Anomalous Diffusion Characterization by Fourier Transform-FRAP with Patterned Illumination

Diffusion and Exchange Kinetics of Microparticle Formulations by Spatial Fourier Transform Fluorescence Recovery after Photobleaching with Patterned Illumination

The mechanism of active pharmaceutical ingredient (API) mobility during release in microparticle formulation was investigated using periodically structured illumination combined with spatial Fourier transform fluorescence recovery after photobleaching (FT-FRAP). FT-FRAP applies structured photobleaching across a given field of view, allowing for the monitoring of molecular mobility through the analysis of recovery patterns in the FT domain. Encoding molecular mobility in the FT domain offers several advantages, including improved signal-to-noise ratio, simplified mathematical calculations, reduced sampling requirements, compatibility with multiphoton microscopy for imaging API molecules within the formulations, and the ability to distinguish between exchange and diffusion processes. To prepare microparticles for FT-FRAP analysis, a homogeneous mixture of dipyridamole and pH-independent methyl methacrylate polymer (Eudragit RS and RL) was processed using laminar jet breakup induced by vibration in a frequency-driven encapsulator. The encapsulated microparticles were characterized based on particle size distribution, encapsulation efficiency, batch size, and morphology. Utilizing FT-FRAP, the internal diffusion and exchange molecular mobility within RL and RS microparticles were discriminated and quantified. Theoretical modeling of exchange- and diffusion-controlled release revealed that both RL and RS microparticles exhibited similar exchange decay rates, but RL displayed a significantly higher diffusion coefficient. This difference in diffusion within RL and RS microparticles was correlated with their macroscopic dissolution performance.

Diffusion Mapping with Diffractive Optical Elements for Periodically Patterned Photobleaching

Fourier transform-fluorescence recovery after photobleaching (FT-FRAP) using a diffractive optical element (DOE) is shown to support distance-dependent diffusion analysis in biologically relevant media. Integration of DOEs enables patterning of a dot array for parallel acquisition of point-bleach FRAP measurements at multiple locations across the field of view. In homogeneous media, the spatial harmonics of the dot array analyzed in the spatial Fourier transform domain yield diffusion recovery curves evaluated over specific well-defined distances. Relative distances for diffusive recovery in the spatial Fourier transform domain are directly connected to the 2D (h,k) Miller indices of the corresponding lattice lines. The distribution of the photobleach power across the entire field of view using a multidot array pattern greatly increases the overall signal power in the spatial FT-domain for signal-to-noise improvements. Derivations are presented for the mathematical underpinnings of FT-FRAP performed with 2D periodicity in the photobleach patterns. Retrofitting of FT-FRAP into instrumentation for high-throughput FRAP analysis (Formulatrix) supports automated analysis of robotically prepared 96-well plates for precise quantification of molecular mobility. Figures of merit are evaluated for FT-FRAP in analysis for both slow diffusion of fluorescent dyes in glassy polymer matrices spanning several days and model proteins and monoclonal antibodies within aqueous solutions recovering in matters of seconds.

Fluorescence photobleaching and recovery of fluorescein sodium in carbomer film

This study investigated fluorescence photobleaching and the recovery of fluorescein sodium (FS)-loaded carbomer films. To mitigate errors caused by the self-quenching effect, the experiments were conducted at FS concentrations of 0.1, 0.5, and 1 wt%. The results revealed a nonlinear relationship between fluorescence intensity and FS concentration (0.1-1 wt%). Moreover, the degree and rate of photobleaching increased with FS concentration. The recovery level and recovery rate exhibited contrasting relationships with FS concentration. Higher FS concentrations were associated with a longer recovery time, which can be attributed to the prolonged irradiation, resulting in a bleached region that was larger than the initially irradiated area.

Fast Diffusion Characterization by Multiphoton Excited Fluorescence Recovery while Photobleaching

Multiphoton-excited fluorescence recovery while photobleaching (FRWP) is demonstrated as a method for quantitative measurements of rapid molecular diffusion over microsecond to millisecond timescales. Diffusion measurements are crucial in assessing molecular mobility in cell biology, materials science, and pharmacology. Optical and fluorescence microscopy techniques enable non-invasive rapid analysis of molecular diffusion but can be challenging for systems with diffusion coefficients exceeding ∼100 μm2/s. As an example, fluorescence recovery after photobleaching (FRAP) operates on the implicit assumption of a comparatively fast photobleaching step prior to a relatively slow recovery and is not generally applicable for systems exhibiting substantial recovery during photobleaching. These challenges are exacerbated in multiphoton excitation by the lower excitation efficiency and competing effects from local heating. Herein, beam-scanning FRWP with patterned line-bleach illumination is introduced as a technique that addresses FRAP limitations and further extends its application range by measuring faster diffusion events. In FRWP, the recovery of fluorescence is continuously probed after each pass of a fast-scanning mirror, and the upper bound of measurable diffusion rates is, therefore, only limited by the mirror scanning frequency. A theoretical model describing transient fluctuations in fluorescence intensity arising as a result of combined contributions from photobleaching and localized photothermal effect is introduced along with a mathematical framework for quantifying fluorescence intensity temporal curves and recovering room-temperature diffusion coefficients. FRWP is then tested by characterization of normal diffusion of rhodamine-labeled bovine serum albumin, green fluorescence protein, and immunoglobulin G molecules in aqueous solutions of varying viscosity.

