Particle transport through hydrogels is charge asymmetric

Nanoliposomes Permeability in a Microfluidic Drug Delivery Platform across a 3D Hydrogel

Nanoliposomes are nano-sized vesicles that can be used as drug delivery carriers with the ability to encapsulate both hydrophobic and hydrophilic compounds. Moreover, their lipid compositions facilitate their internalization by cells. However, the interaction between nanoliposomes and the membrane barrier of the human body is not well-known. If cellular tests and animal testing offer a solution, their lack of physiological relevance and ethical concerns make them unsuitable to properly mimic human body complexity. Microfluidics, which allows the environment of the human body to be imitated in a controlled way, can fulfil this role. However, existing models are missing the presence of something that would mimic a basal membrane, often consisting of a simple cell layer on a polymer membrane. In this study, we investigated the diffusion of nanoliposomes in a microfluidic system and found the optimal parameters to maximize their diffusion. Then, we incorporated a custom made GelMA with a controlled degree of substitution and studied the passage of fluorescently labeled nanoliposomes through this barrier. Our results show that highly substituted GelMA was more porous than lower substitution GelMA. Overall, our work lays the foundation for the incorporation of a hydrogel mimicking a basal membrane on a drug delivery microfluidic platform.

Nonspecific membrane-matrix interactions influence diffusivity of lipid vesicles in hydrogels

The diffusion of extracellular vesicles and liposomes in vivo is affected by different tissue environmental conditions and is of great interest in the development of liposome-based therapeutics and drug-delivery systems. Here, we use a bottom-up biomimetic approach to better isolate and study steric and electrostatic interactions and their influence on the diffusivity of synthetic large unilamellar vesicles in hydrogel environments. Single-particle tracking of these extracellular vesicle-like particles in agarose hydrogels as an extracellular matrix model shows that membrane deformability and surface charge affect the hydrogel pore spaces that vesicles have access to, which determines overall diffusivity. Moreover, we show that passivation of vesicles with PEGylated lipids, as often used in drug-delivery systems, enhances diffusivity, but that this effect cannot be fully explained with electrostatic interactions alone. Finally, we compare our experimental findings with existing computational and theoretical work in the field to help explain the nonspecific interactions between diffusing particles and gel matrix environments.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Mechanical deformation affects the counterion condensation in highly-swollen polyelectrolyte hydrogels

Polyelectrolyte gels can generate electric potentials under mechanical deformation. While the underlying mechanism of such a response is often attributed to changes in counterion-condensation levels or alterations in the ionic conditions in the pervaded volume of the hydrogel, the exact molecular origins are largely unknown. By using all-atom molecular dynamics simulations of a polyacrylic acid hydrogel in explicit water as a model system, we simulate the uniaxial compression and uniaxial stretching of weakly to highly swollen (i.e., between 60-90% solvent content) hydrogel networks and calculate the microscopic condensation levels of counterions around the hydrogel chains. The counterion condensation under deformation is highly non-monotonic. Ionic condensation around the constituting chains of the deformed hydrogel tends to increase as the chains are stretched. This increase reaches a maximum and decreases as the chains are strongly stretched. The condensation around the collapsed chains of the hydrogel is weakly affected by the deformation. As a result, both compressing and stretching the model hydrogel lead to an overall increase in the counterion condensation. The effect vanishes for weakly swollen hydrogels, for which most ions are already condensed. The simulations with single, stretched polyelectrolyte chains show a qualitatively similar response, suggesting the effect of chain elongation on the ionic distribution throughout the hydrogel. Notably, this deformation-induced counterion condensation phenomenon does not occur in a polyelectrolyte solution at its critical concentration, indicating the role of hydrogel topology constraining the chain ends. Our results indicate that counterion condensation in a deforming polyelectrolyte hydrogel can be highly heterogeneous and exhibit a rich behaviour of electrostatic responses.

