Aneuploidy theory explains tumor formation, the absence of immune surveillance, and the failure of chemotherapy

The autocatalyzed progression of aneuploidy accounts for all cancer-specific phenotypes, the Hayflick limit of cultured cells, carcinogen-induced tumors in mice, the age distribution of human cancer, and multidrug-resistance. Here aneuploidy theory addresses tumor formation. The logistic equation, φn+1 = rφn (1 − φn), models the autocatalyzed progression of aneuploidy in vivo and in vitro. The variable φn+1 is the average aneuploid fraction of a population of cells at the n+1 cell division and is determined by the value at the nth cell division. The value r is the growth control parameter. The logistic equation was used to compute the probability distribution for values of φ after numerous divisions of aneuploid cells. The autocatalyzed progression of aneuploidy follows the laws of deterministic chaos, which means that certain values of φ are more probable than others. The probability map of the logistic equation shows that: 1) an aneuploid fraction of at least 0.30 is necessary to sustain a population of cancer cells; and 2) the most likely aneuploid fraction after many population doublings is 0.70, which is equivalent to a DNAindex=1.7, the point of maximum disorder of the genome that still sustains life. Aneuploidy theory also explains the lack of immune surveillance and the failure of chemotherapy.