Modelling perspectives on aging: can mathematics help us stay young?

We survey several types of mathematical models that keep track of age distributions in a population, or follow some aspects of aging, such as loss of replicative potential of stem cells. The properties of a class of linear models of this type are discussed and compared. We illustrate the applicability of such models with a simple example based on hypothetical stem cell dynamics developed to address age-related telomere loss in the human granulocyte pool. We then describe the contrasting behaviour of nonlinear systems. Examples are drawn from the class of "dynamical diseases" to illustrate some of the aspects of nonlinear systems. Applications of these, and other models to the problems of aging and replicative aging are discussed.

[1]  P. Lansdorp,et al.  Asymmetric Cell Divisions Sustain Long-Term Hematopoiesis from Single-sorted Human Fetal Liver Cells , 1998, The Journal of experimental medicine.

[2]  James P. Keener,et al.  Mathematical physiology , 1998 .

[3]  J M M,et al.  Hematopoietic Model with Moving Boundary Condition and State Dependent Delay : Applications in Erythropoiesis , 1998 .

[4]  L. Glass,et al.  PATHOLOGICAL CONDITIONS RESULTING FROM INSTABILITIES IN PHYSIOLOGICAL CONTROL SYSTEMS * , 1979, Annals of the New York Academy of Sciences.

[5]  Anne Beuter,et al.  Tremor: Is Parkinson's disease a dynamical disease? , 1995, Chaos.

[6]  John Milton,et al.  Dynamic diseases in neurology and psychiatry. , 1995, Chaos.

[7]  K. Krajnak,et al.  Menopause: The Aging of Multiple Pacemakers , 1996, Science.

[8]  M. Loeffler,et al.  Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. Lessons for and from the crypt. , 1990, Development.

[9]  L. Hayflick.  THE LIMITED IN VITRO LIFETIME OF HUMAN DIPLOID CELL STRAINS. , 1965, Experimental cell research.

[10]  H. Caswell.  Matrix population models : construction, analysis, and interpretation , 2001 .

[11]  Sadri Hassani,et al.  Nonlinear Dynamics and Chaos , 2000 .

[12]  Leon Glass,et al.  Dynamical disease: Identification, temporal aspects and treatment strategies of human illness. , 1995, Chaos.

[13]  P. Lansdorp,et al.  Self-Renewal of Stem Cells , 1998 .

[14]  T. Kirkwood,et al.  Network theory of aging , 1997, Experimental Gerontology.

[15]  B. Gompertz,et al.  On the Nature of the Function Expressive of the Law of Human Mortality , 1825 .

[16]  J. Stark,et al.  Modelling the control of ovulation and polycystic ovary syndrome , 1997, Journal of mathematical biology.

[17]  N. Kopell.  Chains of coupled oscillators , 1998 .

[18]  H. Lacker.  Regulation of ovulation number in mammals. A follicle interaction law that controls maturation. , 1981, Biophysical journal.

[19]  Nathalie Rufer,et al.  Telomere Fluorescence Measurements in Granulocytes and T Lymphocyte Subsets Point to a High Turnover of Hematopoietic Stem Cells and Memory T Cells in Early Childhood , 1999, The Journal of experimental medicine.

[20]  T B Kirkwood,et al.  Towards a network theory of ageing: a model combining the free radical theory and the protein error theory. , 1994, Journal of theoretical biology.

[21]  M. Mackey,et al.  Age-structured and two-delay models for erythropoiesis. , 1995, Mathematical biosciences.

[22]  C B Harley,et al.  Telomere loss: mitotic clock or genetic time bomb? , 1991, Mutation research.

[23]  M. C. Mackey,et al.  Cyclical neutropenia and the peripheral control of white blood cell production. , 1998, Journal of theoretical biology.

[24]  T. