Determination of local diffusion properties in heterogeneous biomaterials

Optimization of Media Change Intervals through Hydrogels Using Mathematical Models

Three-dimensional cell culture in engineered hydrogels is increasingly used in tissue engineering and regenerative medicine. The transfer of nutrients, gases, and waste materials through these hydrogels is of utmost importance for cell viability and response, yet the translation of diffusion coefficients into practical guidelines is not well established. Here, we combined mathematical modeling, fluorescent recovery after photobleaching, and hydrogel diffusion experiments on cell culture inserts to provide a multiscale practical approach for diffusion. We observed a dampening effect of the hydrogel that slowed the response to concentration changes and the creation of a diffusion gradient in the hydrogel by media refreshment. Our designed model combined with measurements provides a practical point of reference for diffusion coefficients in real-world culture conditions, enabling more informed choices on hydrogel culture conditions. This model can be improved in the future to simulate more complicated intrinsic hydrogel properties and study the effects of secondary interactions on the diffusion of analytes through the hydrogel.

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.

Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels

We present a numerical study on the effect of hydrodynamic interactions (HI) on the diffusion of inert point tracer particles in several fixed random structures. As expected, the diffusion is hampered by the extra hydrodynamic friction introduced by the obstacle network. However, a non-trivial effect due to HI appears in the analysis of the van-Hove displacement probability close to the percolation threshold, where tracers diffuse through critical fractal paths. We show that the tracer dynamics can be split up into short and long jumps, the latter being ruled by either exponential or Gaussian van Hove distribution tails. While at short time HI slow down the tracer diffusion, at long times, hydrodynamic interactions with the obstacles increase the probability of longer jumps, which circumvent the traps of the labyrinth more easily. Notably, the relation between the anomalous diffusion exponent and the fractal dimension of the critical (intricate) paths is greater than one, which implies that the long-time (long-jump) diffusion is mildly superdiffuse. A possible reason for such a hastening of the diffusion along the network corridors is the hydrodynamically induced mobility anisotropy, which favours displacements parallel to the walls, an effect which has already been experimentally observed in collagen gels.

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.

Spatiotemporal Heterogeneity of κ-Carrageenan Gels Investigated via Single-Particle-Tracking Fluorescence Microscopy

Hydrogels made of the polysaccharide κ-carrageenan are widely used in the food and personal care industry as thickeners or gelling agents. These hydrogels feature dense regions embedded in a coarser bulk network, but the characteristic size and behavior of these regions have remained elusive. Here, we use single-particle-tracking fluorescence microscopy (sptFM) to quantitatively describe κ-carrageenan gels. Infusing fluorescent probes into fully gelated κ-carrageenan hydrogels resulted in two distinct diffusional behaviors. Obstructed self-diffusion of the probes revealed that the coarse network consists of κ-carrageenan strands with a typical diameter of 3.2 ± 0.3 nm leading to a nanoprobe diffusion coefficient of ∼1-5 × 10^-12 m²/s. In the dense network regions, we found a fraction with a largely decreased diffusion coefficient of ∼1 × 10^-13 m²/s. We also observed dynamic exchange between these states. The computation of spatial mobility maps from the diffusional data indicated that the dense network regions have a characteristic diameter of ∼1 μm and show mobility on the second-to-minute timescale. sptFM provides an unprecedented view of spatiotemporal heterogeneity of hydrogel networks, which we believe bears general relevance for understanding transport and release of both low- and high-molecular weight solutes.

Complex Diffusion in Bacteria

Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this is far from the truth. Here we shed light on the complexity and importance of diffusion in bacteria, illustrating the similarities and differences of diffusive behaviors of molecules within different compartments of bacterial cells. We first describe common methodologies used to probe diffusion and the associated models and analyses. We then discuss distinct diffusive behaviors of molecules within different bacterial cellular compartments, highlighting the influence of metabolism, size, crowding, charge, binding, and more. We also explicitly discuss where further research and a united understanding of what dictates diffusive behaviors across the different compartments of the cell are required, pointing out new research avenues to pursue.