Electrochemical Wearable Biosensors and Bioelectronic Devices Based on Hydrogels: Mechanical Properties and Electrochemical Behavior

Hydrogel-based wearable electrochemical biosensors (HWEBs) are emerging biomedical devices that have recently received immense interest. The exceptional properties of HWEBs include excellent biocompatibility with hydrophilic nature, high porosity, tailorable permeability, the capability of reliable and accurate detection of disease biomarkers, suitable device-human interface, facile adjustability, and stimuli responsive to the nanofiller materials. Although the biomimetic three-dimensional hydrogels can immobilize bioreceptors, such as enzymes and aptamers, without any loss in their activities. However, most HWEBs suffer from low mechanical strength and electrical conductivity. Many studies have been performed on emerging electroactive nanofillers, including biomacromolecules, carbon-based materials, and inorganic and organic nanomaterials, to tackle these issues. Non-conductive hydrogels and even conductive hydrogels may be modified by nanofillers, as well as redox species. All these modifications have led to the design and development of efficient nanocomposites as electrochemical biosensors. In this review, both conductive-based and non-conductive-based hydrogels derived from natural and synthetic polymers are systematically reviewed. The main synthesis methods and characterization techniques are addressed. The mechanical properties and electrochemical behavior of HWEBs are discussed in detail. Finally, the prospects and potential applications of HWEBs in biosensing, healthcare monitoring, and clinical diagnostics are highlighted.

Electro-optical Study of the Anomalous Rotational Diffusion in Polymer Solutions

Brownian diffusion of spherical nanoparticles is usually exploited to ascertain the rheological properties of complex media. However, the behavior of the tracer particles is affected by a number of phenomena linked to the interplay between the dynamics of the particles and polymer coils. For this reason, the characteristic lengths of the dispersed entities, depletion phenomena, and the presence of sticking conditions have been observed to affect the translational diffusion of the probes. On the other hand, the retardation effect of the host fluid on the rotational diffusion of nonspherical particles is less understood. We explore the possibility of studying this phenomenon by analyzing the electro-orientation of the particles in different scenarios in which we vary the ratio between the particle and polymer characteristic size, and the geometry of the particles, including both elongated and oblate shapes. We find that the Stokes-Einstein relation only applies if the radius of gyration of the polymer is much shorter than the particle size and when some repulsive interaction between both is present.

Molecular Dynamics Simulations of Rhodamine B Zwitterion Diffusion in Polyelectrolyte Solutions

Polyelectrolytes continue to find wide interest and application in science and engineering, including areas such as water purification, drug delivery, and multilayer thin films. We have been interested in the dynamics of small molecules in a variety of polyelectrolyte (PE) environments; in this paper, we report simulations and analysis of the small dye molecule rhodamine B (RB) in several very simple polyelectrolyte solutions. Translational diffusion of the RB zwitterion has been measured in fully atomistic, 2 μs long molecular dynamics simulations in four different polyelectrolyte solutions. Two solutions contain the common polyanion sodium poly(styrene sulfonate) (PSS), one with a 30-mer chain and the other with 10 trimers. The other two solutions contain the common polycation poly(allyldimethylammonium) chloride (PDDA), one with two 15-mers and the other with 10 trimers. RB diffusion was also simulated in several polymer-free solutions to verify its known experimental value for the translational diffusion coefficient, D_RB, of 4.7 × 10^-6 cm²/s at 300 K. RB diffusion was slowed in all four simulated PE solutions, but to varying degrees. D_RB values of 3.07 × 10^-6 and 3.22 × 10^-6 cm²/s were found in PSS 30-mer and PSS trimer solutions, respectively, whereas PDDA 15-mer and trimer solutions yielded values of 2.19 × 10^-6 and 3.34 × 10^-6 cm²/s. Significant associations between RB and the PEs were analyzed and interpreted via a two-state diffusion model (bound and free diffusion) that describes the data well. Crowder size effects and anomalous diffusion were also analyzed. Finally, RB translation along the polyelectrolytes during association was characterized.

Polyzwitterionic Hydrogels for Efficient Atmospheric Water Harvesting

Atmospheric water harvesting (AWH) is regarded as one of the promising strategies for freshwater production desirable to provide sustainable water for landlocked and arid regions. Hygroscopic materials have attracted widespread attention because of their water harvesting performance. However, the introduction of many inorganic salts often leads to aggregation and leakage issues in practical use. Here, polyzwitterionic hydrogels are developed as an effective AWH material platform. Via anti-polyelectrolyte effects, the hygroscopic salt coordinated with polymer chains could capture moisture and enhance the swelling property, leading to a strong moisture sorption capacity. The hydrogel shows superior AWH performance (0.62 g g^-1 , 120 minutes for equilibrium at 30 % relative humidity) and produces 5.87 L kg^-1 freshwater per day. It is anticipated that the polyzwitterionic hydrogels with unique salt-responsive properties could provide new insights into the design and synthesis of next-generation AWH materials.

