A pixel-based likelihood framework for analysis of fluorescence recovery after photobleaching data

Glucose stockpile in the intestinal apical brush border in C. elegans

Revealing the mechanisms of glucose transport is crucial for studying pathological diseases caused by glucose toxicities. Numerous studies have revealed molecular functions involved in glucose transport in the nematode Caenorhabditis elegans, a commonly used model organism. However, the behavior of glucose in the intestinal lumen-to-cell remains elusive. To address that, we evaluated the diffusion coefficient of glucose in the intestinal apical brush border of C. elegans by using fluorescent glucose and fluorescence recovery after photobleaching. Fluorescent glucose taken in the intestine of worms accumulates in the apical brush border, and its diffusion coefficient of ∼10-8 cm2/s is two orders of magnitude slower than that in bulk. This result indicates that the intestinal brush border is a viscous layer. ERM-1 point mutations at the phosphorylation site, which shorten the microvilli length, did not significantly affect the diffusion coefficient of fluorescent glucose in the brush border. Our findings imply that glucose enrichment is dominantly maintained by the viscous layer composed of the glycocalyx and molecular complexes on the apical surface.

Evidence of residual micellar structures in a lipid nanocapsule dispersion. A multi-technique approach

Nanoemulsions are metastable emulsions in the nanometric range which can be obtained using low-energy processes. A decade ago, it was demonstrated that a non-negligible amount of residual surfactant micelles may coexist with the oil nanodroplets in a model oil/surfactant system. Those micelles were called "wasted" micelles as they did not participate in the formation of the nanodroplets. Little attention has been focused on the potential presence or effect of such secondary structures in nanoemulsions used as drug delivery systems. Here, we present an extensive characterization of lipid nanocapsules, a nanoemulsion obtained from a medium-chain triglyceride mixed with a pegylated surfactant by a process comprising a temperature-dependent phase inversion followed by a cold-water quench. Lipid nanocapsules demonstrate a very good shelf stability. First, for clarity and academic purposes, we briefly present the pros and the cons of the various diffusion-based characterization techniques used i.e., multi-angle and single-angle dynamic light scattering, nanoparticle tracking analysis, fluorescence recovery after photobleaching, and diffusometry nuclear magnetic resonance. Then, combining all these techniques, we show that up to 40 wt% of the surfactant is not involved in the lipid nanocapsule construction but forms residual micellar structures. Those micelles also contain a small quantity of medium-chain triglyceride (2 wt% of the initial amount) and encapsulate around 40 wt% of a fluorescent dye originally dispersed in the oily phase.

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.

Heterogeneity of Network Structures and Water Dynamics in κ-Carrageenan Gels Probed by Nanoparticle Diffusometry

A set of functionalized nanoparticles (PEGylated dendrimers, d = 2.8-11 nm) was used to probe the structural heterogeneity in Na⁺/K⁺ induced κ-carrageenan gels. The self-diffusion behavior of these nanoparticles as observed by ¹H pulsed-field gradient NMR, fluorescence recovery after photobleaching, and raster image correlation spectroscopy revealed a fast and a slow component, pointing toward microstructural heterogeneity in the gel network. The self-diffusion behavior of the faster nanoparticles could be modeled with obstruction by a coarse network (average mesh size <100 nm), while the slower-diffusing nanoparticles are trapped in a dense network (lower mesh size limit of 4.6 nm). Overhauser dynamic nuclear polarization-enhanced NMR relaxometry revealed a reduced local solvent water diffusivity near 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO)-labeled nanoparticles trapped in the dense network, showing that heterogeneity in the physical network is also reflected in heterogeneous self-diffusivity of water. The observed heterogeneity in mesh sizes and in water self-diffusivity is of interest for understanding and modeling of transport through and release of solutes from heterogeneous biopolymer gels.

Quantitative Assessment of Nanoparticle Biodistribution by Fluorescence Imaging, Revisited

Fluorescence-based whole-body imaging is widely used in the evaluation of nanoparticles (NPs) in small animals, often combined with quantitative analysis to indicate their spatiotemporal distribution following systemic administration. An underlying assumption is that the fluorescence label represents NPs and the intensity increases with the amount of NPs and/or the labeling dyes accumulated in the region of interest. We prepare DiR-loaded poly(lactic- co-glycolic acid) (PLGA) NPs with different surface layers (polyethylene glycol with and without folate terminus) and compare the distribution of fluorescence signals in a mouse model of folate-receptor-expressing tumors by near-infrared fluorescence whole-body imaging. Unexpectedly, we observe that fluorescence distribution patterns differ far more dramatically with DiR loading than with the surface ligand, reaching opposite conclusions with the same type of NPs (tumor-specific delivery vs predominant liver accumulation). Analysis of DiR-loaded PLGA NPs reveals that fluorescence quenching, dequenching, and signal saturation, which occur with the increasing dye content and local NP concentration, are responsible for the conflicting interpretations. This study highlights the critical need for validating fluorescence labeling of NPs in the quantitative analysis of whole-body imaging. In light of our observation, we make suggestions for future whole-body fluorescence imaging in the in vivo evaluation of NP behaviors.

