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.
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        • Hansemann D.
        Ueber asymmetrische Zelltheilung in epithel Krebsen und deren biologische Bedeutung.
        Virschows Arch Pathol Anat. 1890; 119 ([On asymmetric mitoses in epithelial cancers and their biological significance]): 299-326
        • Mitelman F.
        Catalogue of chromosome aberrations in cancer. Wiley-Liss, New York1994
        • Sandberg A.A.
        The chromosomes in human cancer and leukemia. Elsevier Science Publishing, New York1990
        • Gebhart E.
        • Liehr T.
        Patterns of genomic imbalances in human solid tumors (review).
        Int J Oncol. 2000; 16: 383-399
        • Mertens F.
        • Johansson B.
        • Hoglund M.
        • Mitelman F.
        Chromosomal imbalance maps of malignant solid tumors.
        Cancer Res. 1997; 57: 2765-2780
        • Levan A.
        Chromosome abnormalities and carcinogenesis.
        in: Lima-de-Faria A. Handbook of molecular cytology. American Elsevier Publishing Co, New York1969: 716-731
        • Boveri T.
        Zur Frage der Entstehung maligner Tumoren. Fischer, Jena1914 ([On the question of the origin of malignant tumors])
        • Duesberg P.
        • Rasnick D.
        Aneuploidy, the somatic mutation that makes cancer a species of its own.
        Cell Motil Cytoskeleton. 2000; 47: 81-107
        • Li R.
        • Sonik A.
        • Stindl R.
        • Rasnick D.
        • Duesberg P.
        Aneuploidy versus gene mutation hypothesis.
        Proc Natl Acad Sci (USA). 2000; 97: 3236-3241
        • Rasnick D.
        • Duesberg P.H.
        How aneuploidy affects metabolic control and causes cancer.
        Biochem J. 1999; 340: 621-630
        • Rasnick D.
        Auto-catalyzed progression of aneuploidy explains the Hayflick limit of cultured cells, carcinogen-induced tumours in mice, and the age distribution of human cancer.
        Biochem J. 2000; 348: 497-506
        • Liu P.
        • Zhang H.
        • McLellan A.
        • Vogel H.
        • Bradley A.
        Embryonic lethality and tumorigenesis caused by segmental aneuploidy on mouse chromosome 11.
        Genetics. 1998; 150: 1155-1168
        • Sell S.
        • Pierce G.B.
        Biology of disease.
        Lab Invest. 1994; 70: 6-22
        • Anderson G.H.
        Chapter 3. W. B. Saunders Co, Philadelphia1991
        • Atkin N.B.
        • Baker M.C.
        Are human cancers ever diploid–or often trisomic? Conflicting evidence from direct preparations and culture.
        Cytogenet Cell Genet. 1990; 53: 58-60
        • Lindsley D.L.
        • Sandler L.
        • et al.
        Segmental aneuploidy and the genetic gross structure of the drosophila genome.
        Genetics. 1972; 71: 157-184
        • Sandler L.
        • Hecht F.
        Genetic effects of aneuploidy.
        Am J Hum Genet. 1973; 25: 332-339
        • Steel G.G.
        • Lamerton L.F.
        Cell population kinetics and chemotherapy. I. The kinetics of tumor cell populations.
        Natl Cancer Inst Monogr. 1969; 30: 29-42
        • Shackney S.E.
        • Berg G.
        • Simon S.R.
        • Cohen J.
        • Amina S.
        • et al.
        Origins and clinical implications of aneuploidy in early bladder cancer.
        Cytometry. 1995; 22: 307-316
        • Oksala T.
        • Therman E.
        Mitotic abnormalities and cancer.
        in: German J. Chromosomes and cancer. John Wiley & Sons, New York1974: 239-263
        • Giaretti W.
        • Santi L.
        Tumor progression by DNA flow cytometry in human colorectal cancer.
        Int J Cancer. 1990; 45: 597-603
        • Shackney S.E.
        • Smith C.A.
        • Miller B.W.
        • Burholt D.R.
        • Murtha K.
        • et al.
        Model for the genetic evolution of human solid tumors.
        Cancer Res. 1989; 49: 3344-3354
        • Shackney S.E.
        • Singh S.G.
        • Yakulis R.
        • Smith C.A.
        • Pollice A.A.
        • et al.
        Aneuploidy in breast cancer.
        Cytometry. 1995; 22: 282-291
        • Shankey T.V.
        • Kallioniemi O.-P.
        • Koslowski J.M.
        • Lieber M.L.
        • Mayall B.H.
        • et al.
        Consensus review of the clinical utility of DNA content cytometry in prostate cancer.
        Cytometry. 1993; 14: 497-500
        • Rous P.
        • Kidd J.G.
        Conditional neoplasms and subthreshold neoplastic states. A study of the tar tumors of rabbits.
        J Exp Med. 1941; 73: 365-389
        • Auer G.U.
        • Caspersson T.O.
        • Wallgren A.S.
        DNA content and survival in mammary carcinoma.
        Anal Quant Cytol Histol. 1980; 2: 161-165
        • Hering B.
        • Horn L.-C.
        • Nenning H.
        • Kühndel K.
        Predictive value of DNA cytometry in CIN 1 and 2.
        Anal Quant Cytol Histol. 2000; 22: 333-337
        • Rzymowska J.
