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

Directional change during active diffusion of viral ribonucleoprotein particles through cytoplasm

A mesh of cytoskeletal fibers, consisting of microtubules, intermediate filaments, and fibrous actin, prevents the Brownian diffusion of particles with a diameter larger than 0.10 μm, such as vesicular stomatitis virus ribonucleoprotein (RNP) particles, in mammalian cells. Nevertheless, RNP particles do move in random directions but at a lower rate than Brownian diffusion, which is thermally driven. This nonthermal biological transport process is called "active diffusion" because it is driven by ATP. The ATP powers motor proteins such as myosin II. The motor proteins bend and cross-link actin fibers, causing the mesh to jiggle. Until recently, little was known about how RNP particles get through the mesh. It has been customary to analyze the tracks of particles like RNPs by computing the slope of the ensemble-averaged mean-squared displacement of the particles as a signature of mechanism. Although widely used, this approach "loses information" about the timing of the switches between physical mechanisms. It has been recently shown that machine learning composed of variational Bayesian analysis, Gaussian mixture models, and hidden Markov models can use "all the information" in a single track to reveal that that the positions of RNP particles are spatially clustered. Machine learning assigns a number, called a state, to each cluster. RNP particles remain in one state for 0.2-1.0 s before switching (hopping) to a different state. This earlier work is here extended to analyze the movements of a particle within a state and to determine particle directionality within and between states.

Exploring Mechanisms of Lipid Nanoparticle-Mucus Interactions in Healthy and Cystic Fibrosis Conditions

Mucus forms the first defense line of human lungs, and as such hampers the efficient delivery of therapeutics to the underlying epithelium. This holds particularly true for genetic cargo such as CRISPR-based gene editing tools which cannot readily surmount the mucosal barrier. While lipid nanoparticles (LNPs) emerge as versatile non-viral gene delivery systems that can help overcome the delivery challenge, many knowledge gaps remain, especially for diseased states such as cystic fibrosis (CF). This study provides fundamental insights into Cas9 mRNA or ribonucleoprotein-loaded LNP-mucus interactions in healthy and diseased states by assessing the impact of the genetic cargo, mucin sialylation, mucin concentration, ionic strength, pH, and polyethylene glycol (PEG) concentration and nature on LNP diffusivity leveraging experimental approaches and Brownian dynamics (BD) simulations. Taken together, this study identifies key mucus and LNP characteristics that are critical to enabling a rational LNP design for transmucosal delivery.

Computational fluid dynamics modeling of aerosol particle transport through lung airway mucosa

Delivery of aerosols to the lung can treat various lung diseases. However, the conducting airways are coated by a protective mucus layer with complex properties that make this form of delivery difficult. Mucus is a non-Newtonian fluid and is cleared from the lungs over time by ciliated cells. Further, its gel-like structure hinders the diffusion of particles through it. Any aerosolized treatment of lung diseases must penetrate the mucosal barrier. Using computational fluid dynamics, a model of the airway mucus and periciliary layer was constructed to simulate the transport of impacted aerosol particles. The model predicts the dosage fraction of particles of a certain size that penetrate the mucus and reach the underlying tissue, as well as the distance downstream of the dosage site where tissue concentration is maximized. Reactions that may occur in the mucus are also considered, with simulated data for the interaction of a model virus and an antibody.

Feedback-controlled solute transport through chemo-responsive polymer membranes

Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we theoretically study the consequences of membrane responsiveness and feedback on the steady-state force-flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, c₀, the driving force, f, and the polymer volume fraction, ϕ. In our model, the solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force-flux relations, j(f), which we quantify in terms of the system's differential permeability, P_sys ^Δ∝dj/df. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force and largely tunable by attractive vs repulsive solute-membrane interactions. Moreover, controlling the inputs, c₀ and f, can lead to the steady-state bistability of ϕ and hysteresis in the force-flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

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.

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.

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.

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.

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.

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

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

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.