Fluorescence recovery after photobleaching on the confocal laser-scanning microscope: generalized model without restriction on the size of the photobleached disk

Fluorophore position of headgroup-labeled Gb3 glycosphingolipids in lipid bilayers

Fluorescent lipid probes are an invaluable tool for investigating lipid membranes. In particular, localizing certain receptor lipids such as glycosphingolipids within phase-separated membranes is of pivotal interest to understanding the influence of protein-receptor lipid binding on membrane organization. However, fluorescent labeling can readily alter the phase behavior of a lipid membrane because of the interaction of the fluorescent moiety with the membrane interface. Here, we investigated Gb3 glycosphingolipids, serving as receptor lipids for the protein Shiga toxin, with a headgroup attached BODIPY fluorophore separated by a polyethylene glycol (PEG) spacer of different lengths. We found that the diffusion coefficients of the fluorescently labeled Gb3 species in 1,2-dioleoyl-sn-glycero-3-phosphocholine/Gb3 (98:2, n/n) supported lipid bilayers are unaltered by the PEG spacer length. However, quenching as well as graphene-induced energy transfer experiments indicated that the length of the PEG spacer (n = 3 and n = 13) alters the position of the BODIPY fluorophore. In particular, the graphene-induced energy transfer technique provided accurate end-to-end distances between the fluorophores in the two leaflets of the bilayer thus enabling us to quantify the distance between the membrane interface and the fluorophore with sub-nanometer resolution. The spacer with three oligo ethylene glycol groups positioned the BODIPY fluorophore directly at the membrane interface favoring its interaction with the bilayer and thus may disturb lipid packing. However, the longer PEG spacer (n = 13) separated the BODIPY moiety from the membrane surface by 1.5 nm.

What's past is prologue: FRAP keeps delivering 50 years later

Fluorescence recovery after photobleaching (FRAP) has emerged as one of the most widely utilized techniques to quantify binding and diffusion kinetics of biomolecules in biophysics. Since its inception in the mid-1970s, FRAP has been used to address an enormous array of questions including the characteristic features of lipid rafts, how cells regulate the viscosity of their cytoplasm, and the dynamics of biomolecules inside condensates formed by liquid-liquid phase separation. In this perspective, I briefly summarize the history of the field and discuss why FRAP has proven to be so incredibly versatile and popular. Next, I provide an overview of the extensive body of knowledge that has emerged on best practices for quantitative FRAP data analysis, followed by some recent examples of biological lessons learned using this powerful approach. Finally, I touch on new directions and opportunities for biophysicists to contribute to the continued development of this still-relevant research tool.

Line-FRAP, A Versatile Method to Measure Diffusion Rates In Vitro and In Vivo

The crowded cellular milieu affect molecular diffusion through hard (occluded space) and soft (weak, non-specific) interactions. Multiple methods have been developed to measure diffusion coefficients at physiological protein concentrations within cells, each with its limitations. Here, we show that Line-FRAP, combined with rigours data analysis, is able to determine diffusion coefficients in a variety of environments, from in vitro to in vivo. The use of Line mode greatly improves time resolution of FRAP data acquisition, from 20-100 Hz in the classical mode to 800 Hz in the line mode. This improves data analysis, as intensity and radius of the bleach at the first post-bleach frame is critical. We evaluated the method on different proteins labelled chemically or fused to YFP in a wide range of environments. The diffusion coefficients measured in HeLa and in E. coli were ~2.5-fold and 15-fold slower than in buffer, and were comparable to previously published data. Increasing the osmotic pressure on E. coli further decreases diffusion, to the point at which proteins virtually stop moving. The method presented here, which requires a confocal microscope equipped with dual scanners, can be applied to study a large range of molecules with different sizes, and provides robust results in a wide range of environments and protein concentrations for fast diffusing molecules.

DeepFRAP: Fast fluorescence recovery after photobleaching data analysis using deep neural networks

