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Tissue Engineering

Developmental Biology and Morphogenesis of Engineered Tissues

Computational model of molecular gradients to inform 3D cell culture design

Friday, October 13, 2023
5:15 PM – 5:30 PM PDT
Location: 338 (Center, Level 3)
Introduction::





Hydrogel-based 3D cell culture systems are a promising tool for reproducing the spatial, structural, and functional features of tissues that cannot be represented in 2D culture (1). However, mass transport through a hydrogel differs from that in liquid media, potentially causing molecules added during experiments to form spatial gradients throughout the hydrogel (2). Diffusion kinetics, the rate of cellular uptake, and cell proliferation can impact the distribution of exogenous molecules across a 3D culture system. Understanding these parameters is critical for the interpretation of experimental results. Here, we create a computational model to predict molecular gradients and the resulting heterogeneity of cell exposure to an exogenous bioactive signaling molecule in a 3D culture system. We apply our computational model to 3D endometrial cultures used to study menstruation and uterine disorders (e.g., endometriosis, adenomyosis, and uterine cancer). We explore how the properties of the molecules of interest, the cells within the culture, and the hydrogel matrix affect the molecular gradients. Finally, we use this insight to provide recommendations for experimental platform design.









Materials and Methods::


We used partial differential equations to model the diffusion of molecules into the 3D gel and molecular uptake by cell-expressed receptors. To estimate changes in cell density over time, we used a computational model of endometrial cell proliferation within 3D endometrial cell culture which we previously created and calibrated using experimental data from (3). We modeled two endometrial cell types, epithelial organoid cells and stromal cells, which could differ in their proliferation rates and molecule uptake via receptors. We estimated the rates of molecule diffusion and uptake using previous in vitro studies and explored ranges in these parameter values in our sensitivity analysis.

Focusing on hemispherical hydrogels, the equations for this model were solved in Matlab in spherical coordinates. We assumed angular symmetry, constant concentration in the media at the gel edge, and no flux through the gel center. The model simulations were ran at equilibrium swelling conditions, meaning the gel radii used in simulations were for the final volumes after gel swelling in media. Since the commonly used polyethylene glycol (PEG)-based gels can double in size after swelling (4,5), we calculated the gel radius using double the initial gel volume for these cultures.

Using the simulated molecular distribution and cell density, we calculated the exposure of cells to molecules over the course of 15 days. We then performed sensitivity analyses to understand how molecular gradients and cell exposure depend on factors such as: gel size, molecule diffusivity, cell seeding density, and the cell uptake rate.






Results, Conclusions, and Discussions::





We first simulated IL-1β distribution in 3D endometrial cell cultures since IL-1β was the largest (17 kDa) signaling molecule added via media to experiments in (3). Endometrial cells express IL-1β receptors, which mediates IL- 1 consumption by cells (6). The rate of IL-1β loss through receptor-mediated internalization was found to be 1 – 6 *10-4 s-1 across multiple cell types in vitro (7,8), so we used this lower value in our starting estimate of cell uptake.





Our model predicted that the average IL-1β concentration across a gel seeded with 4*10^7 endometrial cells per mL reaches the concentration in the surrounding media (10 ng/mL) within 12 hours. This was consistent with an independent study that cultured endometrial cells for 2 days in a 25 μL gel (radius of 0.3 cm) (4) (Fig. 1a-b). Although the average IL-1β across the gel was predicted to be at least 9 ng/mL for 10 days, our model could show which regions of the gel had less IL-1β and how many cells were in those regions. We found the concentration across the gel to range from 7 – 10 ng/mL on day 10, and the percentage of cells exposed to at least 9 ng/mL halved between days 5 and 10 (Fig. 1c). Keeping the same cell density curves, we found this variance in IL-1β distribution and cell exposure could be minimized by reducing the gel radius from 0.3 to 0.14 cm (i.e., reducing the gel culture volume from 25 to 3 μL). This roughly ten-fold decrease in gel volume would lead to all cells being exposed to the same concentration of IL-1β as in the media for all 15 days, even if media concentration is also reduced ten-fold. Our analyses showed 3 μL cultures were also less sensitive to differences in cell proliferation rates and uptake rates than large cultures, suggesting smaller cultures would be ideal for platforms designed to compare multiple cell types or cells from different donors. Although the results discussed here are for 3D endometrial cultures in a hemispherical gel, model parameters can be adjusted to study different cell types and gel geometries.





Acknowledgements (Optional): :

References (Optional): :

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  2. Griffith LG, Swartz MA. Capturing complex 3D tissue physiology in vitro. Nat Rev Mol Cell Biol. 2006;7(3):211–24.

  3. Gnecco JS, Brown A, Buttrey K, Ives C, Brittany BA, Baugh L, et al. Organoid co-culture model of the cycling human endometrium in a fully-defined synthetic extracellular matrix reveals epithelial-stromal crosstalk. bioRxiv [Internet]. 2022; Available from: https://doi.org/10.1101/2021.09.30.462577

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  6. Tabibzadeh S, Kaffka KL, Satyaswaroop PG, Kilian PL. Interleukin-1 (IL-1) regulation of human endometrial function: Presence of IL-1 receptor correlates with IL-1-stimulated prostaglandin E2 production. Journal of Clinical Endocrinology and Metabolism. 1990;70(4).

  7. Mizel SB, Kilian PL, Lewis JC, Paganelli KA, Chizzonite RA. The interleukin 1 receptor. Dynamics of interleukin 1 binding and internalization in T cells and fibroblasts. The Journal of Immunology. 1987;138(9):2906–12.

  8. Lowenthal JW, MacDonald HR. Binding and internalization of interleukin 1 by T cells. J Exp Med. 1986;164(October):1060–74.