Electrodiffusion-Mediated Swelling of a Two-Phase Gel Model of Gastric Mucus

Deswelling Dynamics of Chemically-Active Polyelectrolyte Gels

Ion-induced volume phase transitions in polyelectrolyte gels play an important role in physiological processes such as mucus storage and secretion in the gut, nerve excitation, and DNA packaging. Experiments have shown that changes in ionic composition can trigger rapid swelling and deswelling of these gels. Based on a previously developed computational model, we carry out 2D simulations of gel deswelling within an ionic bath. The dynamics of the volume phase transition are governed by the balance of chemical and mechanical forces on components of the gel. Our simulation results highlight the close connections between the patterns of deswelling, the ionic composition, and the relative magnitude of particle-particle interaction energies.

A Computational Framework for the Swelling Dynamics of Mucin-like Polyelectrolyte Gels

Gastric mucus is a polyelectrolyte gel that serves as the primary defense of the stomach lining against acid and digestive enzymes. Mucus is released from granules in specialized cells where it is stored at very high concentration. Experiments show that such a dense mucus gel may swell explosively within a short time period, and that this is accompanied by a massive transport of monovalent cations from the extracellular environment into the densely packed mucus in exchange for divalent calcium that had crosslinked the negatively-charged mucus fibers. We propose a 2D computational method for simulating mucus swelling with a two-fluid model. The model includes electro-diffusive transport of ionic species, the coupled motion of the glycoprotein network and hydrating fluid, and chemical interactions between the network and dissolved ions. Each ionic species in the solvent phase is subject to a Nernst-Planck type equation. Together with the electro-neutrality constraint, these equations constitute a system of non-linear parabolic PDEs subject to an algebraic constraint. The discretized system is solved by a Schur complement reduction scheme. Numerical results indicate that the method is very efficient, robust and accurate, even for problems which exhibit large spatial gradients in the concentration of ions. The new method is combined with our previously-published numerical methods for solving the coupled momentum equations of the solvent and network, extended to account for the chemical forces determined from the distribution of ions between solvent and network and in space. The computational effectiveness of the new methods is demonstrated through accuracy and efficiency metrics and through investigation of some of the factors that influence swelling dynamics.

Mathematical modelling of cross-linked polyacrylic-based hydrogels: physical properties and drug delivery

Recently, hydrogels have gained significant importance in different applications, such as tissue engineering and drug delivery. They are 3D structures of hydrophilic polymers held together through physical or chemical crosslinking. Important is their ability to swell in presence of solvents, forming elastic gels able to maintain their original shape. Furthermore, these scaffolds slowly degrade in the physiological environment, leading the growing tissue to replace the former filled site. In this work, hydrogels have been synthetized using branched polyacrylic acid (carbomer) cross-linked with an aliphatic polyetherdiamine (elastamine). In particular, we focused on the description of their equilibrium conditions in swollen state and the dynamic simulation of the swelling process. These hydrogels exhibited a peculiar swelling behaviour characterized by an overshoot of the volume increase before reaching the equilibrium. Notably, such behaviour was found at different pH values. In this manuscript, the swelling behaviour was studied by mathematical modelling. Moreover, the ability of these devices to release drugs was also examined through a literature model to understand the different operating transport mechanisms.

Modeling and Simulation of the Ion-Binding-Mediated Swelling Dynamics of Mucin-like Polyelectrolyte Gels

Volume phase transitions in polyeletrolyte gels play important roles in many biophysical processes such as DNA packaging, nerve excitation, and cellular secretion. The swelling and deswelling of these charged polymer gels depend strongly on their ionic environment. In this paper, we present an extension to our previous two-fluid model for ion-binding-mediated gel swelling. The extended model eliminates the assumptions about the size similarity between the network and solvent particles, which makes it suitable for investigating of a large family of biologically relevant problems. The model treats the polyeletrolyte gel as a mixture of two materials, the network and the solvent. The dynamics of gel swelling is governed by the balance between the mechanical and chemical forces on each of these two materials. Simulations based on the model illustrate that the chemical forces are significantly influenced by the binding/unbinding reactions between the ions and the network, as well as the resulting distribution of charges within the gel. The dependence of the swelling rate on ionic bath concentrations is analyzed and this analysis highlights the importance of the electromigration of ions and the induced electric field in regulating gel swelling.

Physiological insights into electrodiffusive maintenance of gastric mucus through sensitivity analysis and simulations

It is generally accepted that the gastric mucosa and adjacent mucus layer are critical in the maintenance of a pH gradient from stomach lumen to stomach wall, protecting the mucosa from the acidic environment of the lumen and preventing auto-digestion of the epithelial layer. No conclusive study has shown precisely which physical, chemical, and regulatory mechanisms are responsible for maintaining this gradient. However, experimental work and modeling efforts have suggested that concentration dependent ion-exchange at the epithelial wall, together with hydrogen ion/mucus network binding, may produce the enormous pH gradients seen in vivo. As of yet, there has been no exhaustive study of how sensitive these modeling results are with respect to variation in model parameters, nor how sensitive such a regulatory mechanism may be to variation in physical/biological parameters. In this work, we perform sensitivity analysis (using Sobol' Indices) on a previously reported model of gastric pH gradient maintenance. We quantify the sensitivity of mucosal wall pH (as a proxy for epithelial health) to variations in biologically relevant parameters and illustrate how variations in these parameters affects the distribution of the measured pH values. In all parameter regimes, we see that the rate of cation/hydrogen exchange at the epithelial wall is the dominant parameter/effect with regards to variation in mucosal pH. By careful sensitivity analysis, we also investigate two different regimes representing high and low hydrogen secretion with different physiological interpretations. By complementing mechanistic modeling and biological hypotheses testing with parametric sensitivity analysis we are able to conclude which biological processes must be tightly regulated in order to robustly maintain the pH values necessary for healthy function of the stomach.

Ion-Induced Volume Transition in Gels and Its Role in Biology

Incremental changes in ionic composition, solvent quality, and temperature can lead to reversible and abrupt structural changes in many synthetic and biopolymer systems. In the biological milieu, this nonlinear response is believed to play an important functional role in various biological systems, including DNA condensation, cell secretion, water flow in xylem of plants, cell resting potential, and formation of membraneless organelles. While these systems are markedly different from one another, a physicochemical framework that treats them as polyelectrolytes, provides a means to interpret experimental results and make in silico predictions. This article summarizes experimental results made on ion-induced volume phase transition in a polyelectrolyte model gel (sodium polyacrylate) and observations on the above-mentioned biological systems indicating the existence of a steep response.

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.