Open Access Open Badges Research article

Techniques for analysing pattern formation in populations of stem cells and their progeny

John A Fozard12, Glen R Kirkham23, Lee DK Buttery23, John R King12, Oliver E Jensen12 and Helen M Byrne12*

Author Affiliations

1 Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

2 Wolfson Centre for Stem Cells, Tissue Engineering & Modelling, Centre for Biomolecular Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

3 Division of Advanced Drug Delivery & Tissue Engineering, School of Pharmacy, University of Nottingham, University Park, Nottingham NG7 2RD, UK

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BMC Bioinformatics 2011, 12:396  doi:10.1186/1471-2105-12-396

Published: 12 October 2011



To investigate how patterns of cell differentiation are related to underlying intra- and inter-cellular signalling pathways, we use a stochastic individual-based model to simulate pattern formation when stem cells and their progeny are cultured as a monolayer. We assume that the fate of an individual cell is regulated by the signals it receives from neighbouring cells via either diffusive or juxtacrine signalling. We analyse simulated patterns using two different spatial statistical measures that are suited to planar multicellular systems: pair correlation functions (PCFs) and quadrat histograms (QHs).


With a diffusive signalling mechanism, pattern size (revealed by PCFs) is determined by both morphogen decay rate and a sensitivity parameter that determines the degree to which morphogen biases differentiation; high sensitivity and slow decay give rise to large-scale patterns. In contrast, with juxtacrine signalling, high sensitivity produces well-defined patterns over shorter lengthscales. QHs are simpler to compute than PCFs and allow us to distinguish between random differentiation at low sensitivities and patterned states generated at higher sensitivities.


PCFs and QHs together provide an effective means of characterising emergent patterns of differentiation in planar multicellular aggregates.