Fractal geometry in rat chimeras demonstrates that a repetitive cell division program may generate liver parenchyma

In the development of mammalian organs, a rapid and robust expansion of the parenchymal compartment must occur following allocation of organ primordia. This expansion must be regulated so that sufficient tissue mass is generated for further organization into functional tissues. The discovery that mosaic patches in the liver of rat chimeras are fractal (a geometric form with characteristic complexity) suggests a possible information storage scheme for programs of parenchyma generation. Since fractal objects are produced by the repetitive application of specific rules, it is possible that such a mechanism is responsible for the generation of organ parenchyma. The model cell division program for the generation of organ parenchyma considered here is to choose a cell at random to divide and place the daughter cell in a randomly chosen adjacent position displacing other cells which might occupy the chosen position. The completion of the division creates a new population of cells representing the input conditions for the next division. When this is repeated over and over in a tissue comprising two genetically distinguishable populations of cells, analysis of the geometry of the mosaic pattern obtained should fulfill specific predictions. If cell division occurred in this manner, the complexity of patch boundaries (patches are contiguous aggregates of cells of the same marker lineage in tissue from a chimera) should be independent of the proportion of the two parental cell lineages which make up the chimera's tissue. However, the complexity of the entire patch pattern should be dependent on this proportion. The complexity of the spatial distribution of the patches within a chimera's tissue should also be dependent on the proportion of the two parental lineages. We have measured the complexity of patch boundaries (surface fractal dimension), the complexity of entire fields of patches (mass fractal dimension), and the complexity of the spatial distribution of patches (fractal fragmentation) in rat liver from chimeras. We have established that the surface fractal dimension does not change as the proportion of the two parental lineages in the chimera's tissue changes, that there is a simple relationship between the complexity of entire patches and this proportion, and that the patches are fractally fragmented. These results are consistent with the hypothesis that repetitive application of this simple cell division program accounts for the generation of liver parenchyma.