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.

Periodic Photobleaching with Structured Illumination for Diffusion Imaging

The use of periodically structured illumination coupled with spatial Fourier-transform fluorescence recovery after photobleaching (FT-FRAP) was shown to support diffusivity mapping within segmented domains of arbitrary shape. Periodic "comb-bleach" patterning of the excitation beam during photobleaching encoded spatial maps of diffusion onto harmonic peaks in the spatial Fourier transform. Diffusion manifests as a simple exponential decay of a given harmonic, improving the signal to noise ratio and simplifying mathematical analysis. Image segmentation prior to Fourier transformation was shown to support pooling for signal to noise enhancement for regions of arbitrary shape expected to exhibit similar diffusivity within a domain. Following proof-of-concept analyses based on simulations with known ground-truth maps, diffusion imaging by FT-FRAP was used to map spatially-resolved diffusion differences within phase-separated domains of model amorphous solid dispersion spin-cast thin films. Notably, multi-harmonic analysis by FT-FRAP was able to definitively discriminate and quantify the roles of internal diffusion and exchange to higher mobility interfacial layers in modeling the recovery kinetics within thin amorphous/amorphous phase-separated domains, with interfacial diffusion playing a critical role in recovery. These results have direct implications for the design of amorphous systems for stable storage and efficacious delivery of therapeutic molecules.

Long-Term Fluorescence Recovery After Photobleaching (FRAP)

Numerous models have been developed for the analysis of fluorescence recovery after photobleaching (FRAP), by which intracellular diffusion and turnover rate are quantitatively evaluated. FRAP analyses typically focus on such events that occur within several minutes, but to precisely evaluate a slow turnover rate of particularly actin stress fibers, achieving long-term FRAP observations of more than 10 min is necessary. In such long-term observations, the effect of intracellular advection is no longer ignored, which motivated us to develop a novel method to decouple the multiple factors associated with the long FRAP response. This method allows us to distinguish the origin of mechanobiological responses of stress fibers that come from either the level of individual actin filaments or that of actin monomers.

CM-FRAP-Continuum Mechanics-Based Fluorescence Recovery After Photobleaching

Fluorescence recovery after photobleaching (FRAP) is widely used to evaluate intracellular molecular turnover or repeated translocation of molecules using confocal laser scanning microscopy. While numerous models have been developed for the analysis of FRAP responses, in which chemical interactions and/or fast diffusion processes are involved, it is inherently difficult to evaluate the long-term behavior of molecular turnover because of the presence of intracellular flow and microscopic deformation of bleached regions. To overcome these difficulties, we have developed a novel continuum mechanics-based FRAP (CM-FRAP) approach that enables simultaneous evaluation of long-term molecular turnover and intracellular flow/deformation. Here we demonstrate the utility of CM-FRAP by using actin molecules associated with stress fibers in rat aortic smooth muscle cells with clarification of the experimental setup and data analysis. © 2023 Wiley Periodicals LLC. Basic Protocol 1: Plasmid construction and sample preparation Basic Protocol 2: How to perform FRAP experiments Basic Protocol 3: Data analysis based on CM-FRAP.

Analysis of chemomechanical behavior of stress fibers by continuum mechanics-based FRAP

Fluorescence recovery after photobleaching (FRAP) is a common technique to analyze the turnover of molecules in living cells. Numerous physicochemical models have been developed to quantitatively evaluate the rate of turnover driven by chemical reaction and diffusion that occurs in a few seconds to minutes. On the other hand, they have limitations in interpreting long-term FRAP responses where intracellular active movement inevitably provides target molecular architectures with additional effects other than chemical reaction and diffusion, namely directed transport and structural deformation. To overcome the limitations, we develop a continuum mechanics-based model that allows for decoupling FRAP response into the intrinsic turnover rate and subcellular mechanical characteristics such as displacement vector and strain tensor. Our approach was validated using fluorescently labeled β-actin in an actomyosin-mediated contractile apparatus called stress fibers, revealing spatially distinct patterns of the multi-physicochemical events, in which the turnover rate, which represents effective off-rate of β-actin, was significantly higher at the center of the cell. We also found that the turnover rate is negatively correlated with the rate of displacement or velocity along stress fibers but, interestingly, not with the absolute magnitude of strain. Moreover, stress fibers are subjected to centripetal flow that is facilitated by the circulation of actin molecules. Taken together, this novel framework for long-term FRAP analysis allows for unveiling the contribution of overlooked microscopic mechanics to molecular turnover in living cells.

