Evaluation of methods for one-dimensional spatial analysis of two-dimensional patterns in mouse chimaeras

Abstract

The relative extent of cell mixing in tissues of mouse chimaeras or mosaics can be studied by comparing the distributions of the two cell populations in the tissues. However, the mean patch size is misleading because it is affected by both the extent of cell mixing and the relative contributions of the two cell populations. Previous work suggested that effects attributable to differences in tissue composition among chimaeras can be factored out either by correcting the mean patch size or by using the median patch size for the minority cell population and restricting the analysis to grossly unbalanced chimaeras. In the present study, computer simulations of two-dimensional mosaic arrays of black and white squares (representing cells) were used to simulate chimaeric tissues. Random arrays simulated tissues with extensive cell mixing, arrays of cell clumps (representing coherent clones) simulated less mixed tissues, and striped arrays simulated tissues with elongated but fragmented descendent clones. The computer simulations predicted that (i) the median patch length (minority cell population) and the corrected mean patch length would both distinguish between random and clumped patterns and (ii) differences in the variation of the composition of two perpendicular series of one-dimensional transects would distinguished between stripes and randomly orientated patches. Both predictions were confirmed by analysis of histological sections of the retinal pigment epithelium from fetal and adult mouse chimaeras. This study demonstrates that two types of non-random two-dimensional variegated patterns (clumps and stripes) can be identified in chimaeras without two-dimensional reconstruction of serial sections.

Fig. 1

Patch length analysis using one-dimensional information from two-dimensional computer simulations of random, clumped and curved stripe arrays. (A–D) Illustrations of four types of arrays of 100 × 100 cells: (A) Random distribution of black and white cells. (B) Random distribution of clumps of four cells (2 × 2 clumps). (C) Random distribution of clumps of 16 cells (4 × 4 clumps). (D) Array comprising curved dark and light stripes, where the dark stripes contain both black and white cells and the light stripes contain only white cells. (E–P) Relationships between the percentage black cells in the arrays and (E–H) mean patch length, (I–L) median patch length and (M–P) corrected mean patch length. The horizontal and vertical patch length distributions are plotted separately for black and white patches in E–P (four plots shown per figure but some are superimposed). P-values shown by asterisks in the figures are for comparisons of mean, median or corrected mean patch lengths for horizontal vs. vertical transects. Separate comparisons for black and white patches for each set of arrays were made by Bonferroni post-hoc tests if a two-way anova with repeated measures showed transect orientation or interaction between transect orientation and percentage black had a significant overall effect on patch length across all array sets. Other statistical comparisons are discussed in the text. (*P<0.05; **P<0.01; ***P<0.001; ****P<0.0001.)

Fig. 2

Comparison of median patch length and corrected mean patch length in simulations of random and clumped arrays. (A–C) Relationships between the median patch length and corrected mean patch lengths in one-dimensional horizontal transect lines from two-dimensional simulations of (A) random arrays, (B) clumps of four cells (2 × 2 clumps) and (C) clumps of 16 cells (4 × 4 clumps). (D–F) Relationships between the median patch length and corrected mean patch length in one-dimensional vertical transect lines from two-dimensional simulations of (D) random arrays, (E) clumps of four cells (2 × 2 clumps) and (F) clumps of 16 cells (4 × 4 clumps). In each case a two-way anova with repeated measures showed that, overall, the patch length was affected by the type of summary statistic (median or corrected mean), the percentage black cells and the interaction between them. P-values shown in the figure are for Bonferroni post-hoc tests comparing median patch length vs. corrected mean patch lengths separately for each array set. (*P<0.05; **P<0.01; ***P<0.001; ****P<0.0001.)

Fig. 3

Patch length analysis using one-dimensional information from two-dimensional computer simulations of striped arrays. (A–D) Illustrations of four types of striped 100 × 100 arrays, comprising straight dark and light stripes, where the dark stripes contain predominantly black cells and the light stripes predominantly white cells. (A) Vertical stripes (0° from the vertical). (B) Stripes orientated 12° from the vertical. (C) Stripes orientated 30° from the vertical. (D) Stripes orientated 45° from the vertical. (E–P) Relationships between the percentage black cells in the arrays and (E–H) mean patch length, (I–L) median patch length and (M–P) corrected mean patch length. P-values shown in the figure are for comparisons of results from horizontal vs. vertical transects that were made for each set of arrays by Bonferroni post-hoc tests if a two-way anova with repeated measures showed transect orientation or interaction between transect orientation and percentage black had a significant overall effect on patch length. (*P<0.05; **P<0.01; ***P<0.001; ****P<0.0001.) ‘All Pairs: ****’ (in E and M) means that pairwise post-hoc tests comparing patch lengths in horizontal vs. vertical transects were highly statistically significant with P<0.0001 for all nine array sets.

