A Generalization of Theory for Two-Dimensional Fluorescence Recovery after Photobleaching Applicable to Confocal Laser Scanning Microscopes

Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells.     

Minimizing the impact of photoswitching of fluorescent proteins on FRAP analysis

Fluorescence recovery after photobleaching (FRAP) is a widely used imaging technique for measuring the mobility of fluorescently tagged proteins in living cells. Although FRAP presumes that high-intensity illumination causes only irreversible photobleaching, reversible photoswitching of many fluorescent molecules, including GFP, can also occur. Here, we show that this photoswitching is likely to contaminate many FRAPs of GFP, and worse, the size of its contribution can be up to 60% under different experimental conditions, making it difficult to compare FRAPs from different studies. We develop a procedure to correct FRAPs for photoswitching and apply it to FRAPs of the GFP-tagged histone H2B, which, depending on the precise photobleaching conditions exhibits apparent fast components ranging from 9-36% before correction and ～1% after correction. We demonstrate how this ～1% fast component of H2B-GFP can be used as a benchmark both to estimate the role of photoswitching in previous FRAP studies of TATA binding proteins (TBP) and also as a tool to minimize the contribution of photoswitching to tolerable levels in future FRAP experiments. In sum, we show how the impact of photoswitching on FRAP can be identified, minimized, and corrected.     

Intracellular macromolecular mobility measured by fluorescence recovery after photobleaching with confocal laser scanning microscopes

Fluorescence recovery after photobleaching (FRAP) is a widely used tool for estimating mobility parameters of fluorescently tagged molecules in cells. Despite the widespread use of confocal laser scanning microscopes (CLSMs) to perform photobleaching experiments, quantitative data analysis has been limited by lack of appropriate practical models. Here, we present a new approximate FRAP model for use on any standard CLSM. The main novelty of the method is that it takes into account diffusion of highly mobile molecules during the bleach phase. In fact, we show that by the time the first postbleach image is acquired in a CLSM a significant fluorescence recovery of fast-moving molecules has already taken place. The model was tested by generating simulated FRAP recovery curves for a wide range of diffusion coefficients and immobile fractions. The method was further validated by an experimental determination of the diffusion coefficient of fluorescent dextrans and green fluorescent protein. The new FRAP method was used to compare the mobility rates of fluorescent dextrans of 20, 40, 70, and 500 kDa in aqueous solution and in the nucleus of living HeLa cells. Diffusion coefficients were lower in the nucleoplasm, particularly for higher molecular weight dextrans. This is most likely caused by a sterical hindrance effect imposed by nuclear components. Decreasing the temperature from 37 to 22 degrees C reduces the dextran diffusion rates by approximately 30% in aqueous solution but has little effect on mobility in the nucleoplasm. This suggests that spatial constraints to diffusion of dextrans inside the nucleus are insensitive to temperature.     

Reversible photobleaching of enhanced green fluorescent proteins

Color variants of green fluorescent protein (GFP) are increasingly used for multicolor imaging, fluorescence resonance energy transfer (FRET), and fluorescence recovery after photobleaching (FRAP). Here we show that experimental settings commonly used in these imaging experiments may induce an as yet uncharacterized reversible photobleaching of fluorescent proteins, which is more pronounced at acidic pH. Whereas the reversible photobleaching spectrum of eCFP corresponds to its absorption spectrum, reversible photobleaching spectra of yellow variants resemble absorption spectra of their protonated states. Fluorescence intensities recover spontaneously with time constants of 25-58 s. The recovery of eCFP can be further accelerated by illumination. The resulting steady-state fluorescence reflects a variable equilibrium between reversible photobleaching, spontaneous recovery, and light-induced recovery. These processes can cause significant artifacts in commonly applied imaging techniques, photobleach-based FRET determinations, and FRAP assays.     

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.     

Lateral diffusion of membrane D-galactosyl glycoconjugates of differentiating neuroblastoma cells

Neuroblastoma cells were induced to differentiate either by serum deprivation or addition of dimethylsulfoxide. Using the “fluorescence recovery after photobleaching method” (FRAP), the lateral diffusion properties of D-galactosyl glycoconjugates revealed with fluorescent labelled peanut agglutinin (PNA) was investigated. Statistical significant modifications were found on process-bearing cells only for the characteristic diffusion time. The mobile fractions of PNA binding sites were distributed about a mean value of 60%. Attempt was made to discuss the FRAP results in term of cell-to-cell variation.     

FRAP analysis of membrane-associated proteins: lateral diffusion and membrane-cytoplasmic exchange

Obtaining quantitative kinetic parameters from fluorescence recovery after photobleaching (FRAP) experiments generally requires a theoretical analysis of protein mobility and appropriate solutions for FRAP recovery derived for a given geometry. Here we provide a treatment of FRAP recovery for a molecule undergoing a combined process of reversible membrane association and lateral diffusion on the plasma membrane for two commonly used bleach geometries: stripes, and boxes. Such analysis is complicated by the fact that diffusion of a molecule during photobleaching can lead to broadening of the bleach area, resulting in significant deviations of the actual bleach shape from the desired bleach geometry, which creates difficulty in accurately measuring kinetic parameters. Here we overcome the problem of deviations between actual and idealized bleach geometries by parameterizing, more accurately, the initial postbleach state. This allows for reconstruction of an accurate and analytically tractable approximation of the actual fluorescence distribution. Through simulated FRAP experiments, we demonstrate that this method can be used to accurately measure a broad range of combinations of diffusion constants and exchange rates. Use of this method to analyze the plextrin homology domain of PLC-δ1 in Caenorhabditis elegans results in quantitative agreement with prior analysis of this domain in other cells using other methods. Because of the flexibility, relative ease of implementation, and its use of standard, easily obtainable bleach geometries, this method should be broadly applicable to investigation of protein dynamics at the plasma membrane.     

