Optimization of Media Change Intervals through Hydrogels Using Mathematical Models.

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

3D Lung-on-Chip Model Based on Biomimetically Microcurved Culture Membranes.

A comparatively straightforward approach to accomplish more physiological realism in organ-on-a-chip (OoC) models is through substrate geometry. There is increasing evidence that the strongly, microscale curved surfaces that epithelial or endothelial cells experience when lining small body lumens, such as the alveoli or blood vessels, impact their behavior. However, the most commonly used cell culture substrates for modeling of these human tissue barriers in OoCs, ion track-etched porous membranes, provide only flat surfaces. Here, we propose a more realistic culture environment for alveolar cells based on biomimetically microcurved track-etched membranes. They recreate the mainly spherical geometry of the cells' native microenvironment. In this feasibility study, the membranes were given the shape of hexagonally arrayed hemispherical microwells by an innovative combination of three-dimensional (3D) microfilm (thermo)forming and ion track technology. Integrated in microfluidic chips, they separated a top from a bottom cell culture chamber. The microcurved membranes were seeded by infusion with primary human alveolar epithelial cells. Despite the pronounced topology, the cells fully lined the alveoli-like microwell structures on the membranes' top side. The confluent curved epithelial cell monolayers could be cultured successfully at the air-liquid interface for 14 days. Similarly, the top and bottom sides of the microcurved membranes were seeded with cells from the Calu-3 lung epithelial cell line and human lung microvascular endothelial cells, respectively. Thereby, the latter lined the interalveolar septum-like interspace between the microwells in a network-type fashion, as in the natural counterpart. The coculture was maintained for 11 days. The presented 3D lung-on-a-chip model might set the stage for other (micro)anatomically inspired membrane-based OoCs in the future.

Mechanistic Computational Models of Epithelial Cell Transporters-the Adorned Heroes of Pharmacokinetics.

Epithelial membrane transporter kinetics portray an irrefutable role in solute transport in and out of cells. Mechanistic models are used to investigate the transport of solutes at the organ, tissue, cell or membrane scale. Here, we review the recent advancements in using computational models to investigate epithelial transport kinetics on the cell membrane. Various methods have been employed to develop transport phenomena models of solute flux across the epithelial cell membrane. Interestingly, we noted that many models used lumped parameters, such as the Michaelis-Menten kinetics, to simplify the transporter-mediated reaction term. Unfortunately, this assumption neglects transporter numbers or the fact that transport across the membrane may be affected by external cues. In contrast, more recent mechanistic transporter kinetics models account for the transporter number. By creating models closer to reality researchers can investigate the downstream effects of physical or chemical disturbances on the system. Evidently, there is a need to increase the complexity of mechanistic models investigating the solute flux across a membrane to gain more knowledge of transporter-solute interactions by assigning individual parameter values to the transporter kinetics and capturing their dependence on each other. This change results in better pharmacokinetic predictions in larger scale platforms. More reliable and efficient model predictions can be made by creating mechanistic computational models coupled with dedicated in vitro experiments. It is also vital to foster collaborative efforts among transporter kinetics researchers in the modeling, material science and biological fields.

The Influence of OAT1 Density and Functionality on Indoxyl Sulfate Transport in the Human Proximal Tubule: An Integrated Computational and In Vitro Study.

Research has shown that traditional dialysis is an insufficient long-term therapy for patients suffering from end-stage kidney disease due to the high retention of uremic toxins in the blood as a result of the absence of the active transport functionality of the proximal tubule (PT). The PT's function is defined by the epithelial membrane transporters, which have an integral role in toxin clearance. However, the intricate PT transporter-toxin interactions are not fully explored, and it is challenging to decouple their effects in toxin removal in vitro. Computational models are necessary to unravel and quantify the toxin-transporter interactions and develop an alternative therapy to dialysis. This includes the bioartificial kidney, where the hollow dialysis fibers are covered with kidney epithelial cells. In this integrated experimental-computational study, we developed a PT computational model that focuses on indoxyl sulfate (IS) transport by organic anionic transporter 1 (OAT1), capturing the transporter density in detail along the basolateral cell membrane as well as the activity of the transporter and the inward boundary flux. The unknown parameter values of the OAT1 density (1.15×107 transporters µm-2), IS uptake (1.75×10-5 µM-1 s-1), and dissociation (4.18×10-4 s-1) were fitted and validated with experimental LC-MS/MS time-series data of the IS concentration. The computational model was expanded to incorporate albumin conformational changes present in uremic patients. The results suggest that IS removal in the physiological model was influenced mainly by transporter density and IS dissociation rate from OAT1 and not by the initial albumin concentration. While in uremic conditions considering albumin conformational changes, the rate-limiting factors were the transporter density and IS uptake rate, which were followed closely by the albumin-binding rate and IS dissociation rate. In summary, the results of this study provide an exciting avenue to help understand the toxin-transporter complexities in the PT and make better-informed decisions on bioartificial kidney designs and the underlining transporter-related issues in uremic patients.

Modeling indoxyl sulfate transport in a bioartificial kidney: Two-step binding kinetics or lumped parameters model for uremic toxin clearance?

Toxin removal by the kidney is deficient in a patient suffering from end-stage kidney disease (ESKD), and current dialysis therapies are insufficient in subsidizing this loss. A bioartificial kidney (BAK) aspires to offer ESKD patients a more effective alternative to dialysis. Mathematical models are necessary to support further developments and improve designs for the BAK before clinical trials. The BAK differentiates itself from dialysis by incorporating a living proximal tubule cell monolayer to account for the active transport of protein-bound uremic toxins, namely indoxyl sulfate (IS) in this study. Optimizing such a device is far from trivial due to the non-intuitive spatiotemporal dynamics of the IS removal process. This study used mathematical models to compare two types of active transport kinetics. i.e., two-step binding and lumped parameter. The modeling results indicated that the transporter density is the most influential parameter for the IS clearance. Moreover, a uniform distribution of transporters increases the IS clearance, highlighting the need for a high-quality, functional proximal tubule monolayer in the BAK. In summary, this study contributed to an improved understanding of IS transport in the BAK, which can be used along with laboratory experiments to develop promising renal replacement therapies in the future.

Ten steps to investigate a cellular system with mathematical modeling.

Cellular and intracellular processes are inherently complex due to the large number of components and interactions, which are often nonlinear and occur at different spatiotemporal scales. Because of this complexity, mathematical modeling is increasingly used to simulate such systems and perform experiments in silico, many orders of magnitude faster than real experiments and often at a higher spatiotemporal resolution. In this article, we will focus on the generic modeling process and illustrate it with an example model of membrane lipid turnover.