A hybrid cellular automaton model of clonal evolution in cancer: The emergence of the glycolytic phenotype

Abstract

We present a cellular automaton model of clonal evolution in cancer aimed at investigating the emergence of the glycolytic phenotype. In the model each cell is equipped with a micro-environment response network that determines the behaviour or phenotype of the cell based on the local environment. The response network is modelled using a feed-forward neural network, which is subject to mutations when the cells divide. This implies that cells might react differently to the environment and when space and nutrients are limited only the fittest cells will survive. With this model we have investigated the impact of the environment on the growth dynamics of the tumour. In particular we have analysed the influence of the tissue oxygen concentration and extra-cellular matrix density on the dynamics of the model. We found that the environment influences both the growth and evolutionary dynamics of the tumour. For low oxygen concentration we observe tumours with a fingered morphology, while increasing the matrix density gives rise to more compact tumours with wider fingers. The distribution of phenotypes in the tumour is also affected, and we observe that the glycolytic phenotype is most likely to emerge in a poorly oxygenated tissue with a high matrix density. Our results suggest that it is the combined effect of the oxygen concentration and matrix density that creates an environment where the glycolytic phenotype has a growth advantage and consequently is most likely to appear.

Necrotic core in EMT6/Ro tumour spheroids: Is it caused by an ATP deficit?

“…More recently the cell energy metabolism, i.e. the intracellular ATP production, has been incorporated in continuous models of spheroid (Venkatasubramanian et al, 2006) and tumour cord growth (Astanin and Tosin, 2007), as well as in cellular automata tumour growth models (Smallbone et al, 2007, Gerlee andAnderson, 2008). Bertuzzi et al (2007) proposed a simple mathematical model of cell ATP production that accounts for the main reactions occurring in the glycolytic and the oxidative pathways.…”

Mathematical modelling of the Warburg effect in tumour cords

“…Their discrete and continuous models and experiments demonstrate that emergence of the acidresistant, glycolytic cell line is an important step towards cancer invasiveness. Another recent work is (Gerlee & Anderson, 2008), where the cellular automaton model demonstrates that an advantage of the glycolytic phenotype may be also conditioned by the density of the matrix. In (Venkatasubramanian et al, 2006) ability of the cells to rely on the glycolytic metabolism was incorporated in the continuous model of tumour spheroid.…”

Multiphase and Multiscale Trends in Cancer Modelling

“…In particular, [8] summarises the characteristics of what in [35,36] it is called evolutionary hybrid cellular automata model (and we prefer here to classify as nested model). In this approach, the evolution of each single cell is accompanied by a micro-environment response network.…”

“…In a spirit similar to [35,36], Jiang et al [39] used a cellular Potts model to describe the growth of an avascular multicellular spheroid, where the behaviour of each single tumour cell is determined by a Boolean network which regulates the expression of some key proteins controlling the cell cycle.…”