The Delivery Challenge of Genome Editing in Human Epithelia

Despite exciting advances in gene editing, their clinical translation is still hampered by the lack of delivery systems that can encapsulate and deliver gene editing tools like CRISPR-Cas9 or prime editors to the target side. This is particularly challenging in human epithelia, such as the skin and the lung; the latter of which being a mucosal surface that is covered by a mucus layer. In this perspective, the design and biological assessment of delivery systems for gene editing tools like CRISPR in skin and mucosal surfaces are discussed. The current state-of-the-art, current knowledge, and translational gaps, and guide toward improved translation are highlighted.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.

Universal description of steric hindrance in flexible polymer gels

In this work, the long-time diffusion of a solute in a chemically crosslinked and flexible hydrogel is computed from a bead-spring model of a polymeric network to assess the effect of steric obstruction. The relative diffusivities obtained for a wide variety of systems can be described by an exponential decay depending on a parameter that differs from that employed for rigid gels. The mathematical expression derived here can approximately predict the diffusivity in flexible gels if steric hindrance is the mechanism ruling diffusion.

A novel modelling and simulation approach for the hindered mobility of charged particles in biological hydrogels

This article presents a novel computational model to study the selective filtering of biological hydrogels due to the surface charge and size of diffusing particles. It is the first model that includes the random three-dimensional fibre orientation and connectivity of the biopolymer network and that accounts for elastic deformations of the fibres by means of beam theory. As a key component of the model, novel formulations are proposed both for the electrostatic and repulsive steric interactions between a spherical particle and a beam. In addition to providing a thorough validation of the model, the presented computational studies yield new insights into the underlying mechanisms of hindered particle mobility, especially regarding the influence of the aforementioned aspects that are unique to this model. It is found that the precise distribution of fibre and thus charge agglomerations in the network have a crucial influence on the mobility of oppositely charged particles and gives rise to distinct motion patterns. Considering the high practical significance for instance with respect to targeted drug release or infection defence, the provided proof of concept motivates further advances of the model towards a truly predictive computational tool that allows a case- and patient-specific assessment for real (biological) systems.

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.

Magnetic poly(acrylic acid)-based hydrogels for rapid ammonium sorption and efficient sorbent separation from sewage

Ammonium sorption and recovery processes typically take place in conventional packed columns, with a configuration that enables maximum sorption by the sorbents. However, batch or semi-continuous operations in packed columns have associated issues such as scaling and frequent backwashing requirements, which are economically prohibitive. As an alternative, ammonium sorption could occur in well-mixed continuously stirred tanks, which would allow for the ammonium sorption process to be retrofitted in existing wastewater treatment plants, provided that efficient sorbent separation can be achieved. This study demonstrates, for the first time, the preparation of magnetic poly(acrylic acid)-based (PAA) ammonium sorbents through the incorporation of magnetic (Fe₃O₄) nanoparticles (MNP) produced via scalable and cost-effective electrochemical synthesis. The MNP and PAA hydrogels were synthesized independently and the MNPs subsequently integrated into the PAA hydrogel network by particle diffusion and physical entrapment. No adverse effects on swelling and ammonium sorption following immersion in either synthetic or real sewage were observed after MNPs were incorporated into the hydrogels. Importantly, PAA-MNP hydrogels demonstrated high ammonium sorption efficiencies (80-93%) in real sewage and achieved rapid ammonium recovery of 73 ± 1.1% within 15 min of mild acid washing (pH 4) 15 min at a maximum recovery.

Facilitating target search in polymer networks: Effects of target size and mixed one-dimensional and three-dimensional diffusion