Core-sheath gelatin based electrospun nanofibers for dual delivery release of biomolecules and therapeutics

Coaxial electrospinning with the ability to use simultaneously two separate solvents provides a promising strategy for drug delivery. Nevertheless, controlled release of hydrophilic and sensitive therapeutics from slow biodegradable polymers is still challenging. To address this gap, we fabricated core-sheath fibers for dual delivery of lysozyme, as a model protein, and phenytoin sodium as a small therapeutic molecule. The sheath was processed by a gelatin solution while the core fibers were fabricated from an aqueous gelatin/PVA solution. Microstructural studies by transmission and scanning electron microscopy reveal the formation of homogeneous core-sheath nanofibers with an outer and inner diameter of 180 ± 48 nm and 106 ± 30 nm, respectively. Thermal gravimetric analysis determines that the mass loss of the core-sheath fibers fall between the mass loss values of individual sheath and core fibers. Swelling studies indicate higher water absorption of the core-sheath mat compared to the separate sheath and core membranes. In vitro drug release studies in Phosphate Buffered Saline (PBS) determine sustained release of the therapeutics from the core-sheath structure. The release trails three stages including non-Fickian diffusion at the early stage followed by the Fickian diffusion mechanism. The present study shows a useful approach to design core-sheath nanofibrous membranes with controlled and programmable drug release profiles.

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.

Dual-functional core-shell electrospun mats with precisely controlled release of anti-inflammatory and anti-bacterial agents

Acute wounds are worldwide problems affecting millions of people and causing heavy economic burden to national healthcare systems. Herein, we describe novel wound dressing materials relying on core/shell electrospun mats incorporated with flurbiprofen and vancomycin for achieving programmable release of anti-inflammatory and anti-bacterial agents. The shell matrix of nanofibers consisted of polyethylene oxide while the core matrix was made from a blend of silk and collagen. Several optimal mat architectures were engineered with distinct configurations, of which release profiles displayed an exponential trend, which indicates a first-order process following Fickian diffusion behavior. The flurbiprofen release lasted from 2 to 6 days, which was much faster compared to the one of vancomycin prolonged up to about 20 days. Mechanical data indicated tensile modulus, tensile strength, elongation before break of core/shell electrospun mats became enhanced or comparable to those for human skin after methanol vapor treatment. Desirable release kinetics and mechanical characteristics achieved by novel core/shell electrospun mats were attributable to induced enrichment of β-sheet phase in silk via methanol vapor treatment as well as water annealing process with time and judicious selections for matrix materials and mat configurations. The design principles considered in this study successfully addressed a range of inflammation and infection requirements in wound healing, potentially guiding construction of other biomedical coatings and devices.

A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media

This work numerically investigates the diffusion of finite inert tracer particles in different types of fixed gels. The mean square displacement (MSD) of the tracers reveals a transition to subdiffusive motion MSD ∼ tα as soon as the accessible volume fraction p in the gel decreases from unity. Individual tracer dynamics reveals two types of particles in the gels: mobile tracers cross the system through percolating pores following subdiffusive dynamics MSDmob ∼ tαmob, while a fraction ptrap(p) of the particles remain trapped in finite pores. Below the void percolation threshold p < pc all the particles get trapped and α → 0. By separately studying both populations we find a simple phenomenological law for the mobile tracers αmob(p) ≈ a ln p + c where c ≈ 1 and a ∼ 0.2 depends on the gel type. On the other hand, a cluster-analysis of the gel accessible volume reveals a power law for the trapping probability ptrap ∼ (p/pc)-γ, with γ ≃ 2.9. This yields a prediction for the ensemble averaged subdiffusion exponent α = αmob(1 - ptrap). Our predictions are successfully validated against the different gels studied here and against numerical and experimental results in the literature (silica gels, polyacrylamide gels, flexible F-actin networks and in different random obstacles). Notably, the parameter a ∼ 0.2 presents small differences amongst all these cases, indicating the robustness of the proposed relation.

