Modeling solute diffusion in aqueous polymer solutions

Nanoscale water-polymer interactions tune macroscopic diffusivity of water in aqueous poly(ethylene oxide) solutions

The separation and anti-fouling performance of water purification membranes is governed by both macroscopic and molecular-scale water properties near polymer surfaces. However, even for poly(ethylene oxide) (PEO) - ubiquitously used in membrane materials - there is little understanding of whether or how the molecular structure of water near PEO surfaces affects macroscopic water diffusion. Here, we probe both time-averaged bulk and local water dynamics in dilute and concentrated PEO solutions using a unique combination of experimental and simulation tools. Pulsed-Field Gradient NMR and Overhauser Dynamic Nuclear Polarization (ODNP) capture water dynamics across micrometer length scales in sub-seconds to sub-nanometers in tens of picoseconds, respectively. We find that classical models, such as the Stokes-Einstein and Mackie-Meares relations, cannot capture water diffusion across a wide range of PEO concentrations, but that free volume theory can. Our study shows that PEO concentration affects macroscopic water diffusion by enhancing the water structure and altering free volume. ODNP experiments reveal that water diffusivity near PEO is slower than in the bulk in dilute solutions, previously not recognized by macroscopic transport measurements, but the two populations converge above the polymer overlap concentration. Molecular dynamics simulations reveal that the reduction in water diffusivity occurs with enhanced tetrahedral structuring near PEO. Broadly, we find that PEO does not simply behave like a physical obstruction but directly modifies water's structural and dynamic properties. Thus, even in simple PEO solutions, molecular scale structuring and the impact of polymer interfaces is essential to capturing water diffusion, an observation with important implications for water transport through structurally complex membrane materials.

Nanogels designed for cell-free nucleic acid sequestration

Chronic wounds exhibit over-expression of cell-free deoxyribonucleic acid (cfDNA), leading to a prolonged inflammation and non-healing wounds. Scavenging excessive cfDNA molecules is a promising strategy for chronic wound treatment. Nanoscopic particles act as efficient cfDNA scavengers due to their large surface area, however their efficiency in cfDNA uptake was limited by adsorption solely on the nanoparticle surface. In contrast, nanogels may provide multiple cfDNA binding sites in the nanoparticle interior, however their use for cfDNA scavenging is yet to be explored. Herein, we report cationic nanogels derived from a copolymer of chitosan and poly{2-[(acryloyloxy)ethyl]trimethylammonium chloride} end-grafted to the chitosan backbone as side chains. The nanogels retain their positive charge at the pH and ionic strength of chronic wound exudate, enabling electrostatically driven cfDNA scavenging. The network structure of the nanogels leads to the cfDNA sequestration in the nanogel interior, in addition to surface attachment. A key factor in cfDNA sequestration is the ratio of the pore size of the nanogel-to-cfDNA molecular dimensions. The enhanced cfDNA scavenging efficiency, along with biocompatibility of the nanogels, makes them a promising component of dressings for chronic wound treatment.

Enhancing the Understanding of Soil Nitrogen Fate Using a 3D-Electrospray Sensor Roll Casted with a Thin-Layer Hydrogel

Accurate and continuous monitoring of soil nitrogen is critical for determining its fate and providing early warning for swift soil nutrient management. However, the accuracy of existing electrochemical sensors is hurdled by the immobility of targeted ions, ion adsorption to soil particles, and sensor reading noise and drifting over time. In this study, polyacrylamide hydrogel with a thickness of 0.45 μm was coated on the surface of solid-state ion-selective membrane (S-ISM) sensors to absorb water contained in soil and, consequently, enhance the accuracy (R² > 0.98) and stability (drifting < 0.3 mV/h) of these sensors monitoring ammonium (NH₄⁺) and nitrate (NO₃^-) ions in soil. An ion transport model was built to simulate the long-term NH₄⁺ dynamic process (R² > 0.7) by considering the soil adsorption process and soil complexity. Furthermore, a soil-based denoising data processing algorithm (S-DDPA) was developed based on the unique features of soil sensors including the nonlinear mass transfer and ion diffusion on the heterogeneous sensor-hydrogel-soil interface. The 14 day tests using real-world soil demonstrated the effectiveness of S-DDPA to eliminate false signals and retrieve the actual soil nitrogen information for accurate (error: <2 mg/L) and continuous monitoring.