We theoretically investigate the problem of diffusive target search and mean first passage times (MFPTs) of a tracer in a three-dimensional (3D) polymer network with a particular focus on the effects of combined one-dimensional (1D) diffusion along the polymer chains and 3D diffusion within the network. For this, we employ computer simulations as well as limiting theories of a single diffusive tracer searching for a spherical target fixed at a cross-link of a homogeneous 3D cubic lattice network. The free parameters are the target size, the ratio of the 1D and 3D friction constants, and the transition probabilities between bound and unbound states. For a very strongly bound tracer on the chains, the expected predominant set of 1D lattice diffusion (LD) is found. The MFPT in the LD process significantly depends on the target size, yielding two distinct scaling behaviors for target sizes smaller and larger than the network mesh size, respectively. In the limit of a pointlike target, the LD search becomes a random walk process on the lattice, which recovers the analytical solution for the MFPT previously reported by S. Condamin, O. Bénichou, and M. Moreau [Phys. Rev. Lett. 95, 260601 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.260601]. For the very weakly bound tracer, the expected 3D free diffusion (FD) dominates, extrapolating to the well-known Smoluchowski limit. A critical target size is found above which the MFPT in the FD process is faster than in the LD process. For intermediate binding, i.e., a combination of LD and FD processes, the target search time can be minimized for an optimal range of target sizes and partitions between FD and LD, for which the MFPTs are substantially faster when compared to the limiting FD or LD processes. Our study may provide a theoretical basis to better understand and predict search and reaction processes in complex structured materials, thereby contributing to practical applications such as designing nanoreactors where catalytic targets are immobilized in polymer networks.

Particle Diffusivity and Free-Energy Profiles in Hydrogels from Time-Resolved Penetration Data

A combined experimental and theoretical method to simultaneously determine diffusivity and free-energy profiles of particles that penetrate into inhomogeneous hydrogel systems is presented. As the only input, arbitrarily normalized concentration profiles from fluorescence intensity data of labeled tracer particles for different penetration times are needed. The method is applied to dextran molecules of varying size that penetrate into hydrogels of polyethylene-glycol chains with different lengths that are covalently cross-linked by hyperbranched polyglycerol hubs. Extracted dextran bulk diffusivities agree well with fluorescence correlation spectroscopy data obtained separately. Empirical scaling laws for dextran diffusivities and free energies inside the hydrogel are identified as a function of the dextran mass. An elastic free-volume model that includes dextran as well as polyethylene-glycol linker flexibility quantitively describes the repulsive dextran-hydrogel interaction free energy, which is of steric origin, and furthermore suggests that the hydrogel mesh-size distribution is rather broad and particle penetration is dominated by large hydrogel pores. Particle penetration into hydrogels for steric particle-hydrogel interactions is thus suggested to be governed by an elastic size-filtering mechanism that involves the tail of the hydrogel pore-size distribution.

Solute diffusion in gels: Thirty years of simulations

In this review, we present a summary of computer simulation studies on solute diffusion in gels carried out in the last three decades. Special attention is paid to coarse-grained simulations in which the role of steric and electrostatic interactions on the particle diffusion can be evaluated. In addition, other important characteristics of particle diffusion in gels, such as the stiffness of the gel structure and hydrodynamic interactions, can be taken into account through coarse-grained simulations. Emphasis is placed on how simulation results help to test phenomenological models and to improve the interpretation interof experimental results. Finally, coarse-grained simulations have also been employed to study the diffusion controlled release of drugs from gels. We believe that scientific advances in this line will be useful to better understand the mechanisms that control the diffusive transport of molecules in a wide variety of biological systems.

Studies of nanoparticle delivery with in vitro bio-engineered microtissues

A variety of engineered nanoparticles, including lipid nanoparticles, polymer nanoparticles, gold nanoparticles, and biomimetic nanoparticles, have been studied as delivery vehicles for biomedical applications. When assessing the efficacy of a nanoparticle-based delivery system, in vitro testing with a model delivery system is crucial because it allows for real-time, in situ quantitative transport analysis, which is often difficult with in vivo animal models. The advent of tissue engineering has offered methods to create experimental models that can closely mimic the 3D microenvironment in the human body. This review paper overviews the types of nanoparticle vehicles, their application areas, and the design strategies to improve delivery efficiency, followed by the uses of engineered microtissues and methods of analysis. In particular, this review highlights studies on multicellular spheroids and other 3D tissue engineering approaches for cancer drug development. The use of bio-engineered tissues can potentially provide low-cost, high-throughput, and quantitative experimental platforms for the development of nanoparticle-based delivery systems.

