Mathematical modelling of cell cluster formations

Mathematicians at the University of Adelaide have devised a method for identifying how cell clusters have formed by analysing an image of the cluster. Described in the Journal of Theoretical Biology, the tool will help biologists and tissue engineers grow human tissue such as liver in the laboratory.

“When any tissue or organ develops, the cells have to organise themselves into the correct structure,” said Dr Edward Green, one of the study authors. The cells form aggregates when cultured in vitro “through a variety of mechanisms,” said the researchers, “including rapid cell proliferation, chemotaxis or direct cell-to-cell contact”.

According to Dr Green, “This self-organisation process is important in regenerative medicine where scientists are trying to grow tissues in the laboratory. Getting the right structure is key to ensuring the tissue is viable and functional.”

But control of the organisation process is very complex, said Dr Green, and not well understood. He noted, “If you are trying to get cells to organise in certain ways, you need to know how they are behaving.” So the researchers developed “an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate”, they said.

Dr Green said the team looked at two ways of producing cell clusters: “by attraction through chemical and other signals and by proliferation (cells dividing)”. They then introduced a quantitative measure of the pattern of clustering from an image, producing a statistic called the ‘pair-correlation function’ which shows the relationship between cells. The researchers said this allows them to “quantify aspects of the spatial patterns produced by our agent-based model”.

“The two clustering mechanisms produce different patterns,” said Dr Green. “In some cases you can spot the differences simply by looking, but the pair-correlation function allows you to distinguish them, even when you can’t see any obvious differences between the pictures by eye.”

They validated their mathematical model experimentally using cells with known clustering mechanisms in collaboration with Queensland University of Technology. Dr Ben Binder, a co-author on the study, confirmed that the tool “gives a basic understanding of the process in clustering” and “will be useful in assessing what factors may be used to enhance the process of growing cells”.

“Next steps will be feeding experimental data back into the model to simulate biological processes,” Dr Binder said. “Instead of running lengthy and expensive experiments, we can look at the potential effects of different factors through the computer.”

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