Effects of Macromolecular Crowding on Nanoparticle Diffusion: New Insights from Mössbauer Spectroscopy

In this work, we used Mössbauer spectroscopy as a new approach for experimental quantification of the self-diffusion coefficient (D_Mössbauer) and hydrodynamic (HD) size of iron-containing nanoparticles (NPs) in complex crowded solutions, mimicking cell cytoplasm. As a probe, we used 9 nm cobalt ferrite NPs (CFNs) dispersed in solutions of bovine serum albumin (BSA) with a volume fraction (φ_BSA) of 0-0.2. Our results show that the broadening of Mössbauer spectra is highly sensitive to the diffusion of CFNs, while when φ_BSA = 0.2, the CFN-normalized diffusivity is reduced by 86% compared to that of a protein-free solution. CFN colloids were also studied by dynamic light scattering (DLS). Comparison of the experimental data shows that DLS significantly underestimates the diffusion coefficient of CFNs and, consequently, overestimates the HD size of CFNs at φ_BSA > 0, which cannot be attributed to the formation of the BSA monolayer on the surface of CFNs.

Tuning the permeability of regular polymeric networks by the cross-link ratio

The amount of cross-linking in the design of polymer materials is a key parameter for the modification of numerous physical properties, importantly, the permeability to molecular solutes. We consider networks with a diamond-like architecture and different cross-link ratios, concurring with a wide range of the polymer volume fraction. We particularly focus on the effect and the competition of two independent component-specific solute-polymer interactions, i.e., we distinguish between chain-monomers and cross-linkers, which individually act on the solutes and are altered to cover attractive and repulsive regimes. For this purpose, we employ coarse-grained, Langevin computer simulations to study how the cross-link ratio of polymer networks controls the solute partitioning, diffusion, and permeability. We observe different qualitative behaviors as a function of the cross-link ratio and interaction strengths. The permeability can be tuned ranging over two orders of magnitude relative to the reference bulk permeability. Finally, we provide scaling theories for the partitioning and diffusion that explicitly account for the component-specific interactions as well as the cross-link ratio and the polymer volume fraction. These are in overall good agreement with the simulation results and grant insight into the underlying physics, rationalizing how the cross-link ratio can be exploited to tune the solute permeability of polymeric networks.

Disentangling Nano- and Macroscopic Viscosities of Aqueous Polymer Solutions Using a Fluorescent Molecular Rotor

The macroscopic viscosity of polymer solutions in general differs strongly from the viscosity at the nanometer scale, and the relation between the two can be complicated. To investigate this relation, we use a fluorescent molecular rotor that probes the local viscosity of its molecular environment. For a range of chain lengths and concentrations, the dependence of the fluorescence on the macroscopic viscosity is well described by the classical Förster-Hoffmann (FH) equation, but the value of the FH exponent depends on the polymer chain length. We show that all data can be collapsed onto a master curve by plotting the fluorescence versus polymer concentration, which we explain in terms of the characteristic mesh size of the polymer solution. Using known scaling laws for polymers then allows us to quantitatively explain the relation between the FH exponent and the polymer chain length, allowing us to link the nano- to the macroviscosity.

Effective Dispensing Methods for Loading Drugs Only to the Tip of DNA Microneedles

Here, we propose a novel and simple method to efficiently capture the diffusion of fluorescein isothiocyanate (FITC)-dextran from a biocompatible substance and load the drug only to the tip of DNA microneedles. A dispensing and suction method was chosen to fabricate the designed microneedles with efficient amounts of FITC as the drug model. Importantly, the vacuum process, which could influence the capturing of FITC diffusion from the tip, was evaluated during the manufacturing process. In addition, the simulations were consistent with the experimental results and showed apparent diffusion. Moreover, dextrans of different molecular weights labeled with FITC were chosen to fabricate the tip of microneedles for demonstrating their applicability. Finally, a micro-jetting system with a micro-nozzle (diameter: 80 μm) was developed to achieve the accurate and rapid loading of small amounts of FITC using the anti-diffusion and micro-jetting methods. Our method not only uses a simple and fast manufacturing process, but also fabricates the tips of microneedles more efficiently with FITC compared with the existing methods. We believe that the proposed method is essential for the clinical applications of the microneedle drug delivery platform.

