motion is attributed to segmental mobility of the N-terminal residues of prophospholipase A2. This demonstrates that this region of the protein is flexible in the zymogen but not in the processed enzyme. The implications of these findings for the mechanism of surface activation of phospholipase A2 are discussed by analogy with a trypsinogen-trypsin activation model.     

Fluorescence correlation spectroscopy in the nanosecond time range: rotational diffusion of bovine carbonic anhydrase B

A fluorescence correlation experiment for measurement of rotational diffusion in the nanosecond time scale is described. Using this method, the rotational diffusion coefficient of bovine carbonic anhydrase B labelled with tetramethylrhodamine isothiocyanate was estimated to be D _r=(1.14±0.15)×10⁷ s^-1 at 22°C. The experiment is based on a cw argon ion laser, a microfluorimeter with local solution flow inside the sample cell, and two photon detectors. The fluorescence intensity autocorrelation function in the nanosecond time range is computed with the help of a time-to-amplitude converter and a multichannel pulse-amplitude analyser.     

Autocorrelation function of finite-length data in fluorescence correlation spectroscopy

The experimental autocorrelation function of fluorescence correlation spectroscopy calculated from finite-length data is a biased estimator of the theoretical correlation function. This study presents a new theoretical framework that explicitly accounts for the data length to allow for unbiased analysis of experimental autocorrelation functions. To validate our theory, we applied it to experiments and simulations of diffusion and characterized the accuracy and precision of the resulting parameter estimates. Because measurements in living cells are often affected by instabilities of the fluorescence signal, autocorrelation functions are typically calculated on segmented data to improve their robustness. Our reformulated theory extends the range of usable segment times down to timescales approaching the diffusion time. This flexibility confers unique advantages for live-cell data that contain intensity variations and instabilities. We describe several applications of short segmentation to analyze data contaminated with unwanted fluctuations, drifts, or spikes in the intensity that are not suited for conventional fluorescence correlation analysis. These results demonstrate the potential of our theoretical framework to significantly expand the experimental systems accessible to fluorescence correlation spectroscopy.     

Lifetime distributions and anisotropy decays of indole fluorescence in cyclohexane/ethanol mixtures by frequency-domain fluorometry

We used frequency-domain fluorometry to measure intensity and anisotropy decay of indole fluorescence in cyclohexane/ethanol mixtures at 20 degrees C. In 100% cyclohexane or 100% ethanol the intensity decay of indole appears to be a single exponential with decay times of 7.66 and 4.10 ns, respectively. In cyclohexane containing a small percentage of ethanol (up to 10%), we observed increased heterogeneity in intensity decay, resulting in a 10-fold increase in chi 2R for the single-exponential fit, as compared with the double-exponential model. We obtained comparable or better fits using unimodal Lorentzian and Gaussian lifetime distributions (two floating parameters) than for the two-exponential model (three floating parameters). We believe that the distribution of decay times reflects a range of indole solvation states in the dominately nonpolar solutions. This result suggests that a variety of hydrogen-bonding configurations could be one origin of the distributions of decay times observed for tryptophan emission from proteins. We also measured rotational diffusion of indole in cyclohexane, ethanol and its mixtures at 20 degrees C. The picosecond correlation times required that the mean decay times be decreased by acrylamide quenching (in ethanol) or energy transfer (in cyclohexane). In ethanol we observed nearly isotropic rotation of indole; in cyclohexane we obtained two correlation times of 17 and 73 ps. The shorter correlation time in cyclohexane appears to be due to the slip boundary condition, which was found to be progressively eliminated by small percentages of ethanol. Hence, hydrogen-bonding interactions appear to have a substantial effect on the rotational dynamics of indole.     

Photoselection in polarized photolysis experiments on heme proteins.