Conventional analysis of fluorescence recovery after photobleaching (FRAP) data for diffusion coefficient estimation typically involves fitting an analytical or numerical FRAP model to the recovery curve data using non-linear least squares. Depending on the model, this can be time consuming, especially for batch analysis of large numbers of data sets and if multiple initial guesses for the parameter vector are used to ensure convergence. In this work, we develop a completely new approach, DeepFRAP, utilizing machine learning for parameter estimation in FRAP. From a numerical FRAP model developed in previous work, we generate a very large set of simulated recovery curve data with realistic noise levels. The data are used for training different deep neural network regression models for prediction of several parameters, most importantly the diffusion coefficient. The neural networks are extremely fast and can estimate the parameters orders of magnitude faster than least squares. The performance of the neural network estimation framework is compared to conventional least squares estimation on simulated data, and found to be strikingly similar. Also, a simple experimental validation is performed, demonstrating excellent agreement between the two methods. We make the data and code used publicly available to facilitate further development of machine learning-based estimation in FRAP. LAY DESCRIPTION: Fluorescence recovery after photobleaching (FRAP) is one of the most frequently used methods for microscopy-based diffusion measurements and broadly used in materials science, pharmaceutics, food science and cell biology. In a FRAP experiment, a laser is used to photobleach fluorescent particles in a region. By analysing the recovery of the fluorescence intensity due to the diffusion of still fluorescent particles, the diffusion coefficient and other parameters can be estimated. Typically, a confocal laser scanning microscope (CLSM) is used to image the time evolution of the recovery, and a model is fit using least squares to obtain parameter estimates. In this work, we introduce a new, fast and accurate method for analysis of data from FRAP. The new method is based on using artificial neural networks to predict parameter values, such as the diffusion coefficient, effectively circumventing classical least squares fitting. This leads to a dramatic speed-up, especially noticeable when analysing large numbers of FRAP data sets, while still producing results in excellent agreement with least squares. Further, the neural network estimates can be used as very good initial guesses for least squares estimation in order to make the least squares optimization convergence much faster than it otherwise would. This provides for obtaining, for example, diffusion coefficients as soon as possible, spending minimal time on data analysis. In this fashion, the proposed method facilitates efficient use of the experimentalist's time which is the main motivation to our approach. The concept is demonstrated on pure diffusion. However, the concept can easily be extended to the diffusion and binding case. The concept is likely to be useful in all application areas of FRAP, including diffusion in cells, gels and solutions.

A Highly Accurate Pixel-Based FRAP Model Based on Spectral-Domain Numerical Methods

We introduce a new, to our knowledge, numerical model based on spectral methods for analysis of fluorescence recovery after photobleaching data. The model covers pure diffusion and diffusion and binding (reaction-diffusion) with immobile binding sites, as well as arbitrary bleach region shapes. Fitting of the model is supported using both conventional recovery-curve-based estimation and pixel-based estimation, in which all individual pixels in the data are utilized. The model explicitly accounts for multiple bleach frames, diffusion (and binding) during bleaching, and bleaching during imaging. To our knowledge, no other fluorescence recovery after photobleaching framework incorporates all these model features and estimation methods. We thoroughly validate the model by comparison to stochastic simulations of particle dynamics and find it to be highly accurate. We perform simulation studies to compare recovery-curve-based estimation and pixel-based estimation in realistic settings and show that pixel-based estimation is the better method for parameter estimation as well as for distinguishing pure diffusion from diffusion and binding. We show that accounting for multiple bleach frames is important and that the effect of neglecting this is qualitatively different for the two estimation methods. We perform a simple experimental validation showing that pixel-based estimation provides better agreement with literature values than recovery-curve-based estimation and that accounting for multiple bleach frames improves the result. Further, the software developed in this work is freely available online.

Characterization of Cell Boundary and Confocal Effects Improves Quantitative FRAP Analysis

Fluorescence recovery after photobleaching (FRAP) is an important tool used by cell biologists to study the diffusion and binding kinetics of vesicles, proteins, and other molecules in the cytoplasm, nucleus, or cell membrane. Although many FRAP models have been developed over the past decades, the influence of the complex boundaries of 3D cellular geometries on the recovery curves, in conjunction with regions of interest and optical effects (imaging, photobleaching, photoswitching, and scanning), has not been well studied. Here, we developed a 3D computational model of the FRAP process that incorporates particle diffusion, cell boundary effects, and the optical properties of the scanning confocal microscope, and validated this model using the tip-growing cells of Physcomitrella patens. We then show how these cell boundary and optical effects confound the interpretation of FRAP recovery curves, including the number of dynamic states of a given fluorophore, in a wide range of cellular geometries-both in two and three dimensions-namely nuclei, filopodia, and lamellipodia of mammalian cells, and in cell types such as the budding yeast, Saccharomyces pombe, and tip-growing plant cells. We explored the performance of existing analytical and algorithmic FRAP models in these various cellular geometries, and determined that the VCell VirtualFRAP tool provides the best accuracy to measure diffusion coefficients. Our computational model is not limited only to these cells types, but can easily be extended to other cellular geometries via the graphical Java-based application we also provide. This particle-based simulation-called the Digital Confocal Microscopy Suite or DCMS-can also perform fluorescence dynamics assays, such as number and brightness, fluorescence correlation spectroscopy, and raster image correlation spectroscopy, and could help shape the way these techniques are interpreted.