Physical chemistry of gastric digestion of proteins gels

In this paper, we present the rich physics and chemistry of the gastric digestion of protein gels. Knowledge of this matter is important for the development of sustainable protein foods that are based on novel proteins sources like plant proteins or insects. Their digestibility is an important question in the design of these new protein foods. As polyelectrolyte gels, they can undergo volume changes upon shifts in pH or ionic strengths, as protein gels experience when entering the gastric environment. We show that these volume changes can be modelled using the Flory-Rehner theory, combined with Gibbs-Donnan theory accounting for the distribution of electrolytes over gel and bath. In-vitro experiments of soy protein gels in simulated gastric fluid indeed show intricate swelling behaviour, at first the gels show swelling but at longer times they shrink again. Simulations performed with the Flory-Rehner/Gibbs-Donnan theory reproduce qualitatively similar behaviour. In the final part of the paper, we discuss how the model must be extended to model realistic conditions existing in the in-vivo gastric environment.

Nanostructured Polymer Monoliths for Biomedical Delivery Applications

Drug delivery systems are designed to control the release rate and location of therapeutic agents in the body to achieve enhanced drug efficacy and to mitigate adverse side effects. In particular, drug-releasing implants provide sustained and localized release. We report nanostructured polymer monoliths synthesized by polymerization-induced microphase separation (PIMS) as potential implantable delivery devices. As a model system, free poly(ethylene oxide) homopolymers were incorporated into the nanoscopic poly(ethylene oxide) domains contained within a cross-linked polystyrene matrix. The in vitro release of these poly(ethylene oxide) molecules from monoliths was investigated as a function of poly(ethylene oxide) loading and molar mass as well as the molar mass and weight fraction of poly(ethylene oxide) macro-chain transfer agent used in the PIMS process for forming the monoliths. We also developed nanostructured microneedles targeting efficient and long-term transdermal drug delivery by combining PIMS and microfabrication techniques. Finally, given the prominence of poly(lactide) in drug delivery devices, the degradation rate of microphase-separated poly(lactide) in PIMS monoliths was evaluated and compared with bulk poly(lactide).

Predicting Drug Release From Degradable Hydrogels Using Fluorescence Correlation Spectroscopy and Mathematical Modeling

Predicting release from degradable hydrogels is challenging but highly valuable in a multitude of applications such as drug delivery and tissue engineering. In this study, we developed a simple mathematical and computational model that accounts for time-varying diffusivity and geometry to predict solute release profiles from degradable hydrogels. Our approach was to use time snapshots of diffusivity and hydrogel geometry data measured experimentally as inputs to a computational model which predicts release profile. We used two model proteins of varying molecular weights: bovine serum albumin (BSA; 66 kDa) and immunoglobulin G (IgG; 150 kDa). We used fluorescence correlation spectroscopy (FCS) to determine protein diffusivity as a function of hydrogel degradation. We tracked changes in gel geometry over the same time period. Curve fits to the diffusivity and geometry data were used as inputs to the computational model to predict the protein release profiles from the degradable hydrogels. We validated the model using conventional bulk release experiments. Because we approached the hydrogel as a black box, the model is particularly valuable for hydrogel systems whose degradation mechanisms are not known or cannot be accurately modeled.

