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.     

Lateral mobility in membranes as detected by fluorescence recovery after photobleaching.

The evaluation of lateral diffusion coefficients of membrane components by the technique of fluorescence recovery after photobleaching (FRAP) is often complicated by uncertainties in the values of the intensities F(O), immediately after bleaching, and F(infinity), after full recovery. These uncertainties arise from instrumental settling time immediately after bleaching and from cell, tissue, microscope, or laser beam movements at the long times required to measure F(infinity). We have developed a method for precise analysis of FRAP data that minimizes these problems. The method is based on the observation that a plot of the reciprocal function R(tau) = F(infinity)/[F(infinity)-F(tau)] is linear over a large time range when (a) the laser beam has a Gaussian profile, (b) recovery involves a single diffusion coefficient, and (c) there is no membrane flow. Moreover, the ratio of intercept to slope of the linear plot is equal to tau 1/2, the time required for the bleached fluorescence to rise to 50% of the full recovery value, F(infinity). The lateral diffusion coefficient D is related to tau 1/2 by tau 1/2 = beta w2/4D where beta is a defined parameter and w is the effective radius of the focused laser beam. These results are shown to indicate that the recovery of fluorescence F(tau) can be represented over a large range of percent bleach, and recovery time tau by the relatively simple expression F(tau) = [ F(o) + F(infinity) (tau/tau 1/2)]/[1 + tau/tau 1/2)]. FRAP data can therefore be easily evaluated by a nonlinear regression analysis with this equation or by a linear fit to the reciprocal function R(tau). It is shown that any error in F(infinity) can be easily detected in a plot of R(tau) vs. tau which deviates significantly from a straight line when F(infinity) is in error by as little as 5%. A scheme for evaluating D by linear analysis is presented. It is also shown that the linear reciprocal plot provides a simple method for detecting flow or multiple diffusion coefficients and for establishing conditions (data precision, differences in multiple diffusion coefficients, magnitude of flow rate compared to lateral diffusion) under which flow or multiple diffusion coefficients can be detected. These aspects are discussed in some detail.     

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.     

Probing the dynamics of photosynthetic membranes with fluorescence recovery after photobleaching

In the past few years, there has been remarkable progress in knowledge of the structures and organization of the protein complexes of photosynthetic membranes. However, static structures do not tell the whole story. Photosynthetic membranes, like other biological membranes, are dynamic systems. Recent technological advances are making it increasingly easy to probe the dynamics of photosynthetic membranes using fluorescence recovery after photobleaching. Here we explain the potential and the limitations of the technique.     

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.     

Determining diffusion coefficients in inhomogeneous tissues using fluorescence recovery after photobleaching

Diffusion plays an important role in the transport of nutrients and signaling molecules in cartilaginous tissues. Diffusion coefficients can be measured by fluorescence recovery after photobleaching (FRAP). Available methods to analyze FRAP data, however, assume homogeneity in the environment of the bleached area and neglect geometrical restrictions to diffusion. Hence, diffusion coefficients in inhomogeneous materials, such as most biological tissues, cannot be assessed accurately. In this study, a new method for analyzing data from FRAP measurements has been developed, which is applicable to inhomogeneous tissues. It is based on a fitting procedure of the intensity recovery after photobleaching with a two-dimensional finite element analysis, which includes Fick's law for diffusion. The finite element analysis can account for distinctive diffusivity in predefined zones, which allows determining diffusion coefficients in inhomogeneous samples. The method is validated theoretically and experimentally in both homogeneous and inhomogeneous tissues and subsequently applied to the proliferation zone of the growth plate. Finally, the importance of accounting for inhomogeneities, for appropriate assessment of diffusivity in inhomogeneous tissues, is illustrated.     

Measurement of protein rotational motion using frequency domain polarized fluorescence depletion.

