Abstract
Multicellular aggregate growth is regulated by nutrient availability and removal of metabolites, but the specifics of growth dynamics are dependent on cell type and environment. Classical models of growth are based on differential equations. While in some cases these classical models match experimental observations, they can only predict growth of a limited number of cell types and so can only be selectively applied. Currently, no classical model provides a general mathematical representation of growth for any cell type and environment. This discrepancy limits their range of applications, which a general modelling framework can enhance. In this work, a hybrid cellular Potts model is used to explain the discrepancy between classical models as emergent behaviours from the same mathematical system. Intracellular processes are described using probability distributions of local chemical conditions for proliferation and death and simulated. By fitting simulation results to a generalization of the classical models, their emergence is demonstrated. Parameter variations elucidate how aggregate growth may behave like one classical growth model or another. Three classical growth model fits were tested, and emergence of the Gompertz equation was demonstrated. Effects of shape changes are demonstrated, which are significant for final aggregate size and growth rate, and occur stochastically.
Highlights
The growth of cell spheroids and tumours exhibits similar behaviours to ontogenetic growth of various animals [1,2], where growth is regulated by competition for nutrient availability provided by environmental conditions
A computational method was developed and employed to demonstrate that differing models of growth dynamics emerge from a phenotype-specific, statistical description of intracellular processes in response to local chemical conditions
This was accomplished by representing the subcellular mechanisms responsible for cell proliferation and death in response to local oxygen conditions as Gaussian probability distributions, which were incorporated into a hybrid cellular Potts model, simulated for diffusion-limited aggregate growth in idealized environmental conditions, and analysed according to the unified Richards model generalization of popular growth models
Summary
The growth of cell spheroids and tumours exhibits similar behaviours to ontogenetic growth of various animals [1,2], where growth is regulated by competition for nutrient availability provided by environmental conditions. Like mammary carcinoma cells, ischaemia leads to massive cell death and produces the so-called necrotic core, an inner region with no oxygen [5], minimal living cells and mostly cellular debris [6]. In this case, increased spheroid size and the onset of ischaemia are believed to induce significant outward diffusion of chemical species (e.g. lactate) that inhibit proliferation at the surface of the spheroid, the total effects of which produce emergent spheroid growth that can be approximated by classical growth models [3]. Other cell phenotypes like mesenchymal stem cells avoid the formation of a necrotic core altogether by adjusting their metabolism, packing density and secretion of extracellular matrix in response to decreasing available nutrients [7]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