Adenosine triphosphate diffusion through poly(ethylene glycol) diacrylate hydrogels can be tuned by cross-link density as measured by PFG-NMR

The diffusion of small molecules through hydrogels is of great importance for many applications. Especially in biological contexts, the diffusion of nutrients through hydrogel networks defines whether cells can survive inside the hydrogel or not. In this contribution, hydrogels based on poly(ethylene glycol) diacrylate with mesh sizes ranging from ξ = 1.1 to 12.9 nm are prepared using polymers with number-average molecular weights between M_n = 700 and 8000 g/mol. Precise measurements of diffusion coefficients D of adenosine triphosphate (ATP), an important energy carrier in biological systems, in these hydrogels are performed by pulsed field gradient nuclear magnetic resonance. Depending on the mesh size, ξ, and on the polymer volume fraction of the hydrogel after swelling, ϕ, it is possible to tune the relative ATP diffusion coefficient D/D₀ in the hydrogels to values between 0.14 and 0.77 compared to the ATP diffusion coefficient D₀ in water. The diffusion coefficients of ATP in these hydrogels are compared with predictions of various mathematical expressions developed under different model assumptions. The experimental data are found to be in good agreement with the predictions of a modified obstruction model or the free volume theory in combination with the sieving behavior of the polymer chains. No reasonable agreement was found with the pure hydrodynamic model.

Dynamics of Nanoparticles in Entangled Polymer Solutions

The mean square displacement ⟨r²⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R_g), are investigated. In simple fluids and for polymer solutions in which d ≫ R_g, long-time particle dynamics obey random-walk statistics ⟨r²⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R_g, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales-from diffusion of molecular probes to macroscopic viscous flow-we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

A novel approach to modeling acute normovolemic hemodilution

Acute normovolemic hemodilution (ANH) was introduced as a blood conservation technique to reduce patient exposure to allogenic blood transfusion during surgery. Despite years of research and experience, the best practice procedure, efficacy and safety of ANH remain in question. In this work, a numerical model is developed for the ANH procedure based upon a multi-compartmental, fluid model of the body. The model also analyzes the most commonly used acellular fluids for ANH or for fluid therapy following hemorrhage. The model allows user input of critical ANH parameters, providing the ability to simulate the patient׳s response in real time to many clinical scenarios, using various types of resuscitation fluids. First, the patient׳s response to a representative, clinical ANH protocol and surgery was simulated. Then, the effect of several variables was investigated including: type/amount of resuscitation fluid, number of blood units collected during ANH, and amount of surgical blood loss. Our simulations highlighted the importance of osmotic molecules within the blood in preventing excessive fluid retention and initiating fluid clearance after surgery. The developed model can be utilized as a tool to simulate and optimize a variety of proposed protocol related to the ANH procedure and surgery. It can also be utilized as an educational or training tool to become familiar with the ANH procedure.

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.

Diffusion properties of inkjet printed ionic self-assembling polyelectrolyte hydrogels

In the present work, Crank's model was used to characterize solute transport in inkjet printed polyelectrolyte gels. The diffusion of a small charged molecule (fluorescein), various size linear uncharged molecules (dextrans), and a globular protein (albumin) in printed PSS-PDDA with near stoichiometric composition happened respectively at about 10-8, 10-9, and 10-10 cm2/sec. Polyelectrolyte complexes printed with non-stoichiometric ratios were found to be non-equilibrium structures consisting of three populations of polymer chains: fully complexed chains, chains in partial electrostatic interaction with the complex, and chains in excess having minimal interaction with the complex. This structure may be multiple phases. The applicability of hydrodynamic and free volume models to describe transport in printed polyelectrolyte gels was discussed.

Investigation of the nanoviscosity effect of a G-quadruplex and single-strand DNA using fluorescence correlation spectroscopy

Guanine (G)-quadruplexes are of interest because of their presence in the telomere sequence and the oncogene promoter region. Their diffusion and change of structure, especially in high viscosity solutions, are important for understanding their dynamics. G-quadruplexes may have less effective viscosity (nanoviscosity) when they are smaller than the solvent molecules. In this paper, we report the difference in the diffusion dynamics of the G-rich DNA sequences of single-strand DNA (ssDNA) and the G-quadruplex in aqueous, sucrose, and polyethylene glycol (PEG) solutions. From experiments with aqueous and sucrose solutions, we confirm that a simple diffusion model according to the viscosity is appropriate. In the PEG experiments, the nanoviscosity effect is observed according to PEG's molecular weight. In the PEG 200 solution, both the ssDNA and the G-quadruplex possess macroviscosity. In the PEG 10,000 solution, the G-quadruplex possesses nanoviscosity and the ssDNA possesses macroviscosity, whereas, in the PEG 35,000 solution, both ssDNA and the G-quadruplex possess nanoviscosity. The experimental results are consistent with the theoretical predictions.