Polarized fluorescence depletion (PFD) methods (Yoshida, T. M. and B. G. Barisas. Biophys. J. 1986. 50:41-53) are approximately 10(3)-10(4) fold more sensitive than other techniques for measuring protein rotational motions in cell membranes and other viscous environments. Proteins labeled with fluorophores having a high quantum yield for triplet formation are examined anaerobically in a fluorescence microscope. In time domain PFD experiments a several-microsecond pulse of linearly polarized light produces an orientationally-asymmetric depletion of ground state fluorescence in the sample. Monitoring the decay of ground state depletion with a probe beam alternatively polarized, parallel, and perpendicular to the depletion pulse permits the triplet lifetime and rotational correlation time to be resolved and evaluated. We have now explored fluorescence depletion methods in the frequency domain to see whether such measurements could provide simpler and more efficient routine measurements of protein rotational relaxation than previous time domain PFD methods. An acousto-optic modulator (AOM) modulates the intensity of a 514.5 nm argon ion laser beam and a Pockels cell (PC) rotates its plane of polarization. These devices are driven by sinusoidal or square waves in fixed frequency relation, and rigidly phase locked, one to another. The fluorescence emitted from a sample then contains various overtones and combinations of the AOM and PC frequencies. The magnitude and phase of individual fluorescence signal frequencies are measured by a lock-in amplifier using a reference also phase-locked to both the AOM and PC. Specific frequencies permit evaluation of the rotational correlation time of the macromolecule and of the fluorophore triplet state lifetime, respectively. Measurement of bovine serum albumin rotation in glycerol solutions by this method is described.     

A reaction-diffusion model to study RNA motion by quantitative fluorescence recovery after photobleaching

Fluorescence recovery after photobleaching (FRAP) is a powerful technique to study molecular dynamics inside living cells. During the past years, several laboratories have used FRAP to image the motion of RNA-protein and other macromolecular complexes in the nucleus and cytoplasm. In the case of mRNAs, there is growing evidence indicating that these molecules assemble into large ribonucleoprotein complexes that diffuse throughout the nucleus by Brownian motion. However, estimates of the corresponding diffusion rate yielded values that differ by up to one order of magnitude. In vivo labeling of RNA relies on indirect tagging with a fluorescent probe, and here we show how the binding affinity of the probe to the target RNA influences the effective diffusion estimates of the resulting complex. We extend current reaction-diffusion models for FRAP by allowing for diffusion of the bound complex. This more general model can be used to fit any fluorescence recovery curve involving two interacting mobile species in the cell (a fluorescent probe and its target substrate). The results show that interpreting FRAP data in light of the new model reconciles the discrepant mRNA diffusion-rate values previously reported.     

Depolarized fluorescence photobleaching recovery

The effects of the fact that the laser sources typically used in fluorescence photobleaching recovery (FPR) experiments in the most commonly employed in-line microscope imaging geometries, are highly linearly polarized, are examined in some detail. The implications of the results, in particular for the interpretation of FPR data in complex cell membrane systems in terms of laterally mobile and immobile sub-populations of the labelled molecular species of concern, are discussed. Methods of experimentally eliminating the potentially major rotational diffusion-based artifacts, different from those appropriate to three-dimensional (solution or suspension) systems which require other than in-line geometries, are delineated.Abbreviations FPR fluorescence photobleaching recovery - FRAP fluorescence recovery after photobleaching - 2- and 3-D two- and three-dimensional     

Theory of fluorescence recovery after photobleaching measurements on cylindrical surfaces.

The theory of fluorescence recovery after photobleaching measurements of isotropic diffusion on a cylindrical surface is developed for Gaussian beam illumination centered perpendicular to an infinitely-long cylinder. A general analytical solution is obtained which is a function of the ratio of the cylindrical radius (r) to the beam exp [-2] radius omega. Numerical analysis of this solution demonstrates that significant deviations from one dimensional recovery are observed for omega less than 3r and from two-dimensional recovery for omega greater than or equal to 0.5r. Numerical data and an algorithm for analysis of recovery data where 0.5r less than or equal to omega less than or equal to 3r is presented.     

Effect of concentration quenching on fluorescence recovery after photobleaching measurements.

