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

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 tissuelike 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.

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

“…Commonly used criteria for cell cycle progression control by contact inhibition on the whole cell level are cell deformation, volume compression, a force threshold or a stress threshold, each of which have proven to qualitatively predict growth limitation in tumor models [144]. A machinery of molecular factors underly the decision processes (e.g., [145,146]).…”

“…Hoehme et al [33,84] implemented this by assuming that cell cycle entrance was possible only after division in a certain time point or small window in G 1 phase mimicking the restriction point. Once a cell passes the restriction point it progresses until divi- of elastic particles to mimic the mechanical resistance of agarose gel [144]. As in the cellular automaton models, growth is first exponential turning into linear growth sion with probability one.…”

“…Schaller and Meyer-Hermann [143] considered cellcycle entrance if the local pressure was below a critical value. Drasdo and Hoehme [144] also compared the consequence of different cell cycle entrance criteria such as a compression threshold, a tension threshold (meaning cells enter cell cycle only if stretched), and different mechanical stress-related criteria, on monolayer growth (Fig. 14).…”

“…However, as the latter measure was considered in growing cell populations with all cells permanently under compression, it differs only by a pressure shift. Defining instead [144]:…”

“…This study was motivated by the experimental findings of Trepat et al [18] suggesting that border cells migrate actively into their environment pulling interior cells behind. Reference [144] studied if the experimental observations could be explained if cell cycle entrance could occur only for cells under negative pressure, here defined such that the cell contacts are subject to stretch. For growing monolayers with all cells under compression, all three measures differ only by moderate shifts of the pres-sure curves.…”