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.

Engineering the Future of Silk Materials through Advanced Manufacturing

Silk is a natural fiber renowned for its outstanding mechanical properties that have enabled the manufacturing of ultralight and ultrastrong textiles. Recent advances in silk processing and manufacturing have underpinned a re-interpretation of silk from textiles to technological materials. Here, it is argued that silk materials-optimized by selective pressure to work in the environment at the biotic-abiotic interface-can be harnessed by human micro- and nanomanufacturing technology to impart new functionalities and opportunities. A critical overview of recent progress in silk technology is presented with emphasis on high-tech applications enabled by recent innovations in multilevel modifications, multiscale manufacturing, and multimodal characterization of silk materials. These advances have enabled successful demonstrations of silk materials across several disciplines, including tissue engineering, drug delivery, implantable medical devices, and biodissolvable/degradable devices.

Directed assembly of bio-inspired hierarchical materials with controlled nanofibrillar architectures

In natural systems, directed self-assembly of structural proteins produces complex, hierarchical materials that exhibit a unique combination of mechanical, chemical and transport properties. This controlled process covers dimensions ranging from the nano- to the macroscale. Such materials are desirable to synthesize integrated and adaptive materials and systems. We describe a bio-inspired process to generate hierarchically defined structures with multiscale morphology by using regenerated silk fibroin. The combination of protein self-assembly and microscale mechanical constraints is used to form oriented, porous nanofibrillar networks within predesigned macroscopic structures. This approach allows us to predefine the mechanical and physical properties of these materials, achieved by the definition of gradients in nano- to macroscale order. We fabricate centimetre-scale material geometries including anchors, cables, lattices and webs, as well as functional materials with structure-dependent strength and anisotropic thermal transport. Finally, multiple three-dimensional geometries and doped nanofibrillar constructs are presented to illustrate the facile integration of synthetic and natural additives to form functional, interactive, hierarchical networks.

Single particle raster image analysis of diffusion

As a complement to the standard RICS method of analysing Raster Image Correlation Spectroscopy images with estimation of the image correlation function, we introduce the method SPRIA, Single Particle Raster Image Analysis. Here, we start by identifying individual particles and estimate the diffusion coefficient for each particle by a maximum likelihood method. Averaging over the particles gives a diffusion coefficient estimate for the whole image. In examples both with simulated and experimental data, we show that the new method gives accurate estimates. It also gives directly standard error estimates. The method should be possible to extend to study heterogeneous materials and systems of particles with varying diffusion coefficient, as demonstrated in a simple simulation example. A requirement for applying the SPRIA method is that the particle concentration is low enough so that we can identify the individual particles. We also describe a bootstrap method for estimating the standard error of standard RICS.

Structural and water diffusion of poly(acryl amide)/poly(vinyl alcohol) blend films: Experiment and molecular dynamics simulations

To study the effects of composition ratios and temperature on the diffusion of water molecules in PVA/PAM blend films, five simulation models of PVA/PAM with ten water molecules at different composition ratios (4/0, 3/1, 2/2, 1/3, 0/4) were constructed and simulated by using a molecular dynamics (MD) simulation. The diffusion behavior of water molecules in blends were investigated from the aspects of the diffusion coefficient, free volume, pair correlation function (PCF) and trajectories of water molecules, respectively. And the hydrophilicity of blend composite was studied based on the contact angle and equilibrium water content (EWC) of the blend films. The simulation results show that the diffusion coefficient of water molecules and fractional free volume (FFV) of blend membranes increase with the addition of PAM, and a higher temperature can also improve the diffusion of water molecules. Additionally, the analysis of PCFs reveals the main reason why the diffusion coefficient of water in blend system increases with the addition of PAM. The measurement results of contact angle and EWC of blend films indicate that the hydrophilicity of blend films decreases with the addition of PAM, but the EWC of blends increases with the addition of PAM.

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.