Standard analysis of fluorescence recovery after photobleaching (FRAP) data is valid only if the quantum yield of unphotobleached fluorophores is independent of concentration, yet close molecular packing in two-dimensional systems may lead to significant fluorescence concentration quenching. Using total internal reflection fluorescence, we quantified the surface concentration dependence of the relative quantum yield of fluorescein isothiocyanate-labeled proteins adsorbed to polymeric surfaces before performing measurements of fluorescence recovery after pattern photobleaching. Adsorbed layers of FITC-labeled ribonuclease A displayed significant concentration quenching, and thus the standard FRAP analysis method was unacceptable. We present an extended FRAP analysis procedure that accounts for the changing quantum yield of diffusing fluorophores in systems that are influenced by concentration quenching. The extended analysis shows that if concentration quenching conditions prevail, there may be significant error in the transport parameters obtained from FRAP measurements by using the standard procedures.     

Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery

Multiphoton fluorescence photobleaching recovery (MP-FPR) is a technique for measuring the three-dimensional (3D) mobility of fluorescent molecules with 3D spatial resolution of a few microns. A brief, intense flash of mode-locked laser light pulses excites fluorescent molecules via multiphoton excitation in an ellipsoidal focal volume and photobleaches a fraction. Because multiphoton excitation of fluorophores is intrinsically confined to the high-intensity focal volume of the illuminating beam, the bleached region is restricted to a known, three-dimensionally defined volume. Fluorescence in this focal volume is measured with multiphoton excitation, using the attenuated laser beam to measure fluorescence recovery as fresh unbleached dye diffuses in. The time course of the fluorescence recovery signal after photobleaching can be analyzed to determine the diffusion coefficient of the fluorescent species. The mathematical formulas used to fit MP-FPR recovery curves and the techniques needed to properly utilize them to acquire the diffusion coefficients of fluorescently labeled molecules within cells are presented here. MP-FPR is demonstrated on calcein in RBL-2H3 cells, using an anomalous subdiffusion model, as well as in aqueous solutions of wild-type green fluorescent protein, yielding a diffusion coefficient of 8.7 x 10(-7) cm(2)s(-1) in excellent agreement with the results of other techniques.     

Effects of organelle shape on fluorescence recovery after photobleaching

The determination of diffusion coefficients from fluorescence recovery data is often complicated by geometric constraints imposed by the complex shapes of intracellular compartments. To address this issue, diffusion of proteins in the lumen of the endoplasmic reticulum (ER) is studied using cell biological and computational methods. Fluorescence recovery after photobleaching (FRAP) experiments are performed in tissue culture cells expressing GFP-KDEL, a soluble, fluorescent protein, in the ER lumen. The three-dimensional (3D) shape of the ER is determined by confocal microscopy and computationally reconstructed. Within these ER geometries diffusion of solutes is simulated using the method of particle strength exchange. The simulations are compared to experimental FRAP curves of GFP-KDEL in the same ER region. Comparisons of simulations in the 3D ER shapes to simulations in open 3D space show that the constraints imposed by the spatial confinement result in two- to fourfold underestimation of the molecular diffusion constant in the ER if the geometry is not taken into account. Using the same molecular diffusion constant in different simulations, the observed speed of fluorescence recovery varies by a factor of 2.5, depending on the particular ER geometry and the location of the bleached area. Organelle shape considerably influences diffusive transport and must be taken into account when relating experimental photobleaching data to molecular diffusion coefficients. This novel methodology combines experimental FRAP curves with high accuracy computer simulations of diffusion in the same ER geometry to determine the molecular diffusion constant of the solute in the particular ER lumen.     

Quantification of transport and binding parameters using fluorescence recovery after photobleaching. Potential for in vivo applications.