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

We introduce a new method to measure the lateral diffusivity of a surfactant monolayer at the fluid-fluid interface, called fluorescence recovery after merging (FRAM). FRAM adopts the same principles as the fluorescence recovery after photobleaching (FRAP) technique, especially for measuring fluorescence recovery after bleaching a specific area, but FRAM uses a drop coalescence instead of photobleaching dye molecules to induce a chemical potential gradient of dye molecules. Our technique has several advantages over FRAP: it only requires a fluorescence microscope rather than a confocal microscope equipped with high power lasers; it is essentially free from the selection of fluorescence dyes; and it has far more freedom to define the measured diffusion area. Furthermore, FRAM potentially provides a route for studying the mixing or inter-diffusion of two different surfactants, when the monolayers at a surface of droplet and at a flat air/water interface are prepared with different species, independently.     

Characterizing fluorescence recovery curves for nuclear proteins undergoing binding events

Fluorescence recovery after photobleaching (FRAP) is an experimental technique used to measure the mobility of proteins within the cell nucleus. After proteins of interest are fluorescently tagged for their visualization and monitoring, a small region of the nucleus is photobleached. The experimental FRAP data are obtained by recording the recovery of the fluorescence in this region over time. In this paper, we characterize the fluorescence recovery curves for diffusing nuclear proteins undergoing binding events with an approximate spatially homogeneous structure. We analyze two mathematical models for interpreting the experimental FRAP data, namely a reaction-diffusionmodel and a compartmental model. Perturbation analysis leads to a clear explanation of two important limiting dynamical types of behavior exhibited by experimental recovery curves, namely, (1) a reduced diffusive recovery, and (2) a biphasic recovery characterized by a fast phase and a slow phase. We show how the two models, describing the same type of dynamics using different approaches, relate and share common ground. The results can be used to interpret experimental FRAP data in terms of protein dynamics and to simplify the task of parameter estimation. Application of the results is demonstrated for nuclear actin and type H1 histone.     

Phase topology and percolation in two-component lipid bilayers: a monte Carlo approach.

Monte Carlo simulations of fluorescence recovery after photobleaching (FRAP) experiments on two-component lipid bilayers systems in the solid-fluid phase coexistence region were carried out to study the geometry and size of fluid domains in these bilayers. The gel phase was simulated by superposable elliptical domains, which were either of predetermined dimensions, increasing in number with increasing gel phase fraction, or of predetermined number, increasing in dimensions with increasing gel phase fraction. The simulations were done from two perspectives: 1) a time-independent analysis of fractional fluorescence recovery as a function of fractional fluid phase in the system; and 2) a time-dependent analysis of fractional fluorescence recovery as a function of time at a given fraction of fluid phase in the system. The time-dependent simulations result in recovery curves that are directly comparable to experimental FRAP curves and provide topological and geometrical models for the coexisting phases that are consistent with the experimental result.     

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.     

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.     

From fixed to FRAP: measuring protein mobility and activity in living cells

Experiments with fluorescence recovery after photobleaching (FRAP) started 30 years ago to visualize the lateral mobility and dynamics of fluorescent proteins in living cells. Its popularity increased when non-invasive fluorescent tagging became possible with the green fluorescent protein (GFP). Many researchers use GFP to study the localization of fusion proteins in fixed or living cells, but the same fluorescent proteins can also be used to study protein mobility in living cells. Here we review the potential of FRAP to study protein dynamics and activity within a single living cell. These measurements can be made with most standard confocal laser-scanning microscopes equipped with photobleaching protocols.     

Three-dimensional fluorescence recovery after photobleaching with the confocal scanning laser microscope

Confocal scanning laser microscopes (CSLMs) are equipped with the feature to photobleach user-defined regions. This makes them a handy tool to perform fluorescence recovery after photobleaching (FRAP) measurements. To allow quantification of such FRAP experiments, a three-dimensional model has been developed that describes the fluorescence recovery process for a disk-shaped geometry that is photobleached by the scanning beam of a CSLM. First the general mathematical basis is outlined describing the bleaching process for an arbitrary geometry bleached by a scanning laser beam. Next, these general expressions are applied to the bleaching by a CSLM of a disk-shaped geometry and an analytical solution is derived that describes three-dimensional fluorescence recovery in the bleached area as observed by the CSLM. The FRAP model is validated through both the Stokes-Einstein relation and the comparison of the measured diffusion coefficients with their theoretical estimates. Finally, the FRAP model is used to characterize the transport of FITC-dextrans through bulk three-dimensional biological materials: vitreous body isolated from bovine eyes, and lung sputum expectorated by cystic fibrosis patients. The decrease in the diffusion coefficient relative to its value in solution was dependent on the size of the FITC-dextrans in vitreous, whereas it was size-independent in cystic fibrosis sputum.