Flexibility and Charge of Solutes as Factors That Determine Their Diffusion in Casein Suspensions and Gels

This work explores the influence of both the physicochemical characteristics of solutes and the solute-matrix interactions on diffusion in casein systems. Diffusion coefficients of three solute groups (dextrans, proteins, and peptides) presenting different physicochemical characteristics, such as molecular flexibility and charge, were measured using the technique of fluorescence recovery after photobleaching (FRAP). The casein systems had the same casein concentration, but different microstructures (suspension or gel), and/or a different pH (5.2 or 6.6). Flexible solutes diffused more rapidly through the casein systems than the rigid ones. Electrostatic interactions between charged solute molecules and the casein matrix were partly screened due to the high ionic strength of the systems. As a consequence, it was the flexibility of the solute molecule (rather than its charge) that most influenced its diffusion through casein systems.

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.

Complex coacervate core micelles as diffusional nanoprobes

Because of their ease of preparation and versatile modification opportunities, complex coacervate core micelles (C3Ms) may be a good alternative for expensive diffusional probes, such as dendrimers. However, C3Ms are unstable at high salt concentrations and may fall apart in contact with other polymers or (solid) materials. Therefore, we designed and characterized small (15 nm radius), stable fluorescent C3Ms. These were formed by electrostatic interactions between poly(ethylene oxide-methacrylic acid) (PEO-PMAA) and fluorescently labelled poly(allylamine hydrochloride) (PAH) and irreversible cross-linking of the core through amide bonds. We compared the properties of the cross-linked and non-cross-linked micelles. The radii of the two types of micelles were quite similar and independent of the ionic strength. Surprisingly, both were found to be stable at salt concentrations as high as 1.5 M. However, unlike the non-cross-linked C3Ms, the stability of the cross-linked C3Ms is independent of the pH. As a first example of their application as diffusional nanoprobes, we present results on the diffusion of the fluorescent micelles measured in xanthan solutions using fluorescence recovery after photobleaching (FRAP).

MRI of plants and foods

The importance and prospects for MRI as applied to intact plants and to foods are presented in view of one of humanity's most pressing concerns, the sustainable and healthy feeding of a worldwide increasing population. Intact plants and foods have in common that their functionality is determined by complex multiple length scale architectures. Intact plants have an additional level of complexity since they are living systems which critically depend on transport and signalling processes between and within tissues and organs. The combination of recent cutting-edge technical advances and integration of MRI accessible parameters has the perspective to contribute to breakthroughs in understanding complex regulatory plant performance mechanisms. In food science and technology MRI allows for quantitative multi-length scale structural assessment of food systems, non-invasive monitoring of heat and mass transport during shelf-life and processing, and for a unique view on food properties under shear. These MRI applications are powerful enablers of rationally (re)designed food formulations and processes. Limitations and bottlenecks of the present plant and food MRI methods are mainly related to short T2 values and susceptibility artefacts originating from small air spaces in tissues/materials. We envisage cross-fertilisation of solutions to overcome these hurdles in MRI applications in plants and foods. For both application areas we witness a development where MRI is moving from highly specialised equipment to mobile and downscaled versions to be used by a broad user base in the field, greenhouse, food laboratory or factory.

Synthesis and characterization of a hydrogel with controllable electroosmosis: a potential brain tissue surrogate for electrokinetic transport