Polarized photolysis experiments have been performed on the carbon monoxide complex of myoglobin to assess the effects of photoselection on the kinetics of ligand rebinding and to investigate the reorientational dynamics of the heme plane. The results are analyzed in terms of the optical theory developed in the preceding paper by Ansari and Szabo. Changes in optical density arising from rotational diffusion of the photoselected population produce large deviations from the true geminate ligand rebinding curves if measurements are made with only a single polarization. The apparent ligand rebinding curves are significantly distorted even at photolysis levels greater than 90%. These deviations are eliminated by obtaining isotropically-averaged optical densities from measurements using both parallel and perpendicular polarizations of the probe pulse. These experiments also yield the optical anisotropy, which gives a novel method for accurately determining the degree of photolysis, as well as important information on the reorientational dynamics of the heme plane. The correlation time for the overall rotational diffusion of the molecule is obtained from the decay of the anisotropy. The anisotropy prior to rotational diffusion is lower than that predicted for a rigidly attached, perfectly circular absorber, corresponding to an apparent order parameter of S = 0.95 +/- 0.02. Polarized absorption data on single crystals suggest that the decreased anisotropy results more from internal motions of the heme plane which take place on time scales shorter than the duration of the laser pulse (10 ns) than from out-of-plane polarized transitions.     

Rotational dynamics of surface probes in lipid vesicles

Translational and rotational diffusion of fluorescent molecules on the surface of small biological systems such as vesicles, proteins and micelles depolarize the fluorescence. A recent study has treated the case of the translational dynamics of surface probes (M.M.G. Krishna, R. Das, N. Periasamy and R. Nityananda, J. Chem. Phys., 112 (2000) 8502-8514) using Monte Carlo and theoretical methods. Here we extend the application of the methodologies to apply the case of rotational dynamics of surface probes. The corresponding fluorescence anisotropy decays were obtained using the Monte Carlo simulation methods for the two cases: surface probes undergoing rotational dynamics on a plane and on a sphere. The results were consistent with the theoretical equations which show that Monte Carlo methods can be used to simulate the surface diffusion problems. The anisotropy decay for the rotational diffusion of a molecule on a planar surface is single exponential and the residual anisotropy is zero. However, residual anisotropy is finite for the case of rotational diffusion on a sphere because of the spatial averaging of the anisotropy function. The rotational correlation time in both the cases is (4Drot)(-1) with Drot being the rotational diffusion coefficient. Rotational dynamics of a surface bound dye in a single giant liposome and in sonicated vesicles were studied and the results were explained according to the theoretical equations. A fast component of fluorescence depolarization was also observed for sonicated vesicles which was interpreted as wobbling-in-cylinder dynamics of the surface-bound dye.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering.

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation from the time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

Fluorescence correlation spectroscopy close to a fluctuating membrane

Compartmentalization of the cytoplasm by membranes should have a strong influence on the diffusion of macromolecules inside a cell, and we have studied how this could be reflected in fluorescence correlation spectroscopy (FCS) experiments. We derived the autocorrelation function measured by FCS for fluorescent particles diffusing close to a soft membrane, and show it to be the sum of two contributions: short timescale correlations come from the diffusion of the particles (differing from free diffusion because of the presence of an obstacle), whereas long timescale correlations arise from fluctuations of the membrane itself (which create intensity fluctuations by modulating the number of detected particles). In the case of thermal fluctuations this second type of correlation depends on the elasticity of the membrane. To illustrate this calculation, we report the results of FCS experiments carried out close to a vesicle membrane. The measured autocorrelation functions display very distinctly the two expected contributions, and allow both to recover the diffusion coefficient of the fluorophore and to characterize the membrane fluctuations in term of a bending rigidity. Our results show that FCS measurements inside cells can lead to erroneous values of the diffusion coefficient if the influence of membranes is not recognized.     

Environmental modulation of M13 coat protein tryptophan fluorescence dynamics

The effects of detergent [deoxycholate (DOC) and phospholipid [dimyristoylphosphatidylcholine (DMPC)] environments on the rotational dynamics of the single tryptophan residue 26 of bacteriophage M13 coat protein have been investigated by using time-resolved single photon counting measurements of the fluorescence intensity and anisotropy decay. The total fluorescence decay of tryptophan-26 is complex but rather similar in DOC as compared to DMPC when analyzed in terms of a lifetime distribution (exponential series method). This similarity, in conjunction with the almost identical steady-state fluorescence spectra, indicates only minor differences between the tryptophan environments in DOC and DMPC. The reorientational dynamics of tryptophan-26 are dominated by slow rotation of the entire protein in both detergent and phospholipid environments. The resolved anisotropy decay in DOC can be approximated by a simple hydrodynamic model of protein/detergent micelle rotational diffusion, although the data indicative slightly greater complexity in the rotational motion. The tryptophan fluorescence anisotropy is not sensitive to protein conformational changes in DOC detected by nuclear magnetic resonance on the basis of pH independence in the range 7.5-9.1. In DMPC bilayers, restricted tryptophan motion with a correlation time of approximately 2 ns is observed together with a second very slow reorientational component. Resolution of the time constant for this slow rotation is obscured by the tryptophan fluorescence time window being too short to clearly locate its anisotropic limit. The possible contribution made by axial rotational diffusion of the protein to this slow rotational process is discussed.(ABSTRACT TRUNCATED AT 250 WORDS)     

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.     

