Quantitative phenotypic variation in single normal and malignant cells from liver and breast occurs along a geometric series

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Abstract
Single cell variability in albumin content of normal rat hepatocytes and hepatoma cells and in a specific breast surface antigen content in normal and malignant human mammary epithelial cells was studied by a quantitative immunoperoxidase method. The range of variability was nearly 10-fold for both normal and malignant cells. This wide range of single cell heterogeneity was generated very rapidly in clonal colonies of less than 30 hepatoma cells. By a grid test for periodicity that we devised, and also by Fourier transform analysis, the distribution of albumin content in single hepatocytes and hepatoma cells, and of a breast surface antigen content in normal and malignant breast cells, was shown to be discontinuous, where the cells distributed with a periodicity that fit a geometric series, of which consecutive values differed by a factor of √2. The fit to this geometric series was best for normal cells. Significant quantal shifts occurred at a high rate (>10−2 per cell per generation) and to higher and lower levels with equal probability. These results demonstrate that geometric phenotypic variability is a normal phenomenon and should be taken into account when studying gene regulation and population dynamics.