Analysis of Active Transport by Fluorescence Recovery after Photobleaching

Fluorescence recovery after photobleaching (FRAP) is a well-established experimental technique to study binding and diffusion of molecules in cells. Although a large number of analytical and numerical models have been developed to extract binding and diffusion rates from FRAP recovery curves, active transport of molecules is typically not included in the existing models that are used to estimate these rates. Here we present a validated numerical method for estimating diffusion, binding/unbinding rates, and active transport velocities using FRAP data that captures intracellular dynamics through partial differential equation models. We apply these methods to transport and localization of mRNA molecules in Xenopus laevis oocytes, where active transport processes are essential to generate developmental polarity. By providing estimates of the effective velocities and diffusion, as well as expected run times and lengths, this approach can help quantify dynamical properties of localizing and nonlocalizing RNA. Our results confirm the distinct transport dynamics in different regions of the cytoplasm, and suggest that RNA movement in both the animal and vegetal directions may influence the timescale of RNA localization in Xenopus oocytes. We also show that model initial conditions extracted from FRAP postbleach intensities prevent underestimation of diffusion, which can arise from the instantaneous bleaching assumption. The numerical and modeling approach presented here to estimate parameters using FRAP recovery data is a broadly applicable tool for systems where intracellular transport is a key molecular mechanism.

Interplay between flow and diffusion in capillary alginate hydrogels

Alginate gels with naturally occurring macroscopic capillaries have been used as a model system to study the interplay between laminar flow and diffusion of nanometer-sized solutes in real time. Calcium alginate gels that contain homogeneously distributed parallel-aligned capillary structures were formed by external addition of crosslinking ions to an alginate sol. The effects of different flow rates (0, 1, 10, 50 and 100 μl min(-1)) and three different probes (fluorescein, 10 kDa and 500 kDa fluorescein isothiocyanate-dextran) on the diffusion rates of the solutes across the capillary wall and in the bulk gel in between the capillaries were investigated using confocal laser scanning microscopy. The flow in the capillaries was produced using a syringe pump that was connected to the capillaries via a tube. Transmission electron microscopy revealed an open aggregated structure close to the capillary wall, followed by an aligned network layer and the isotropic network of the bulk gel. The most pronounced effect was observed for the 1 nm-diameter fluorescein probe, for which an increase in flow rate increased the mobility of the probe in the gel. Fluorescence recovery after photobleaching confirmed increased mobility close to the channel, with increasing flow rate. Mobility maps derived using raster image correlation spectroscopy showed that the layer with the lowest mobility corresponded to the anisotropic layer of ordered network chains. The combination of microscopy techniques used in the present study elucidates the flow and diffusion behaviors visually, qualitatively and quantitatively, and represents a promising tool for future studies of mass transport in non-equilibrium systems.

Complex Coacervate Core Micelles with Spectroscopic Labels for Diffusometric Probing of Biopolymer Networks

We present the design, preparation, and characterization of two types of complex coacervate core micelles (C3Ms) with cross-linked cores and spectroscopic labels and demonstrate their use as diffusional probes to investigate the microstructure of percolating biopolymer networks. The first type consists of poly(allylamine hydrochloride) (PAH) and poly(ethylene oxide)-poly(methacrylic acid) (PEO-b-PMAA), labeled with ATTO 488 fluorescent dyes. We show that the size of these probes can be tuned by choosing the length of the PEO-PMAA chains. ATTO 488-labeled PEO113-PMAA15 micelles are very bright with 18 dye molecules incorporated into their cores. The second type is a (19)F-labeled micelle, for which we used PAH and a (19)F-labeled diblock copolymer tailor-made from poly(ethylene oxide)-poly(acrylic acid) (mPEO79-b-PAA14). These micelles contain approximately 4 wt % of (19)F and can be detected by (19)F NMR. The (19)F labels are placed at the end of a small spacer to allow for the necessary rotational mobility. We used these ATTO- and (19)F-labeled micelles to probe the microstructures of a transient gel (xanthan gum) and a cross-linked, heterogeneous gel (κ-carrageenan). For the transient gel, sensitive optical diffusometry methods, including fluorescence correlation spectroscopy, fluorescence recovery after photobleaching, and super-resolution single nanoparticle tracking, allowed us to measure the diffusion coefficient in networks with increasing density. From these measurements, we determined the diameters of the constituent xanthan fibers. In the heterogeneous κ-carrageenan gels, bimodal nanoparticle diffusion was observed, which is a signpost of microstructural heterogeneity of the network.

