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Figure 3 | BMC Bioinformatics

Figure 3

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

Figure 3

Characterising patterns with spatial statistics. (a,d) show two representative model simulations, computed with different parameter values ((a) Sdiff = 40, λ = 10; (b) Sdiff = 1, λ = 40); colours indicate R/G differentiation states; non-overlapping disks represent individual cells. (b,e) show the corresponding PCFs and (c,f) the QHs. In (b,e), the dashed line is the cross PCF g S (r) for pairs of cells of the same type; the solid line is the PCF g(r) for all pairs of cells. The numbers on the QH (c) indicate the normalised frequencies (and corresponding percentages) for the end bins (which exceed the vertical scale of the histogram). In (a,b,c), the cells are organised into distinct patches, reflected in the behaviour of the PCFs; g S (r) > g(r) for r < r P (i.e., nearby pairs of cells are more likely to be of the same type than two cells selected at random), the intersection point r = r p giving a quantitative estimate of pattern scale. The QH (c) also indicates the formation of patches, as the majority of the quadrats contain cells of one type (the range 0 <p < 1 is divided into 50 bins, and the values are normalised such that the total area is one). In (d,e,f), the cells appear to have differentiated at random, with no discernible structure. This can be seen from the PCFs in (e), with g S ≈ g(r) for all r (i.e., two nearby cells selected at random are no more likely to be of the same type than two well-separated cells). Similarly, the QH (f) shows that most of the quadrats contain a mixture of cells of different types, and the proportion of cells of type R in each quadrat is well described by a truncated normal distribution on [0,1] with mean 1/2 and variance M q 2 ∕4N (solid line).

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