Recent Advances in Fluorescence Recovery after Photobleaching for Decoupling Transport and Kinetics of Biomacromolecules in Cellular Physiology

Among the new molecular tools available to scientists and engineers, some of the most useful include fluorescently tagged biomolecules. Tools, such as green fluorescence protein (GFP), have been applied to perform semi-quantitative studies on biological signal transduction and cellular structural dynamics involved in the physiology of healthy and disease states. Such studies focus on drug pharmacokinetics, receptor-mediated endocytosis, nuclear mechanobiology, viral infections, and cancer metastasis. In 1976, fluorescence recovery after photobleaching (FRAP), which involves the monitoring of fluorescence emission recovery within a photobleached spot, was developed. FRAP allowed investigators to probe two-dimensional (2D) diffusion of fluorescently-labelled biomolecules. Since then, FRAP has been refined through the advancements of optics, charged-coupled-device (CCD) cameras, confocal microscopes, and molecular probes. FRAP is now a highly quantitative tool used for transport and kinetic studies in the cytosol, organelles, and membrane of a cell. In this work, the authors intend to provide a review of recent advances in FRAP. The authors include epifluorescence spot FRAP, total internal reflection (TIR)/FRAP, and confocal microscope-based FRAP. The underlying mathematical models are also described. Finally, our understanding of coupled transport and kinetics as determined by FRAP will be discussed and the potential for future advances suggested.

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

FRAP (fluorescence recovery after photo bleaching) is a method for determining diffusion in material science. In industrial applications such as medications, foods, Medtech, hygiene, and textiles, the diffusion process has a substantial influence on the overall qualities of goods. All these complex and heterogeneous systems have diffusion-based processes at the local level. FRAP is a fluorescence-based approach for detecting diffusion; in this method, a high-intensity laser is made for a brief period and then applied to the samples, bleaching the fluorescent chemical inside the region, which is subsequently filled up by natural diffusion. This brief Review will focus on the existing research on employing FRAP to measure colloidal system heterogeneity and explore diffusion into complicated structures. This description of FRAP will be followed by a discussion of how FRAP is intended to be used in colloidal science. When constructing the current Review, the most recent publications were reviewed for this assessment. Because of the large number of FRAP articles in colloidal research, there is currently a dearth of knowledge regarding the growth of FRAP's significance to colloidal science. Colloids make up only 2% of FRAP papers, according to ISI Web of Knowledge.

Fluorescence-Detected Mid-Infrared Photothermal Microscopy

We demonstrate instrumentation and methods to enable fluorescence-detected photothermal infrared (F-PTIR) microscopy and then demonstrate the utility of F-PTIR to characterize the composition within phase-separated domains of model amorphous solid dispersions (ASDs) induced by water sorption. In F-PTIR, temperature-dependent changes in fluorescence quantum efficiency are shown to sensitively report on highly localized absorption of mid-infrared radiation. The spatial resolution with which infrared spectroscopy can be performed is dictated by fluorescence microscopy, rather than the infrared wavelength. Intrinsic ultraviolet autofluorescence of tryptophan and protein microparticles enabled label-free F-PTIR microscopy. Following proof of concept F-PTIR demonstration on model systems of polyethylene glycol (PEG) and silica gel, F-PTIR enabled the characterization of chemical composition within inhomogeneous ritonavir/polyvinylpyrrolidone-vinyl acetate (PVPVA) amorphous dispersions. Phase separation is implicated in the observation of critical behaviors in ASD dissolution kinetics, with the results of F-PTIR supporting the formation of phase-separated drug-rich domains upon water sorption in spin-cast films.

A noninvasive fluorescence imaging-based platform measures 3D anisotropic extracellular diffusion

Diffusion is a major molecular transport mechanism in biological systems. Quantifying direction-dependent (i.e., anisotropic) diffusion is vitally important to depicting how the three-dimensional (3D) tissue structure and composition affect the biochemical environment, and thus define tissue functions. However, a tool for noninvasively measuring the 3D anisotropic extracellular diffusion of biorelevant molecules is not yet available. Here, we present light-sheet imaging-based Fourier transform fluorescence recovery after photobleaching (LiFT-FRAP), which noninvasively determines 3D diffusion tensors of various biomolecules with diffusivities up to 51 µm2 s-1, reaching the physiological diffusivity range in most biological systems. Using cornea as an example, LiFT-FRAP reveals fundamental limitations of current invasive two-dimensional diffusion measurements, which have drawn controversial conclusions on extracellular diffusion in healthy and clinically treated tissues. Moreover, LiFT-FRAP demonstrates that tissue structural or compositional changes caused by diseases or scaffold fabrication yield direction-dependent diffusion changes. These results demonstrate LiFT-FRAP as a powerful platform technology for studying disease mechanisms, advancing clinical outcomes, and improving tissue engineering.

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.