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.

Diffusion of macromolecules in self-assembled cellulose/hemicellulose hydrogels

Cellulose hydrogels are extensively applied in many biotechnological fields and are also used as models for plant cell walls. We synthesised model cellulosic hydrogels containing hemicelluloses, as a biomimetic of plant cell walls, in order to study the role of hemicelluloses on their mass transport properties. Microbial cellulose is able to self-assemble into composites when hemicelluloses, such as xyloglucan and arabinoxylan, are present in the incubation media, leading to hydrogels with different nano and microstructures. We investigated the diffusivities of a series of fluorescently labelled dextrans, of different molecular weight, and proteins, including a plant pectin methyl esterase (PME), using fluorescence recovery after photobleaching (FRAP). The presence of xyloglucan, known to be able to crosslink cellulose fibres, confirmed by scanning electron microscopy (SEM) and (13)C NMR, reduced mobility of macromolecules of molecular weight higher than 10 kDa, reflected in lower diffusion coefficients. Furthermore PME diffusion was reduced in composites containing xyloglucan, despite the lack of a particular binding motif in PME for this polysaccharide, suggesting possible non-specific interactions between PME and this hemicellulose. In contrast, hydrogels containing arabinoxylan coating cellulose fibres showed enhanced diffusivity of the molecules studied. The different diffusivities were related to the architectural features found in the composites as a function of polysaccharide composition. Our results show the effect of model hemicelluloses in the mass transport properties of cellulose networks in highly hydrated environments relevant to understanding the role of hemicelluloses in the permeability of plant cell walls and aiding design of plant based materials with tailored properties.

Probe diffusion in phase-separated bicontinuous biopolymer gels

Probe diffusion was determined in phase separated bicontinuous gels prepared by acid-induced gelation of the whey protein isolate-gellan gum system. The topological characterization of the phase-separated gel systems is achieved by confocal microscopy and the diffusion measurements are performed using pulsed field gradient (PFG) NMR and fluorescence recovery after photo-bleaching (FRAP). These two techniques gave complementary information about the mass transport at different time- and length scales, PFG NMR provided global diffusion rates in the gel systems, while FRAP enabled the measurements of diffusion in different phases of the phase-separated gels. The results revealed that the phase-separated gel with the largest characteristic wavelength had the fastest diffusion coefficient, while the gel with smaller microstructures had a slower probe diffusion rate. By using the diffusion data obtained by FRAP and the structural data from confocal microscopy, modelling through the lattice-Boltzmann framework was carried out to simulate the global diffusion and verify the validity of the experimental measurements. With this approach it was found that discrepancies between the two experimental techniques can be rationalized in terms of probe distribution between the different phases of the system. The combination of different techniques allowed the determination of diffusion in a phase-separated biopolymer gel and gave a clearer picture of this complex system. We also illustrate the difficulties that can arise if precautions are not taken to understand the system-probe interactions.

Interactions and diffusion in fine-stranded β-lactoglobulin gels determined via FRAP and binding

The effects of electrostatic interactions and obstruction by the microstructure on probe diffusion were determined in positively charged hydrogels. Probe diffusion in fine-stranded gels and solutions of β-lactoglobulin at pH 3.5 was determined using fluorescence recovery after photobleaching (FRAP) and binding, which is widely used in biophysics. The microstructures of the β-lactoglobulin gels were characterized using transmission electron microscopy. The effects of probe size and charge (negatively charged Na2-fluorescein (376Da) and weakly anionic 70kDa FITC-dextran), probe concentration (50 to 200 ppm), and β-lactoglobulin concentration (9% to 12% w/w) on the diffusion properties and the electrostatic interaction between the negatively charged probes and the positively charged gels or solutions were evaluated. The results show that the diffusion of negatively charged Na2-fluorescein is strongly influenced by electrostatic interactions in the positively charged β-lactoglobulin systems. A linear relationship between the pseudo-on binding rate constant and the β-lactoglobulin concentration for three different probe concentrations was found. This validates an important assumption of existing biophysical FRAP and binding models, namely that the pseudo-on binding rate constant equals the product of the molecular binding rate constant and the concentration of the free binding sites. Indicators were established to clarify whether FRAP data should be analyzed using a binding-diffusion model or an obstruction-diffusion model.