Fluorescence Recovery After Photobleaching (FRAP) has been used extensively in the study of transport and binding in biological media in vitro. The present study adapts and further develops FRAP so that it may be utilized for the in vivo quantification of binding parameters. The technique is validated in vitro by measuring mass transport and binding parameters for the Concanavalin A/Mannose binding system (a diffusion-limited system). The pseudo-equilibrium constant (the product of the equilibrium constant and the total concentration of binding sites) for this system was determined to be 26 +/- 15 which compares favorably with literature values ranging between 16 and 32. The applicability of this technique to measure parameters for monoclonal antibody/antigen interactions in a thin tissue preparation such as the rabbit ear chamber tissue preparation is also examined. Unlike other methods for measuring binding parameters, this is the only technique which has the potential to measure parameters relevant to antibody delivery in vivo. The proposed technique is noninvasive and does not require a priori knowledge of, independent measurement of, or variation in the concentration of binding sites or total concentration of binding species.     

Monitoring and quantifying dynamic physiological processes in live neurons using fluorescence recovery after photobleaching

The direct visualization of subcellular dynamic processes is often hampered by limitations in the resolving power achievable with conventional microscopy techniques. Fluorescence recovery after photobleaching has emerged as a highly informative approach to address this challenge, permitting the quantitative measurement of the movement of small organelles and proteins in living functioning cells, and offering detailed insights into fundamental cellular phenomena of physiological importance. In recent years, its implementation has benefited from the increasing availability of confocal microscopy systems and of powerful labeling techniques based on genetically encoded fluorescent proteins or other chemical markers. In this review, we present fluorescence recovery after photobleaching and related techniques in the context of contemporary neurobiological research and discuss quantitative and semi‐quantitative approaches to their interpretation.     

Theoretical analysis of fluorescence photobleaching recovery experiments.

We derive an exact closed formula for the fluorescence recovery curve measured in fluorescence photobleaching recovery experiments employing uniform circular laser beams. In contrast to the expression used currently, this result is very simple and free of mathematical drawbacks, thus facilitating the quantitative analysis of experimental data.     

An ultrastructural readout of fluorescence recovery after photobleaching using correlative light and electron microscopy

Fluorescence recovery after photobleaching (FRAP) provides an important quantitative readout of the mobility of fluorescently tagged structures in live tissue. Here we present a protocol for visualizing FRAP signal at the ultrastructural level, permitting the nature of recovered fluorescence signal to be studied at greater resolution than afforded by conventional light microscopy. Specifically we use FRAP, fixation, photoconversion and correlative light and electron microscopy (CLEM) to examine the ultrastructural organization of mobile FM1-43-labeled vesicles in synapses of cultured hippocampal neurons. At photobleached synapses, the FRAP signal can be visualized as photoconverted electron-dense vesicles. The combination of FRAP and CLEM provides a powerful tool for examining the specific localization of imported vesicles in relation to synaptic architecture. Moreover, with the increasing availability of photoconvertible fluorophores, this approach should be readily applicable to other systems where an ultrastructural characterization of FRAP signal is desirable. After cultures are prepared and ready to use, this protocol takes 2-3 days.     

Macromolecular diffusion of biological polymers measured by confocal fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching with an unmodified confocal laser scanning microscope (confocal FRAP) was used to determine the diffusion properties of network forming biological macromolecules such as aggrecan. The technique was validated using fluorescein isothiocyanate (FITC)-labeled dextrans and proteins (molecular mass 4-2000 kDa) at 25 degrees C and with fluorescent microspheres (207 nm diameter) over a temperature range of 5-50 degrees C. Lateral diffusion coefficients (D) were independent of the focus position, and the degree and extent of bleach. The free diffusion coefficient (Do) of FITC-aggrecan determined by confocal FRAP was 4.25 +/- 0.6 x 10(-8) cm2 s-1, which is compatible with dynamic laser light scattering measurements. It appeared to be independent of concentration below 2.0 mg/ml, but at higher concentrations (2-20 mg/ml) the self-diffusion coefficient followed the function D = Do(e)(-Bc). The concentration at which the self-diffusion coefficient began to fall corresponded to the concentration predicted for domain overlap. Multimolecular aggregates of aggrecan ( approximately 30 monomers) had a much lower free diffusion coefficient (Do = 6.6 +/- 1.0 x 10(-9) cm2 s-1) but showed a decrease in mobility with concentration of a form similar to that of the monomer. The method provides a technique for investigating the macromolecular organization in glycan-rich networks at concentrations close to those found physiologically.