Understanding the Diffusion of Dextrans in ‘Click' PNIPAAm Hydrogels

Arguably the most important property of a hydrogel is the ability to allow the diffusion of solutes through the crosslinked network. Studies of the diffusion in hydrogels are important for providing information on the rate and extent of the passage of the solute and on the details of the microstructure of the hydrogel. Such knowledge is directly relevant for applications such as controlled drug delivery systems. The structure of novel poly(N-isopropylacrylamide) (PNIPAAm) hydrogels can be revealed by the restricted diffusion of appropriate probe molecules. Dextran molecules, labelled with fluorescent moieties, were incorporated into well-defined PNIPAAm hydrogels to investigate the effects of hydrogel mesh size and dextran molecular size on the diffusivities of solute molecules.

Gel network photodisruption: a new strategy for the codelivery of plasmid DNA and drugs

In the last 5 years, we have gained further insight on the physical/chemical field of DNA gels. Our expertise on the gel swelling behavior, compaction of DNA by cationic entities, as lipids and surfactants, as well as on the assembly structures of these complexes allow us for the development of novel systems to be used in a variety of biomedical applications. In our previous reports, the physicochemical characterization has been well-established, and now one can evolve to the challenge of using DNA-based carriers in the biological area. Moreover, a new plasmid DNA (pDNA) hydrogel that is porous, is able to swell in the presence of additives, is biocompatible and, thus, is suitable to be used therapeutically was prepared. Here, the dual release of pDNA and solutes with pharmaceutical interest was the main challenge, and thus, we report on the photodisruption of plasmid DNA (pDNA) gels cross-linked with ethylene glycol diglycidyl ether (EGDE) as a strategy for this simultaneous release. The disruption over time, after the irradiation of the gel with ultraviolet light (400 nm), was characterized through the cumulative plasmid DNA release, the evolution in dry weight, the extent of swelling, and also the variations in the gel mesh size. The controlled release of different molecular weight solutes from plasmid DNA gels was investigated, and the influence of both the hydrogel degradation and cross-linker density on the release kinetics were addressed. While the release of lysozyme follows a Fickian process, the release of bovine serum albumin (BSA) and fluoresceinisothiocyanato-dextran (FITC-dextran) is characteristic of a Super Case II release phenomena. In addition, the size of the three solutes partially influences the release behavior; polymer chain mobility and the degree of swelling also play a role. To gain a fundamental understanding of drug release profile from pDNA matrices, in vitro release studies were evaluated using several anti-inflammatory drugs. The quantification of the release mechanism indicates a Super Case II release profile, which can be related with the gel swelling degree. A correlation between the drug release trend and the drug hydrophobicity can be found, with more hydrophobic drugs showing a slower release rate. In brief, this new pDNA gel system is biocompatible, is degradable upon light irradiation, and allows for the controlled and sustained release of plasmid DNA and incorporated solutes. This codelivery of pDNA and drugs would find relevant clinical uses due to the possibility of gene and nongene therapy combination in order to improve the therapeutic efficiency.