Fluorescence correlation spectroscopy as a tool to investigate single molecule probe dynamics in thin polymer films

Fluorescence correlation experiments were performed on rhodamine 6G in PDMS spin-coated films on glass surfaces. With polarised excitation, ensemble bleaching of the dye and single molecule intensity fluctuations were observed. From the statistics of single molecule intensity data taken at different positions in the film, correlation functions were calculated. Two modes of motion with exponential decay shapes and correlation times of tau(c) = 0.15 s and tau(c) = 0.7 s could be detected. Potential origins of intensity fluctuations are lateral diffusion, rotational diffusion or intramolecular fluctuations of dyes involving spectral diffusion or photoinduced processes. From the experimental results, lateral diffusion can be ruled out as a motional mode. Single molecule fluctuations are assigned to changes of the molecular configuration of the dyes, which are rigidly bound to the glass. To assess the environmental influence on such molecular motions, the bulk viscosity of the PDMS was varied over two orders of magnitude, leading to changes of tau(c) of the slow mode by a factor of four. This result proves the sensitivity of the single molecule fluctuations to the molecular scale dynamics of the surrounding polymer matrix and makes the correlation time a measure of the local environment of dye probes.     

Which fluorophore is brightest? A comparison of the staining obtained using fluorescein, tetramethylrhodamine, lissamine rhodamine, Texas red, and cyanine 3.18.

There are several red-emitting fluorophores available for immunofluorescence studies, including tetramethylrhodamine, lissamine rhodamine, Texas Red, and cyanine 3.18; however, it is unclear which of these is best. The present study compared the brightness of these fluorophores to that of fluorescein. Staining was attempted using a primary antibody raised against serotonin and a secondary antibody that was conjugated with either fluorescein or one of the red fluorophores. The intensity of staining was determined densitometrically. It was found that a conjugate of cyanine 3.18 provided significantly brighter staining that conjugates of any of the other fluorophores, including fluorescein. It is concluded that cyanine 3.18 should be useful for multicolor fluorescence experiments and that it may be the brightest fluorophore available for single-color fluorescence immunocytochemistry.     

The orientation of eosin-5-maleimide on human erythrocyte band 3 measured by fluorescence polarization microscopy.

The dominant motional mode for membrane proteins is uniaxial rotational diffusion about the membrane normal axis, and investigations of their rotational dynamics can yield insight into both the oligomeric state of the protein and its interactions with other proteins such as the cytoskeleton. However, results from the spectroscopic methods used to study these dynamics are dependent on the orientation of the probe relative to the axis of motion. We have employed polarized fluorescence confocal microscopy to measure the orientation of eosin-5-maleimide covalently reacted with Lys-430 of human erythrocyte band 3. Steady-state polarized fluorescence images showed distinct intensity patterns, which were fit to an orientation distribution of the eosin absorption and emission dipoles relative to the membrane normal axis. This orientation was found to be unchanged by trypsin treatment, which cleaves band 3 between the integral membrane domain and the cytoskeleton-attached domain. this result suggests that phosphorescence anisotropy changes observed after trypsin treatment are due to a rotational constraint change rather than a reorientation of eosin. By coupling time-resolved prompt fluorescence anisotropy with confocal microscopy, we calculated the expected amplitudes of the e-Dt and e-4Dt terms from the uniaxial rotational diffusion model and found that the e-4Dt term should dominate the anisotropy decay. Delayed fluorescence and phosphorescence anisotropy decays of control and trypsin-treated band 3 in ghosts, analyzed as multiple uniaxially rotating populations using the amplitudes predicted by confocal microscopy, were consistent with three motional species with uniaxial correlation times ranging from 7 microseconds to 1.4 ms.     