Simultaneous FRAP, FLIM and FAIM for measurements of protein mobility and interaction in living cells

We present a novel integrated multimodal fluorescence microscopy technique for simultaneous fluorescence recovery after photobleaching (FRAP), fluorescence lifetime imaging (FLIM) and fluorescence anisotropy imaging (FAIM). This approach captures a series of polarization-resolved fluorescence lifetime images during a FRAP recovery, maximizing the information available from a limited photon budget. We have applied this method to analyse the behaviour of GFP-labelled coxsackievirus and adenovirus receptor (CAR) in living human epithelial cells. Our data reveal that CAR exists in oligomeric states throughout the cell, and that these complexes occur in conjunction with high immobile fractions of the receptor at cell-cell junctions. These findings shed light on previously unknown molecular associations between CAR receptors in intact cells and demonstrate the power of combined FRAP, FLIM and FAIM microscopy as a robust method to analyse complex multi-component dynamics in living cells.

Fluorescence recovery after photobleaching in material and life sciences: putting theory into practice

Fluorescence recovery after photobleaching (FRAP) is a versatile tool for determining diffusion and interaction/binding properties in biological and material sciences. An understanding of the mechanisms controlling the diffusion requires a deep understanding of structure–interaction–diffusion relationships. In cell biology, for instance, this applies to the movement of proteins and lipids in the plasma membrane, cytoplasm and nucleus. In industrial applications related to pharmaceutics, foods, textiles, hygiene products and cosmetics, the diffusion of solutes and solvent molecules contributes strongly to the properties and functionality of the final product. All these systems are heterogeneous, and accurate quantification of the mass transport processes at the local level is therefore essential to the understanding of the properties of soft (bio)materials. FRAP is a commonly used fluorescence microscopy-based technique to determine local molecular transport at the micrometer scale. A brief high-intensity laser pulse is locally applied to the sample, causing substantial photobleaching of the fluorescent molecules within the illuminated area. This causes a local concentration gradient of fluorescent molecules, leading to diffusional influx of intact fluorophores from the local surroundings into the bleached area. Quantitative information on the molecular transport can be extracted from the time evolution of the fluorescence recovery in the bleached area using a suitable model. A multitude of FRAP models has been developed over the years, each based on specific assumptions. This makes it challenging for the non-specialist to decide which model is best suited for a particular application. Furthermore, there are many subtleties in performing accurate FRAP experiments. For these reasons, this review aims to provide an extensive tutorial covering the essential theoretical and practical aspects so as to enable accurate quantitative FRAP experiments for molecular transport measurements in soft (bio)materials.

Fluorescence in two-photon-excited diffusible samples exposed to photobleaching: a simulation-based study

We created a simulation model to investigate the characteristics of fluorescence in two-photon-excited samples. In the model, the sample is a diffusible solution of fluorophore molecules, which is divided into cubic cells and illuminated by a train of focused laser pulses described as a Gaussian beam. Simulating the state transitions according to a multilevel photodynamic model (also including photobleaching and intersystem crossing), the simulator provides the expected number and the spatial distribution of emitted photons over time. Our simulations demonstrated how the illumination laser power, diffusion, and the photodynamic parameters of the fluorophore affect fluorescence. We revealed the unusual fluorescent profile that evolves as photobleaching progresses: the most photons are not emitted from the focus (where a "dark hole" appears) but from an ellipsoid around the focus. The model could be adapted to several fluorescent techniques (such as two-photon microscopy and fluorescence recovery after photobleaching). Furthermore, it might help to optimize the operating parameters of the measurement devices (e.g., in order to reach higher image quality and lower photobleaching).

The autodepalmitoylating activity of APT maintains the spatial organization of palmitoylated membrane proteins

The localization and signaling of S-palmitoylated peripheral membrane proteins is sustained by an acylation cycle in which acyl protein thioesterases (APTs) depalmitoylate mislocalized palmitoylated proteins on endomembranes. However, the APTs are themselves reversibly S-palmitoylated, which localizes thioesterase activity to the site of the antagonistc palmitoylation activity on the Golgi. Here, we resolve this conundrum by showing that palmitoylation of APTs is labile due to autodepalmitoylation, creating two interconverting thioesterase pools: palmitoylated APT on the Golgi and depalmitoylated APT in the cytoplasm, with distinct functionality. By imaging APT-substrate catalytic intermediates, we show that it is the depalmitoylated soluble APT pool that depalmitoylates substrates on all membranes in the cell, thereby establishing its function as release factor of mislocalized palmitoylated proteins in the acylation cycle. The autodepalmitoylating activity on the Golgi constitutes a homeostatic regulation mechanism of APT levels at the Golgi that ensures robust partitioning of APT substrates between the plasma membrane and the Golgi.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Revisiting point FRAP to quantitatively characterize anomalous diffusion in live cells

