Analysis of variability in albumin content of sister hepatoma cells and a model for geometric phenotypic variability (quantitative shift model)

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Abstract
A model (quantitative shift model) is presented that can account for the phenomenon termed geometric phenotypic variability in which quantitative variation occurs along a √2-fold geometric series. The model is based on data for variability in albumin content in hepatoma cells and has three basic assumptions: (i) The albumin genes on each chromosome are active and under independent quantitative regulation, (ii) The rate of albumin gene transcription per cell is the sum of the rates of transcription of the genes of each chromosome. (iii) The mechanism that controls the rate of transcription is highly variable so that at each cell cycle there is a high probability (P=0.1–0.3) that on the newly synthesized chromatid the rate of transcription of the albumin gene will be different from that of the old chromatid. However, if the rate is different, it will usually be either half or twice the levels of the old chromatid. A computer program was developed based on the model that can generate quantitative diversity in single cells that mimics the pattern of variability in albumin content between sister hepatoma cells, among cells in clonal colonies, and in cell populations where the periodicities in single-cell distributions are compared by Fourier transform analysis. It was determined that the rate of phenotypic variability is indirectly proportional to the magnitude of the quantitative shift in albumin content and that it can be as high as 0.3 per cell per generation. Also, the √2 factor in geometric phenotypic variability appears to be an average of a family of values and not the actual value of the smallest quantal shift.