Which fluorophore is brightest? A comparison of the staining obtained using fluorescein,tetramethylrhodamine, lissamine rhodamine,texas red,and cyanine 3.18

Summary There are several red-emitting fluorophores available for immunofluorescence studies, including tetramethylrhodamine, lissamine rhodamine, Texas Red, and cyanine 3.18; however, it is unclear which of these is best. The present study compared the brightness of these fluorophores to that of fluorescein. Staining was attempted using a primary antibody raised against serotonin and a secondary antibody that was conjugated with either fluorescein or one of the red fluorophores. The intensity of staining was determined densitometrically. It was found that a conjugate of cyanine 3.18 provided significantly brighter staining that conjugates of any of the other fluorophores, including fluorescein. It is concluded that cyanine 3.18 should be useful for multicolor fluorescence experiments and that it may be the brightest fluorophore available for single-color fluorescence immunocytochemistry.     

Measurement of restricted rotational diffusion of fluorescent lipids in supported planar phospholipid monolayers using angle-dependent polarized fluorescence photobleaching recovery

A theory describing the shapes of polarized fluorescence photobleaching recovery (PFPR) curves for a population of fluorophores undergoing restricted rotational diffusion in two-dimensional systems such as planar membranes has been developed. In this model, restricted rotational diffusion of the fluorophores is described by using reflective boundary conditions, in which the fluorophores are assumed to diffuse freely but only within an angular space of width 2ω. The magnitude and apparent rate of the PFPR postbleach fluorescence curves are a function of both ω and the angle between the bleaching and observation beam polarizations ψ. It is shown that estimates of the degree of rotational restriction ω may be obtained from changes in the ψ-dependent postbleach fluorescence intensities. Using angle-dependent PFPR, slow rotational reorientations of the fluorescent lipid analogue 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine in distearoylphosphatidylcholine Langmuir–Blodgett monolayers deposited on octadecyltrichlorosilane-treated fused quartz were measured. As theoretically predicted for a rotationally restricted fluorophore population, both the initial F_ψ(0) and final F_ψ(∞) postbleach fluorescence intensities varied as a function of ψ, and no measurable change in the postbleach fluorescence intensities was observed for ψ = 45°. Using the theory for restricted rotational motion, the ψ-dependent variations of the final fluorescence intensities F_ψ(∞) obtained at two bleaching intensities gave an average apparent ω ≈? 52°. However, to adequately fit the F_ψ(0) data, inclusion of the theoretical effects of rapid (faster than the duration of the photobleaching pulse) fluorophore dynamics was also required. Best fits of the F_ψ(0) and F_ψ(∞) data were obtained when the fluorophores were assumed to rapidly wobble within a cone of semiangle δ ≈? 30°–50° while slowly rotating within an angular space defined by semiangle ω ≈? 35°–60°. Subsequent analysis of the time- and ψ-dependent changes in the postbleach fluorescence curves F_ψ(t) gave apparent diffusion coefficients ranging from D ≈? 10^?3 s^?1 to 4 × 10^?2 s^?1. © 1993 John Wiley & Sons, Inc.     

Polarized fluorescence photobleaching recovery for measuring rotational diffusion in solutions and membranes.

A variation of fluorescence photobleaching recovery (FPR) suitable for measuring the rate of rotational molecular diffusion in solution and cell membranes is presented in theory and experimental practice for epi-illumination microscopy. In this technique, a brief flash of polarized laser light creates an anisotropic distribution of unbleached fluorophores which relaxes by rotational diffusion, leading to a time-dependent postbleach fluorescence. Polarized FPR (PFPR) is applicable to any time scales from seconds to microseconds. However, at fast (microsecond) time scales, a partial recovery independent of molecular orientation tends to obscure rotational effects. The theory here presents a method for overcoming this reversible photobleaching, and includes explicit results for practical geometries, fast wobble of fluorophores, and arbitrary bleaching depth. This variation of a polarized luminescence "pump-and-probe" technique is compared with prior ones and with "pump-only" time-resolved luminescence anisotropy decay methods. The technique is experimentally verified on small latex beads with a variety of diameters, common fluorophore labels, and solvent viscosities. Preliminary measurements on a protein (acetylcholine receptor) in the membrane of nondeoxygenated cells in live culture (rat myotubes) show a difference in rotational diffusion between clustered and nonclustered receptors. In most experiments, signal averaging, high laser power, and automated sample translation must be employed to achieve adequate statistical accuracy.