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Power Law Distribution of Chromosome Aberrations in Cancer¹

Centre for Mathematical Sciences, Mathematical Statistics, Lund University [A. F.], and Department of Clinical Genetics, University Hospital, Lund [D. G., F. M., M. H.], Sweden

Cancer cells are characterized by having aberrant chromosomes. The number of aberrations and the specific chromosomes affected are correlated with tumor progression. We show that for breast, colorectal, and renal cell carcinomas the distribution of the number of such aberrations per tumor follow a power law distribution with an exponent close to unity. We present two stochastic models that in simulation experiments result in power law distributions of the number of changes per tumor. The first model is based on a multiplicative fluctuation process and the second on a preferential attachment principle linked to an observation process, i.e., a tumor detection and treatment process. Because almost identical power law distributions are seen in breast, colorectal, and renal cell carcinomas we suggest that the obtained distributions are consequences of a common mechanism operating in malignant epithelial tumors.