Microstructural, mechanical and mass transport properties of isotropic and capillary alginate gels

Macroscopically homogeneous and inhomogeneous calcium alginate gels are formed via internal or external addition of various amounts of calcium to an alginate solution. The externally formed gels contain parallel aligned capillary structures. The mechanical and mass transport properties and the microstructure of the differently set gels were characterized by rheological measurements, fluorescence recovery after photobleaching (FRAP) and transmission electron microscopy (TEM). TEM images show a zone of distorted anisotropic gel structure in the vicinity of the capillaries as well as indications of a lower degree of void connectivity. The diffusion rates of dextran at large distances from the capillaries were fast and capillary gels showed a plastic behaviour in comparison to the internally set gels. The results presented show large functional differences between the internally and externally set gels, which cannot be explained by the presence of capillaries alone.

Straightforward FRAP for quantitative diffusion measurements with a laser scanning microscope

Confocal or multi-photon laser scanning microscopes are convenient tools to perform FRAP diffusion measurements. Despite its popularity, accurate FRAP remains often challenging since current methods are either limited to relatively large bleach regions or can be complicated for non-specialists. In order to bring reliable quantitative FRAP measurements to the broad community of laser scanning microscopy users, here we have revised FRAP theory and present a new pixel based FRAP method relying on the photo bleaching of rectangular regions of any size and aspect ratio. The method allows for fast and straightforward quantitative diffusion measurements due to a closed-form expression for the recovery process utilizing all available spatial and temporal data. After a detailed validation, its versatility is demonstrated by diffusion studies in heterogeneous biopolymer mixtures.

Pixel-based analysis of FRAP data with a general initial bleaching profile

In Jonasson et al. (2008), we presented a new pixel-based maximum likelihood framework for the estimation of diffusion coefficients from data on fluorescence recovery after photobleaching (FRAP) with confocal laser scanning microscopy (CLSM). The main method there, called the Gaussian profile method below, is based on the assumption that the initial intensity profile after photobleaching is approximately Gaussian. In the present paper, we introduce a method, called the Monotone profile method, where the maximum likelihood framework is extended to a general initial bleaching profile only assuming that the profile is a non-decreasing function of the distance to the bleaching centre. The statistical distribution of the image noise is further assumed to be Poisson instead of normal, which should be a more realistic description of the noise in the detector. The new Monotone profile method and the Gaussian profile method are applied to FRAP data on swelling of super absorbent polymers (SAP) in water with a Fluorescein probe. The initial bleaching profile is close to a step function at low degrees of swelling and close to a Gaussian profile at high degrees of swelling. The results obtained from the analysis of the FRAP data are corroborated with NMR diffusometry analysis of SAP with a polyethylene glycol probe having size similar to the Fluorescein. The comparison of the Gaussian and Monotone profile methods is also performed by use of simulated data. It is found that the new Monotone profile method is accurate for all types of initial profiles studied, but it suffers from being computationally slow. The fast Gaussian profile method is sufficiently accurate for most of the profiles studied, but underestimates the diffusion coefficient for profiles close to a step function. We also provide a diagnostic plot, which indicates whether the Gaussian profile method is acceptable or not.

Determination of local diffusion properties in heterogeneous biomaterials

The coupling between structure and diffusion properties is essential for the functionality of heterogeneous biomaterials. Structural heterogeneity is defined and its implications for time-dependent diffusion are discussed in detail. The effect of structural heterogeneity in biomaterials on diffusion and the relevance of length scales are exemplified with regard to different biomaterials such as gels, emulsions, phase separated biopolymer mixtures and chocolate. Different diffusion measurement techniques for determination of diffusion properties at different length and time scales are presented. The interplay between local and global diffusion is discussed. New measurement techniques have emerged that enable simultaneous determination of both structure and local diffusion properties. Special emphasis is given to fluorescence recovery after photobleaching (FRAP). The possibilities of FRAP at a conceptual level is presented. The method of FRAP is briefly reviewed and its use in heterogeneous biomaterials, at barriers and during dynamic changes of the structure is discussed.