Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth

Abstract

We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal. We demonstrate that SCs play a central role in normal and cancer colon organoids. Spatial patterning of the SC self-renewal promoter gives rise to SC clusters, which mimic stem cell niches, around the organoid surface, and drive the development of invasive fingers. We also study the effects of externally applied signaling factors. Applying bone morphogenic proteins, which inhibit SC and CP self-renewal, reduces invasiveness and organoid size. Applying hepatocyte growth factor, which enhances SC self-renewal, produces larger sizes and enhances finger development at low concentrations but suppresses fingers at high concentrations. These results are consistent with recent experiments on colon organoids. Because many cancers are hierarchically organized and are subject to feedback regulation similar to that in normal tissues, our results suggest that in cancer, control of cancer stem cell self-renewal should influence the size and shape in similar ways, thereby opening the door to novel therapies.

Morphophenotypic classification of tumor organoids as an indicator of drug exposure and penetration potential

“…Various modeling frameworks were employed to investigate organoid development, metabolic variability and interactions with other components of tumor microenvironment. These include cellular automata models [24–27], particle-force models [28–30], Cellular Potts models [31–33], continuous models [34] and our own immersed boundary model [35, 36]. Our recent review [37] provides more details on these models and summarizes latest achievements in the mathematical modeling of tumor organoids.…”

Collective cell mechanics of epithelial shells with organoid-like morphologies

“…Organoid shape depends on many factors and processes including the intrinsic physical features of individual cells, cell growth and division rates, cell differentiation, etc. So far, theoretical studies of the role of these factors were mostly carried out by representing the tissue as a continuous concentration field in a model of Cahn-Hilliard type 8,9 or as an ensemble of spherical entities using discrete models 7,10 . These approaches account for the biochemical regulation of organoid growth, yielding invaluable insight into, e.g., strategies of anticancer therapy 9 .…”

“…So far, theoretical studies of the role of these factors were mostly carried out by representing the tissue as a continuous concentration field in a model of Cahn-Hilliard type 8,9 or as an ensemble of spherical entities using discrete models 7,10 . These approaches account for the biochemical regulation of organoid growth, yielding invaluable insight into, e.g., strategies of anticancer therapy 9 . Recently, a 3D vertex model was employed to study how chemical patterning controlling the local cell-growth rate may feed back to the mechanics to determine organoid morphology 11 .…”

Mathematical Models of Organoid Cultures

“…(C) Representation of a simulated optic-cup organoid (Okuda et al, 2018a). (D) Computational model of colon organoids created to study the effect of exogenous substances in the growth pattern and spatial distributions, to compare them with cancer phenotypes (Yan et al, 2018). (E) Diffusion model of a spheroid that simulates the consumption of nutrients in cerebral organoids to predict growth patterns (McMurtrey, 2016).…”