Ordered mesoporous polymer-silica hybrid nanoparticles as vehicles for the intracellular controlled release of macromolecules

A two-dimensional hexagonal ordered mesoporous polymer-silica hybrid nanoparticle (PSN) material was synthesized by polymerization of acrylate monomers on the surface of SBA-15 mesoporous silica nanoparticles. The structure of the PSN material was analyzed using a series of different techniques, including transmission electron microscopy, powder X-ray diffraction, and N(2) sorption analysis. These structurally ordered mesoporous polymer-silica hybrid nanoparticles were used for the controlled release of membrane-impermeable macromolecules inside eukaryotic cells. The cellular uptake efficiency and biocompatibility of PSN with human cervical cancer cells (HeLa) were investigated. Our results show that the inhibitory concentration (IC(50)) of PSN is very high (>100 μg/mL per million cells), while the median effective concentration for the uptake (EC(50)) of PSN is low (EC(50) = 4.4 μg/mL), indicating that PSNs are fairly biocompatible and easily up-taken in vitro. A membrane-impermeable macromolecule, 40 kDa FITC-Dextran, was loaded into the mesopores of PSNs at low pH. We demonstrated that the PSN material could indeed serve as a transmembrane carrier for the controlled release of FITC-Dextran at the pH level inside live HeLa cells. We believe that further developments of this PSN material will lead to a new generation of nanodevices for intracellular controlled delivery applications.

Hindered Diffusion of Oligosaccharides in High Strength Poly(ethylene glycol)/Poly(acrylic acid) Interpenetrating Network Hydrogels: Hydrodynamic Versus Obstruction Models

Diffusion coefficients of small oligosaccharides within high strength poly(ethylene glycol)/poly(acrylic acid) interpenetrating network (PEG/PAA IPN) hydrogels were measured by diffusion through hydrogel slabs. The ability of hindered diffusion models previously presented in the literature to fit the experimental data is examined. A model based solely on effects due to hydrodynamics is compared to a model based solely on solute obstruction. To examine the effect of polymer volume fraction on the observed diffusion coefficients, the equilibrium volume fraction of polymer in PEG/PAA IPNs was systematically varied by changing the initial PEG polymer concentration in hydrogel precursor solutions from 20 to 50 wt./wt.%. To examine the effect of solute radius on the observed diffusion coefficients, solute radii were varied from 3.3 to 5.1 Å by measuring diffusion coefficients of glucose, a monosaccharide; maltose, a disaccharide; and maltotriose, a trisaccharide. Both the hydrodynamic and obstruction models rely on scaling relationships to predict diffusion coefficients. The proper scaling relationship for each of the hindered diffusion models is evaluated based on fits to experimental data. The scaling relationship employed is found to have a greater significance for the hydrodynamic model than the obstruction model. Regardless of the scaling relationship employed, the obstruction model provides a better fit to our experimental data than the hydrodynamic model.

Transport theory for HIV diffusion through in vivo distributions of topical microbicide gels

Topical microbicide products are being developed for the prevention of sexually transmitted infections. These include vaginally-applied gels that deliver anti-HIV molecules. Gels may also provide partial barriers that slow virion diffusion from semen to vulnerable epithelium, increasing the time during which anti-HIV molecules can act. To explore the barrier function of microbicide gels, we developed a deterministic mathematical model for HIV diffusion through realistic gel distributions. We applied the model to experimental data for in vivo coating distributions of two vaginal gels in women. Time required for a threshold number of virions to reach the tissue surface was used as a metric for comparing different scenarios. Results delineated how time to threshold increased with increasing gel layer thickness and with decreasing diffusion coefficient. We note that for gel layers with average thickness > approximately 100 microm, the fractional area coated, rather than the gel layer thickness, was the primary determinant of time to threshold. For gel layers < approximately 100 microm, time to threshold was brief, regardless of fractional area coated. Application of the model to vaginal coating data showed little difference in time to threshold between the two gels tested. However, the protocol after gel application (i.e., with or without simulated coitus) had a much more significant effect. This study suggests that gel distribution in layers of thickness >100 microm and fractional area coated >0.8 is critical in determining the ability of the gel to serve as a barrier to HIV diffusion.

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.