Fig. 4

Variation in percentage black cells in one-dimensional transects of two-dimensional computer simulations of random, clumped and curved stripe arrays. (A–D) Illustrations of four types of arrays of 100 × 100 cells as described in Fig. 1. (E–H) Relationships between the total percentage black cells in the arrays and the variance of the percentage black cells, shown separately for the horizontal transects and the vertical transects. The difference between variances for horizontal and vertical transects (h–v) is also shown. (I–L) Relationships between the total percentage black cells in the arrays and the percentage coefficient of variation (%CV) of the percentage black cells shown separately for the horizontal transects and the vertical transects. The difference between the %CV for horizontal and vertical transects (h–v) is also shown. P-values shown in the figure are for comparisons of results from horizontal vs. vertical transects that were made for each set of arrays by Bonferroni post-hoc tests if a two-way anova with repeated measures showed transect orientation or interaction between transect orientation and percentage black had a significant overall effect on the variance or the percentage coefficient of variation of the percentage black cells. ‘All Pairs: ****’ means that pairwise post-hoc tests comparing variance (in H) or %CV (in L) in horizontal vs. vertical transects were highly statistically significant with P<0.0001 for all nine array sets. No pairwise comparisons in E–G or I–K were significant.

Fig. 5

Variation in percentage black cells in one-dimensional transects of two-dimensional computer simulations of striped arrays. (A–D) Illustrations of four types of striped 100 × 100 arrays, as described in Fig 3. (E–H) Relationships between the total percentage black cells in the arrays and the variance of the percentage black cells, shown separately for the horizontal transects and the vertical transects. The difference between variances for horizontal and vertical transects (h–v) is also shown. (I–L) Relationships between the total percentage black cells in the arrays and the percentage coefficient of variation (%CV) of the percentage black cells shown separately for the horizontal transects and the vertical transects. The difference between the %CV for horizontal and vertical transects (h–v) is also shown. P-values shown in the figure are for comparisons of results from horizontal vs. vertical transects that were made for each set of arrays by Bonferroni post-hoc tests if a two-way anova with repeated measures showed transect orientation or interaction between transect orientation and percentage black had a significant overall effect on the variance or the percentage coefficient of variation of the percentage black cells. (*P<0.05; **P<0.01; ***P<0.001; ****P<0.0001.) ‘All Pairs: ****’ means that pairwise post-hoc tests comparing variance (in E and F) or %CV (in I and J) in horizontal vs. vertical transects were highly statistically significant with P<0.0001 for all nine array sets.

Fig. 6

(A) Side view of the left eye of adult chimaera AdCA18 showing stripes in the RPE towards the iris (bottom of figure). Scale bar: 1 mm. (B). Plastic section of adult eye of chimaera AdCA29 showing patches in RPE (arrows). Scale bar: 50 μm.

Fig. 7

Intact left (A,C,E) and right (B,D,E) eyes of E12.5-day chimaeras showing patch distribution of pigmented cells in the RPE. (A,B) chimaera XM24; (C,D) chimaera XM28; (E,F) chimaera XP19. (Results of the analysis of mid-sections of eyes from chimaeras XM28 and XP19 are shown in Table 3 and two-dimensional reconstructions of RPE pigment distributions are shown in Fig. 8.) The diameter of each eye is approximately 0.5 mm.

Fig. 8

Diagrams of two-dimensional reconstructions of RPE pigment patterns from one-dimensional measurements of patch lengths in sections of fetal chimaeric eyes. Each pair of diagrams shows a planar (left) and annular (right) reconstruction of the same eye (see text for further details). (A) Right eye of XM28; (B) left eye of XM28; (C) right eye of XP19; (D) left eye of XP19. Left and right eyes were sectioned at different orientations. (Results of the analysis of mid-sections of eyes from chimaeras XM28 and XP19 are shown in Table 3 and photographs of the intact eyes at the time of dissection are shown in Fig. 7.) cor, cornea; on, optic nerve. Numbered arrows indicate equivalent regions on both forms of reconstruction. The arrows and the words ‘Inside’ and ‘Outside’ indicate matching edges of the planar and annular reconstruction.

Fig. 9

Histological sections of eye from E12.5 fetal chimaera showing pigmented patches in the RPE (arrows). (A) Low power view (nr = neural retina); (B) high power view; scale bar: 10 μm.

Fig. 10

Diagram showing expected relationship between planes of sections and radial stripes in the distal retinal pigment epithelium (RPE). The RPE is orientated so the proximal-distal axis is vertical (the proximal region is at the bottom). (A) Horizontal (‘latitudinal’) sections are orientated perpendicular to the stripes. (B) Vertical (‘longitudinal’) sections near the middle of the RPE are orientated nearly parallel to the stripes but because the RPE is cup-shaped, the more peripheral sections are not completely parallel to the stripes.