        • Skierski J.
        • Kurylcio L.
        • Dyrda Z.
        DNA index as prognostic factor in breast cancer.
        Neoplasma. 1995; 42: 239-242
        • Lengauer C.
        • Kinzler K.W.
        • Vogelstein B.
        Genetic instabilities in human cancers.
        Nature. 1998; 396: 643-649
        • Levan A.
        • Biesele J.J.
        Role of chromosomes in cancerogenesis, as studied in serial tissue culture of mammalian cells.
        Ann NY Acad Sci. 1958; 71: 1022-1053
      1. Lucas C. Complexity philosophy as a computing paradigm. In: Self-organizing systems—future prospects for computing. Manchester, UK: UMIST Workshop, 1999. Available at:

        • Kato A.
        • Kubo K.
        • Kurokawa F.
        • Okita K.
        • Oga A.
        • Murakami T.
        Numerical aberrations of chromosomes 16, 17, and 18 in hepatocullular carcinoma.
        Dig Dis Sci. 1998; 43: 1-7
        • Jensen R.V.
        Classical chaos.
        Am Sci. 1987; 75: 168-181
        • Duesberg P.
        • Li R.
        • Rasnick D.
        • Rausch C.
        • Willer A.
        • et al.
        Aneuploidy precedes and segregates with chemical carcinogenesis.
        Cancer Genet Cytogenet. 2000; 119: 83-93
      2. Heylighen F. The science of self-organization and adaptivity. Center “Leo Apostel”, Free University of Brussels, Belgium, Brussels1999
        • Stutman O.
        Immunodepression and malignancy.
        Adv Cancer Res. 1975; 22: 261-422
        • Edinburgh
        Report of the medical committee of the society for investigating the nature and cure of cancer.
        Edinburgh Medical Surgery Journal. 1806; 2: 382
        • Burnet F.M.
        Cancer—a biological approach.
        Br Med J. 1957; 1: 779-786
        • Thomas L.
        Cellular and humoral aspects of the hypersensitive state (discussion). Harper, New York1959
        • Burnet F.M.
        Immunological surveillance in neoplasia.
        Transplant Rev. 1971; 7: 3-25
        • Gold M.
        A conspiracy of cells. State University of New York Press, New York1986
        • Herberman R.B.
        Possible role of natural killer cells and other effector cells in immune surveillance against cancer.
        J Invest Dermatol. 1984; 83: 137s-140s
        • Hewitt H.B.
        • Blake E.R.
        • Walder A.S.
        A critique of the evidence for active host defence against cancer, based on personal studies of 27 murine tumours of spontaneous origin.
        Br J Cancer. 1976; 33: 241-259
      3. Tannock IF. Conventional cancer therapy: promise broken or promise delayed? Lancet 1998;351(Suppl 2):SII9–16.

        • Epstein S.S.
        The politics of cancer revisited. East Ridge Press, New York1998
        • Whitman R.C.
        Somatic mutation as a factor in the production of cancer; a critical review of v. Hansemann's theory of anaplasia in the light of modern knowledge of genetics.
        J Cancer Res. 1919; 4: 181-202
        • Duesberg P.
        • Stindl R.
        • Hehlmann R.
        Explaining the high mutation rates of cancer cells to drug and multidrug resistance by chromosome reassortments that are catalyzed by aneuploidy.
        Proc Natl Acad Sci USA. 2000; 97: 14295-14300
        • Li C.I.
        • Malone K.E.
        • Weiss N.S.
        • Daling J.R.
        Tamoxifen therapy for primary breast cancer and risk of contralateral breast cancer.
        J Natl Cancer Inst. 2001; 93: 1008-1013
        • Gorre M.E.
        • Mohammed M.
        • Ellwood K.
        • Hsu N.
        • Paquette R.
        • et al.
        Clinical resistance to STI-571 cancer therapy caused by BCR-ABL gene mutation or amplification.
        Science. 2001; 293: 876-880
        • Nowell P.
        • Rowley J.
        • Knudson A.
        Cancer genetics, cytogenetics—defining the enemy within.
        Nat Med. 1998; 4: 1107-1111
        • Boveri T.
        Die Blastomerenkerne von Ascaris megalocephala und die Theorie der Chromosomenindividualität.
        Archiv Zellforschung. 1909; 3 ([The nuclei of blastomeres of (from) Ascaris megalocephalia and the theory of chromosomal individuality]): 181-268
        • Hayflick L.
        The limited in vitro lifetime of human diploid cell strains.
        Experimental Cell Res. 1965; 37: 614-636
        • Foulds L.
        The experimental study of tumor progression.
        Cancer Res. 1954; 14: 327-339
        • Niakan B.
        A mechanism of the spontaneous remission and regression of cancer.
        Cancer Biother Radiopharm. 1998; 13: 209-210
        • Challis G.B.
        • Stam H.J.
        The spontaneous regression of cancer.
        Acta Oncologica. 1990; 29: 545-550
        • Kappauf H.
        • Gallmeier W.M.
        • Wunsch P.H.
        • Mittelmeier H.O.
        • Birkmann J.
        • et al.
        Complete spontaneous remission in a patient with metastatic non-small-cell lung cancer. Case report, review of the literature, and discussion of possible biological pathways involved.
        Ann Oncol. 1997; 8: 1031-1039