Electroosmosis is the bulk fluid flow initiated by application of an electric field to an electrolyte solution in contact with immobile objects with a nonzero ζ-potential such as the surface of a porous medium. Electroosmosis may be used to assist analytical separations. Several gel-based systems with varying electroosmotic mobilities have been made in this context. A method was recently developed to determine the ζ-potential of organotypic hippocampal slice cultures (OHSC) as a representative model for normal brain tissue. The ζ-potential of the tissue is significant. However, determining the role of the ζ-potential in solute transport in tissue in an electric field is difficult because the tissue's ζ-potential cannot be altered. We hypothesized that mass transport properties, namely the ζ-potential and tortuosity, could be modulated by controlling the composition of a set of hydrogels. Thus, poly(acrylamide-co-acrylic acid) gels were prepared with three compositions (by monomer weight percent): acrylamide/acrylic acid 100/0, 90/10, and 75/25. The ζ-potentials of these gels at pH 7.4 are distinctly different, and in fact vary approximately linearly with the weight percent of acrylic acid. We discovered that the 25% acrylic acid gel is a respectable model for brain tissue, as its ζ-potential is comparable to the OHSC. This series of gels permits the experimental determination of the importance of electrokinetic properties in a particular experiment or protocol. Additionally, tortuosities were measured electrokinetically and by evaluating diffusion coefficients. Hydrogels with well-defined ζ-potential and tortuosity may find utility in biomaterials and analytical separations, and as a surrogate model for OHSC and living biological tissues.

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

Fluorescence recovery after photobleaching (FRAP) carried out on a confocal laser-scanning microscope (CLSM) performs well for photobleached disks that are large compared to the resolution of the bleaching beam. For smaller disks approaching this resolution, current FRAP models providing a closed-form solution do not allow one to extract the diffusion coefficient accurately. The new generalized disk model we present addresses this shortcoming by bringing into account the bleaching resolution and the total confocal imaging resolution. A closed-form solution is obtained under the assumption of linear photobleaching. Furthermore, simultaneous analysis of FRAP data collected at various disk sizes allows for the intrinsic determination of the instrumental resolution parameters, thereby obviating the need for an extrinsic calibration. A new method to estimate the variance of FRAP data is introduced to allow for proper weighting in this global analysis approach by nonlinear least squares. Experiments are performed on two independent CLSMs on homogeneous samples providing validation over a large range of diffusion coefficients.

Erratum to: Hydrodynamic dispersion in β-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through β-lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

Hydrodynamic dispersion in β-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through [Formula: see text] -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

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.

Uptake of tritiated liquids by individual breakfast cereal flakes

Surface liquid adhesion (SLA) and liquid absorption (LA) of tritiated liquids, including water and skim, low-fat, whole, and fat-enriched milks, by cornflakes (CF) and frosted flakes (FF) were determined by scintillation counting using water-[(3)H] at 0.5 microCi/mL. SLA or the liquid adhering to individual flakes after a short immersion period was the same for CF and FF in the case of water (approximately 0.011 microL mm(-2) of flake) but were always higher for CF than for FF and increased as the fat content in milks augmented. LA of individual flakes, followed for 300 s of soaking, increased with time and was always higher for CF than for FF (for the same liquid), however, data did not follow a regular pattern. Flakes showed quite compact outer surfaces and an internal porous matrix composed of air cells of various sizes separated by dense walls of different thicknesses. This heterogeneous microstructure of individual flakes may be the cause of the lack of a simple kinetics during the soaking process. Previous results obtained by soaking a mass of flakes overestimated the uptake of fluid by individual because they included the liquid occluded between the flakes.

Effects of macromolecular crowding on intracellular diffusion from a single particle perspective

Compared to biochemical reactions taking place in relatively well-defined aqueous solutions in vitro, the corresponding reactions happening in vivo occur in extremely complex environments containing only 60-70% water by volume, with the remainder consisting of an undefined array of bio-molecules. In a biological setting, such extremely complex and volume-occupied solution environments are termed 'crowded'. Through a range of intermolecular forces and pseudo-forces, this complex background environment may cause biochemical reactions to behave differently to their in vitro counterparts. In this review, we seek to highlight how the complex background environment of the cell can affect the diffusion of substances within it. Engaging the subject from the perspective of a single particle's motion, we place the focus of our review on two areas: (1) experimental procedures for conducting single particle tracking experiments within cells along with methods for extracting information from these experiments; (2) theoretical factors affecting the translational diffusion of single molecules within crowded two-dimensional membrane and three-dimensional solution environments. We conclude by discussing a number of recent publications relating to intracellular diffusion in light of the reviewed material.