Tuning the selective permeability of polydisperse polymer networks

We study the permeability and selectivity ('permselectivity') of model membranes made of polydisperse polymer networks for molecular penetrant transport, using coarse-grained, implicit-solvent computer simulations. In our work, permeability P is determined on the linear-response level using the solution-diffusion model, P = KDin, i.e., by calculating the equilibrium penetrant partition ratio K and penetrant diffusivity Din inside the membrane. We vary two key parameters, namely the network-network interaction, which controls the degree of swelling and collapse of the network, and the network-penetrant interaction, which tunes the selective penetrant uptake and microscopic energy landscape for diffusive transport. We find that the partitioning K covers four orders of magnitude and is a non-monotonic function of the parameters, well interpreted by a second-order virial expansion of the free energy of transferring one penetrant from a reservoir into the membrane. Moreover, we find that the penetrant diffusivity Din in the polydisperse networks, in contrast to highly ordered membrane structures, exhibits relatively simple exponential decays. We propose a semi-empirical scaling law for the penetrant diffusion that describes the simulation data for a wide range of densities and interaction parameters. The resulting permeability P turns out to follow the qualitative behavior (including maximization and minimization) of partitioning. However, partitioning and diffusion are typically anti-correlated, yielding large quantitative cancellations, controlled and fine-tuned by the network density and interactions, as rationalized by our scaling laws. We finally demonstrate that even small changes of network-penetrant interactions, e.g., by half a kBT, modify the permselectivity by almost one order of magnitude.

A Microscopically Motivated Model for Particle Penetration into Swollen Biological Networks

Biological gels (bio-gels) are hydrated polymer networks that serve diverse biological functions, which often lead to intentional or unintentional exposure to particulate matter. In this work, we derive a microscopically motivated framework that enables the investigation of penetration mechanisms into bio-gels. We distinguish between two types of mechanisms: spontaneous (unforced) penetration and forced penetration. Using experimental data available in the literature, we exploit the proposed model to characterize and compare between the microstructures of respiratory, intestinal, and cervicovaginal mucus and two types of biofilms. Next, we investigate the forced penetration process of spherical and ellipsoidal particles into a locally quadrilateral network. The proposed framework can be used to improve and complement the analysis of experimental findings in vitro, ex vivo, and in vivo. Additionally, the insights from this work pave the way towards enhanced designs of nano-medicines and allow the assessment of risk factors related to the nano-pollutants exposure.

Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy

The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant-matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap's length scale is also accessed. On the other hand, by tuning the pH value, the diffusant-matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.

Physicochemical Changes and in Vitro Gastric Digestion of Modified Soybean Protein Induced by Lipoxygenase Catalyzed Linoleic Acid Oxidation

Protein oxidation results in structural modification which affects its digestion. The objective of this work was to investigate the influence of lipoxygenases (LOX) catalyzed linoleic acid (LA) oxidation on the structure and in vitro gastric digests of soybean protein isolate (SPI). Fluorescence recovery after photobleaching (FRAP) was used to evaluate the relationship between pepsin diffusion and gastric digestion. Results indicated that oxidation induced carbonyl formation and loss of free sulfhydryl. Increased surface hydrophobicity and zeta-potential verified the protein unfolding and thus resulted in a small particle size and low fluorescence intensity. Fourier transform infrared spectroscopy (FTIR) showed that oxidation caused the increases in β-sheets mostly at the expense of α-helix and random coils. Fluorescein isothiocyanate (FITC)-pepsin in SPI solution modified with 3 mL LA showed a faster diffusion rate with 80.51 μm²/s as well as a higher DH value of 9.11%, showing that pepsin diffusivity might play an important role in protein gastric digestion.

Particle Trapping Mechanisms Are Different in Spatially Ordered and Disordered Interacting Gels

Using stochastic simulations, we study the influence of spatial disorder on the diffusion of a single particle through a gel that consists of rigid, straight fibers. The interaction between the particle and the gel fibers consists of an invariant short-range repulsion, the steric part, and an interaction part that can be attractive or repulsive and of varying range. The effect that spatial disorder of the gel structure has on the particle diffusivity depends crucially on the presence of nonsteric interactions. For attractive interactions, disorder slows down diffusion, because in disordered gels, the particle becomes strongly trapped in regions of locally increased fiber density. For repulsive interactions, the diffusivity is minimal for intermediate disorder strength, because highly disordered lattices exhibit abundant passageways of locally low fiber density. The comparison with experimental data on protein and fluorophore diffusion through various hydrogels is favorable. Our findings shed light on particle-diffusion mechanisms in biogels and thus on biological barrier properties, which can be helpful for the optimal design of synthetic diffusors as well as synthetic mucus constructs.