Fluorescence recovery after photobleaching (FRAP) is widely used to interrogate diffusion and binding of proteins in live cells. Herein, we apply two-photon excited FRAP with a diffraction limited bleaching and observation volume to study anomalous diffusion of unconjugated green fluorescence protein (GFP) in vitro and in cells. Experiments performed on dilute solutions of GFP reveal that reversible fluorophore bleaching can be mistakenly interpreted as anomalous diffusion. We derive a reaction-diffusion FRAP model that includes reversible photobleaching, and demonstrate that it properly accounts for these photophysics. We then apply this model to investigate the diffusion of GFP in HeLa cells and polytene cells of Drosophila larval salivary glands. GFP exhibits anomalous diffusion in the cytoplasm of both cell types and in HeLa nuclei. Polytene nuclei contain optically resolvable chromosomes, permitting FRAP experiments that focus separately on chromosomal or interchrosomal regions. We find that GFP exhibits anomalous diffusion in chromosomal regions but diffuses normally in regions devoid of chromatin. This observation indicates that obstructed transport through chromatin and not crowding by macromolecules is a source of anomalous diffusion in polytene nuclei. This behavior is likely true in other cells, so it will be important to account for this type of transport physics and for reversible photobleaching to properly interpret future FRAP experiments on DNA-binding proteins.

Simplified equation to extract diffusion coefficients from confocal FRAP data

Quantitative measurements of diffusion can provide important information about how proteins and lipids interact with their environment within the cell and the effective size of the diffusing species. Confocal fluorescence recovery after photobleaching (FRAP) is one of the most widely accessible approaches to measure protein and lipid diffusion in living cells. However, straightforward approaches to quantify confocal FRAP measurements in terms of absolute diffusion coefficients are currently lacking. Here, we report a simplified equation that can be used to extract diffusion coefficients from confocal FRAP data using the half time of recovery and effective bleach radius for a circular bleach region, and validate this equation for a series of fluorescently labeled soluble and membrane-bound proteins and lipids. We show that using this approach, diffusion coefficients ranging over three orders of magnitude can be obtained from confocal FRAP measurements performed under standard imaging conditions, highlighting its broad applicability.

Ensemble and single particle fluorimetric techniques in concerted action to study the diffusion and aggregation of the glycine receptor α3 isoforms in the cell plasma membrane

The spatio-temporal membrane behavior of glycine receptors (GlyRs) is known to be of influence on receptor homeostasis and functionality. In this work, an elaborate fluorimetric strategy was applied to study the GlyR α3K and L isoforms. Previously established differential clustering, desensitization and synaptic localization of these isoforms imply that membrane behavior is crucial in determining GlyR α3 physiology. Therefore diffusion and aggregation of homomeric α3 isoform-containing GlyRs were studied in HEK 293 cells. A unique combination of multiple diffraction-limited ensemble average methods and subdiffraction single particle techniques was used in order to achieve an integrated view of receptor properties. Static measurements of aggregation were performed with image correlation spectroscopy (ICS) and, single particle based, direct stochastic optical reconstruction microscopy (dSTORM). Receptor diffusion was measured by means of raster image correlation spectroscopy (RICS), temporal image correlation spectroscopy (TICS), fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT). The results show a significant difference in diffusion coefficient and cluster size between the isoforms. This reveals a positive correlation between desensitization and diffusion and disproves the notion that receptor aggregation is a universal mechanism for accelerated desensitization. The difference in diffusion coefficient between the clustering GlyR α3L and the non-clustering GlyR α3K cannot be explained by normal diffusion. SPT measurements indicate that the α3L receptors undergo transient trapping and directed motion, while the GlyR α3K displays mild hindered diffusion. These findings are suggestive of differential molecular interaction of the isoforms after incorporation in the membrane.

FRAP analysis: accounting for bleaching during image capture

The analysis of Fluorescence Recovery After Photobleaching (FRAP) experiments involves mathematical modeling of the fluorescence recovery process. An important feature of FRAP experiments that tends to be ignored in the modeling is that there can be a significant loss of fluorescence due to bleaching during image capture. In this paper, we explicitly include the effects of bleaching during image capture in the model for the recovery process, instead of correcting for the effects of bleaching using reference measurements. Using experimental examples, we demonstrate the usefulness of such an approach in FRAP analysis.