How domain growth is implemented determines the long term behaviour of a cell population through its effect on spatial correlations

Robert J. H. Ross; R. E. Baker; C. A. Yates

In this work we have studied two different implementations of domain growth. We chose two different, yet potentially biologically relevant growth mechanisms [42] [43] [44] , to highlight how understanding the form of domain growth is crucial. These growth mechanisms originated from thinking about the different ways in which new sites could be added to the IBM domain, and the consequences this may have on agent density. As has been shown in this work, GM1 is an implementation of domain growth that conserves colinear correlations in comparison to diagonal correlations, and GM2 is one that reduces colinear correlations as a rate proportional to the size of the domain. This difference between GM1 and GM2 is why GM2 exhibits a length dependency and GM1 does not. It is important to stress we have used GM1 as an extreme example of growth in which the cell cycles of adjacent cells that are causing the domain to grow are synchronous (i.e. the cells in the underlying tissue), and GM2 as an example of when they are not. In reality, it is unlikely that domain growth in biological systems can be captured by algorithms as simple as GM1 and GM2. However, they represent the simplest and most tractable domain growth mechanisms for this initial study.