Protein diffusion from microwells with contrasting hydrogel domains

Understanding and controlling molecular transport in hydrogel materials is important for biomedical tools, including engineered tissues and drug delivery, as well as life sciences tools for single-cell analysis. Here, we scrutinize the ability of microwells-micromolded in hydrogel slabs-to compartmentalize lysate from single cells. We consider both (i) microwells that are "open" to a large fluid (i.e., liquid) reservoir and (ii) microwells that are "closed," having been capped with either a slab of high-density polyacrylamide gel or an impermeable glass slide. We use numerical modeling to gain insight into the sensitivity of time-dependent protein concentration distributions on hydrogel partition and protein diffusion coefficients and open and closed microwell configurations. We are primarily concerned with diffusion-driven protein loss from the microwell cavity. Even for closed microwells, confocal fluorescence microscopy reports that a fluid (i.e., liquid) film forms between the hydrogel slabs (median thickness of 1.7 μm). Proteins diffuse from the microwells and into the fluid (i.e., liquid) layer, yet concentration distributions are sensitive to the lid layer partition coefficients and the protein diffusion coefficient. The application of a glass lid or a dense hydrogel retains protein in the microwell, increasing the protein solute concentration in the microwell by ∼7-fold for the first 15 s. Using triggered release of Protein G from microparticles, we validate our simulations by characterizing protein diffusion in a microwell capped with a high-density polyacrylamide gel lid (p > 0.05, Kolmogorov-Smirnov test). Here, we establish and validate a numerical model useful for understanding protein transport in and losses from a hydrogel microwell across a range of boundary conditions.

Thaw-Induced Gelation of Alginate Hydrogels for Versatile Delivery of Therapeutics

Alginate hydrogels have been extensively used and successfully validated as delivery vehicles of bioactive factors in many tissue engineering applications. This work describes and characterizes a singular alternative method to create alginate hydrogels designated as thaw-induced gelation (TIG). The TIG method involves gelation through the time-dependent release of the polymer or crosslinker by melting into solution. Alginate TIG hydrogels were validated for spatial-temporal control delivery of different cargos including albumin, dextran, and doxorubicin. Chitosan was incorporated into TIG hydrogels to investigate the electrostatic interactions between alginate and the tested cargos. Interestingly, while 90% of doxorubicin was released after 8 h from hydrogels formed with frozen calcium, hydrogels formulated from frozen alginate took 72 h. In addition, the storage modulus of TIG hydrogels prepared from frozen alginate was double that of a hydrogel formed without freezing alginate. Therefore, the utility of TIG strategies are particularly promising for the delivery of therapeutic cargos smaller than the mesh size of the alginate hydrogel, as it enables controlled release of these cargos without any further chemical modifications of the hydrogels. These TIG alginate hydrogels with tunable mechanical properties and control over the delivery of smaller cargos could be useful in many tissue engineering applications.

Cross-linker effect on solute adsorption in swollen thermoresponsive polymer networks

Molecular dynamics study on the solute adsorption to thermoresponsive polymers estimating the cross-link impact on particle partitioning in swollen hydrogels.

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.

Mucus-penetrating phage-displayed peptides for improved transport across a mucus-like model

The objective of this work is to use phage display libraries as a screening tool to identify peptides that facilitate transport across the mucus barrier. Mucus is a complex selective barrier to particles and molecules, limiting penetration to the epithelial surface of mucosal tissues. In mucus-associated diseases such as cystic fibrosis (CF), mucus has increased viscoelasticity and a higher concentration of covalent and non-covalent physical entanglements compared to healthy tissues, which greatly hinders permeability and transport of drugs and particles across the mucosae for therapeutic delivery. Treatment of CF lung diseases and associated infections must overcome this abnormal mucosal barrier. Critical bottlenecks hindering effective drug penetration remain and while recent studies have shown hydrophilic, net-neutral charge polymers can improve the transport of nanoparticles and minimize interactions with mucus, there is a dearth of alternative carriers available. We hypothesized that the screening of a phage peptide library against a CF mucus model would lead to the identification of phage-displayed peptide sequences able to improve transport in mucus. These combinatorial libraries possess a large diversity of peptide-based formulations (10⁸-10⁹) to achieve unprecedented screening for potential mucus-penetrating peptides. Here, phage clones displaying discovered peptides were shown to have up to 2.6-fold enhanced diffusivity in the CF mucus model. In addition, we demonstrate reduced binding affinities to mucin compared to wild-type control. These findings suggest that phage display libraries can be used as a strategy to improve transmucosal delivery.

