Modeling the impact of granular embedding media, and pulling versus pushing cells on growing cell clones

Dirk Drasdo,Stefan Hoehme

doi:10.1088/1367-2630/14/5/055025

Abstract

In this paper, we explore how potential biomechanical influences on cell cycle entrance and cell migration affect the growth dynamics of cell populations. We consider cell populations growing in free, granular and tissue-like environments using a mathematical single-cell-based model. In a free environment we study the effect of pushing movements triggered by proliferation versus active pulling movements of cells stretching cell–cell contacts on the multi-cellular kinetics and the cell population morphotype. By growing cell clones embedded in agarose gel or cells of another type, one can mimic aspects of embedding tissues. We perform simulation studies of cell clones expanding in an environment of granular objects and of chemically inert cells. In certain parameter ranges, we find the formation of invasive fingers reminiscent of viscous fingering. Since the simulation studies are highly computation-time consuming, we mainly study one-cell-thick monolayers and show that for selected parameter settings the results also hold for multi-cellular spheroids. Finally, we compare our model to the experimentally observed growth dynamics of multi-cellular spheroids in agarose gel.

Highlights

Comparisons of experiments with mathematical models have shown that the increase of the cell population diameter as well as of the cell proliferation pattern, in both growing monolayers [24, 25] and growing multi-cellular spheroids [24,25,26,27], could largely be explained by a biomechanical form of contact inhibition, controlled by a force threshold, a pressure threshold or a deformation threshold, above which cells become quiescent
A careful analysis of EMT6/Ro multi-cellular spheroids revealed that the size of a multi-cellular spheroid is almost unaffected even when the external glucose concentration is varied by a factor of 20 from 0.8 to 16.5 mM, while at the same time the cell population sizes varied significantly
Examples are the Mullins–Sekerka instability of a growing crystal in a supercooled melt driven by undercooling at the solid–liquid interface, and an elasticity-driven growth instability as a consequence of an applied stress [39], a buckling instability driven by the competition of cell proliferation and stabilizing effects such as bending or shear, or an undulation stability as it may occur at the epithelial stromal

Summary

Introduction

Comparisons of experiments with mathematical models have shown that the increase of the cell population diameter as well as of the cell proliferation pattern, in both growing monolayers [24, 25] and growing multi-cellular spheroids [24,25,26,27], could largely be explained by a biomechanical form of contact inhibition, controlled by a force threshold, a pressure threshold or a deformation threshold, above which cells become quiescent. [29]) in cancer where the tissue phenotype changes from an epithelium-type phenotype to a mesenchymal phenotype by active intracellular regulation facilitating cell detachment [30,31,32]. Another example is that cells are able to enter blood vessels by a process called intravasation involving cancer-cell-induced src activation, leading to the degradation of contacts among endothelial cells, and thereby decrease the mechanical resistance of the blood vessel walls against cancer cell invasion [33]. Cell birth and death may facilitate cell movement in tissues which on short time scales appear as elastic material [16] These examples suggest that there is a complex interplay of mechanical and active regulative components during different stages of tumor growth, development and invasion. Different morphotypes have observed bacterial growth which could be explained by different types of instabilities [44]

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Conclusion