Stochastic simulation of signal transduction: impact of the cellular architecture on diffusion

The transduction of signals depends on the translocation of signaling molecules to specific targets. Undirected diffusion processes play a key role in the bridging of spaces between different cellular compartments. The diffusion of the molecules is, in turn, governed by the intracellular architecture. Molecular crowding and the cytoskeleton decrease macroscopic diffusion. This article shows the use of a stochastic simulation method to study the effects of the cytoskeleton structure on the mobility of macromolecules. Brownian dynamics and single particle tracking were used to simulate the diffusion process of individual molecules through a model cytoskeleton. The resulting average effective diffusion is in line with data obtained in the in vitro and in vivo experiments. It shows that the cytoskeleton structure strongly influences the diffusion of macromolecules. The simulation method used also allows the inclusion of reactions in order to model complete signaling pathways in their spatio-temporal dynamics, taking into account the effects of the cellular architecture.

Diffusion of molecular probes and the effects of their interactions with polymer matrices as studied by pulsed-field gradient NMR spectroscopy

Pulsed-field gradient NMR spectroscopy was used to study the interactions between small molecular probes and polymers bearing interacting groups. The self-diffusion coefficients of ethylene glycol and its oligomers and their methyl ester derivatives in poly(vinyl alcohol) gels were measured to study the effect of hydrogen bonding. The self-diffusion coefficients of small molecular probes containing hydroxyl, amine, and carboxylic acid groups were determined in several polymer matrices including poly(vinyl alcohol), poly(allylamine), and poly(acrylic acid) bearing lateral hydroxyl, amine, and carboxylic acid groups, respectively. The ionic interactions between the functional groups of the diffusants and of the polymers exhibited a marked effect on the diffusion of the molecular probes. For example, the reduced self-diffusion coefficients measured for a diffusant with a carboxylic acid group in a poly(allylamine) matrix were shown to be lower even though the molecular masses of the diffusants are similar.Key words: pulsed-field gradient NMR spectroscopy, self-diffusion, intermolecular interactions.

Combining small angle neutron scattering (SANS) and fluorescence correlation spectroscopy (FCS) measurements to relate diffusion in agarose gels to structure

Small angle neutron scattering (SANS) and fluorescence correlation spectroscopy (FCS) measurements were carried out on agarose hydrogels to link their microscopic structure to the diffusivity of solutes at different scales. SANS allowed for the determination of the distribution of void volumes within the gels. They were shown to be compatible with a random network of cylindrical fibers as described by the Ogston model. FCS measured solute diffusivity in spaces similar in size to the void volumes, and thus, the results reflected the gel heterogeneity. Solute diffusivity was predicted by modeling the gel as microscopic geometrical cells. Variations in the diffusivity of solutes of different sizes could be predicted from the structural parameters of the gel using theory, taking into account obstruction by cylindrical cells and solute hydrodynamics. Prediction of the FCS autocorrelation functions for solutes from a cell model demonstrated a lack of sensitivity of this technique for multicomponent analysis.

Mesophase separation and probe dynamics in protein-polyelectrolyte coacervates

Protein-polyelectrolyte coacervates are self-assembling macroscopically monophasic biomacromolecular fluids whose unique properties arise from transient heterogeneities. The structures of coacervates formed at different conditions of pH and ionic strength from poly(dimethyldiallylammonium chloride) and bovine serum albumin (BSA), were probed using fluorescence recovery after photobleaching. Measurements of self-diffusion in coacervates were carried out using fluorescein-tagged BSA, and similarly tagged Ficoll, a non-interacting branched polysaccharide with the same size as BSA. The results are best explained by temporal and spatial heterogeneities, also inferred from static light scattering and cryo-TEM, which indicate heterogeneous scattering centers of several hundred nm. Taken together with previous dynamic light scattering and rheology studies, the results are consistent with the presence of extensive dilute domains in which are embedded partially interconnected 50-700 nm dense domains. At short length scales, protein mobility is unobstructed by these clusters. At intermediate length scales, proteins are slowed down due to tortuosity effects within the blind alleys of the dense domains, and to adsorption at dense/dilute domain interfaces. Finally, at long length scales, obstructed diffusion is alleviated by the break-up of dense domains. These findings are discussed in terms of previously suggested models for protein-polyelectrolyte coacervates. Possible explanations for the origin of mesophase separation are offered.