Spectroscopic methods for assessing the molecular origins of macroscopic solution properties of highly concentrated liquid protein solutions

In cases of subcutaneous injection of therapeutic monoclonal antibodies, high protein concentrations (>50 mg/ml) are often required. During the development of these high concentration liquid formulations (HCLF), challenges such as aggregation, gelation, opalescence, phase separation, and high solution viscosities are more prone compared to low concentrated protein formulations. These properties can impair manufacturing processes, as well as protein stability and shelf life. To avoid such unfavourable solution properties, a detailed understanding about the nature of these properties and their driving forces are required. However, the fundamental mechanisms that lead to macroscopic solution properties, as above mentioned, are complex and not fully understood, yet. Established analytical methods for assessing the colloidal stability, i.e. the ability of a native protein to remain dispersed in solution, are restricted to dilute conditions and provide parameters such as the second osmotic virial coefficient, B₂₂, and the diffusion interaction coefficient, k_D. These parameters are routinely applied for qualitative estimations and identifications of proteins with challenging solution behaviours, such as high viscosities and aggregation, although the assays are prepared for low protein concentration conditions, typically between 0.1 and 20 mg/ml ("ideal" solution conditions). Quantitative analysis of samples of high protein concentration is difficult and it is hard to obtain information about the driving forces of such solution properties and corresponding protein-protein self-interactions. An advantage of using specific spectroscopic methods is the potential of directly analysing highly concentrated protein solutions at different solution conditions. This allows for collecting/gaining valuable information about the fundamental mechanisms of solution properties of the high protein concentration regime. In addition, the derived parameters might be more predictive as compared to the parameters originating from assays which are optimized for the low protein concentration range. The provided information includes structural data, molecular dynamics at various timescales and protein-solvent interactions, which can be obtained at molecular resolution. Herein, we provide an overview about spectroscopic techniques for analysing the origins of macroscopic solution behaviours in general, with a specific focus on pharmaceutically relevant high protein concentration and formulation conditions.

Particle Diffusion in Polymeric Hydrogels with Mixed Attractive and Repulsive Interactions

All biogels are heterogeneous, consisting of functional groups with different biophysical properties arrayed on spatially disordered polymer networks. Nanoparticles diffusing in such biogels experience a mixture of attractive and repulsive interactions. Here, we present experimental and theoretical studies of charged particle diffusion in gels with a random distribution of attractive and repulsive electrostatic interaction sites inside the gel. In addition to interaction disorder, we theoretically investigate the effect of spatial disorder of the polymer network. Our coarse-grained simulations reveal that attractive interactions primarily determine the diffusive behavior of the particles in systems with mixed attractive and repulsive interactions. As a consequence, charged particles of either sign are immobilized in mixed cationic/anionic gels because they are trapped near oppositely charged interaction sites, whereas neutral particles diffuse rapidly. Even small fractions of oppositely charged interaction sites lead to strong trapping of a charged particle. Translational diffusion coefficients of charged probe molecules in gels consisting of mixed cationic and anionic dextran polymers are determined by fluorescence correlation spectroscopy and quantitatively confirm our theoretical predictions.

Controlling the length of self-assembled nanotubes by sonication followed by polymer wrapping

In this work, we report that sonication, followed by polymer-wrapping, is an effective strategy to reduce the length of self-assembled nanotubes and suspend their propensity to self-heal into their elongated precursors.

Designing hydrogels for controlled drug delivery

Hydrogel delivery systems can leverage therapeutically beneficial outcomes of drug delivery and have found clinical use. Hydrogels can provide spatial and temporal control over the release of various therapeutic agents, including small-molecule drugs, macromolecular drugs and cells. Owing to their tunable physical properties, controllable degradability and capability to protect labile drugs from degradation, hydrogels serve as a platform in which various physiochemical interactions with the encapsulated drugs control their release. In this Review, we cover multiscale mechanisms underlying the design of hydrogel drug delivery systems, focusing on physical and chemical properties of the hydrogel network and the hydrogel-drug interactions across the network, mesh, and molecular (or atomistic) scales. We discuss how different mechanisms interact and can be integrated to exert fine control in time and space over the drug presentation. We also collect experimental release data from the literature, review clinical translation to date of these systems, and present quantitative comparisons between different systems to provide guidelines for the rational design of hydrogel delivery systems.

Quantifying the Influence of the Crowded Cytoplasm on Small Molecule Diffusion

Cytosolic crowding can influence the thermodynamics and kinetics of in vivo chemical reactions. Most significantly, proteins and nucleic acid crowders reduce the accessible volume fraction, ϕ, available to a diffusing substrate, thereby reducing its effective diffusion rate, Deff, relative to its rate in bulk solution. However, Deff can be further hindered or even enhanced, when long-range crowder/diffuser interactions are significant. To probe these effects, we numerically estimated Deff values for small, charged molecules in representative, cytosolic protein lattices up to 0.1 × 0.1 × 0.1 μm(3) in volume via the homogenized Smoluchowski electro-diffusion equation. We further validated our predictions against Deff estimates from ϕ-dependent analytical relationships, such as the Maxwell-Garnett (MG) bound, as well as explicit solutions of the time-dependent electro-diffusion equation. We find that in typical, moderately crowded cell cytoplasm (ϕ ≈ 0.8), Deff is primarily determined by ϕ; in other words, diverse protein shapes and heterogeneous distributions only modestly impact Deff. However, electrostatic interactions between diffusers and crowders, particularly at low electrolyte ionic strengths, can substantially modulate Deff. These findings help delineate the extent that cytoplasmic crowders influence small molecule diffusion, which ultimately may shape the efficiency and timing of intracellular signaling pathways. More generally, the quantitative agreement between computationally expensive solutions of the time-dependent electro-diffusion equation and its comparatively cheaper homogenized form suggest that the latter is a broadly effective model for diffusion in wide-ranging, crowded biological media.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Nanoparticle filtering in charged hydrogels: Effects of particle size, charge asymmetry and salt concentration

The understanding of particle transport mechanisms in biological and synthetic hydrogels is crucial for the development of advanced drug delivery methods. We propose a simple model for the diffusion of charged nanoparticles in cross-linked, charged hydrogels based on a cubic periodic environment and an electrostatic interaction potential of varying range and strength, encompassing attractive and repulsive scenarios. The long-time diffusive properties are investigated by use of Brownian dynamics simulations and analytical methods. A number of experimentally observed phenomena attributed to nonsteric interactions between hydrogel polymers and diffusing particle are naturally reproduced by our model. Charged particles diffuse slower than uncharged particles, regardless of the sign of the surface charge, but with a stronger hindrance effect for attractive electrostatic interactions. This is explained in terms of charged particles sticking to the polymer network in regions of strong opposite charge and their exclusion from similarly charged regions. In the case of attractive interactions between hydrogel polymers and the diffusing particle, smaller charged particles diffuse slower than larger ones. This stands in contrast to a size filtering scenario but is in agreement with experimental findings. In the case of repulsive interactions, a range of differently sized particles diffuse equally fast. We compare our model predictions with published experiments on charged particle diffusion in hydrogels and confirm that electrostatic interactions are a key factor influencing the diffusivity of charged nanoparticles and that oppositely charged gels are much more effective in slowing down a charged particle than similarly charged gels.

Droplet formation and growth inside a polymer network: A molecular dynamics simulation study

We present a molecular dynamics simulation study that focuses on the formation and growth of nanoscale droplets inside polymer networks. Droplet formation and growth are investigated by the liquid-vapor phase separation of a dilute Lennard-Jones (LJ) fluid inside regularly crosslinked, polymer networks with varying mesh sizes. In a polymer network with small mesh sizes, droplet formation can be suppressed, the extent of which is dependent on the attraction strength between the LJ particles. When droplets form in a polymer network with intermediate mesh sizes, subsequent growth is significantly slower when compared with that in bulk without a polymer network. Interestingly, droplet growth beyond the initial nucleation stage occurs by different mechanisms depending on the mesh size: droplets grow mainly by diffusion and coalescence inside polymer networks with large mesh sizes (as observed in bulk), whereas Ostwald ripening becomes a more dominant mechanism for droplet growth for small mesh sizes. The analysis of droplet trajectories clearly reveals the obstruction effect of the polymer network on the movement of growing droplets, which leads to Ostwald ripening of droplets. This study suggests how polymer networks can be used to control the growth of nanoscale droplets.

Optimization and universality of Brownian search in a basic model of quenched heterogeneous media

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.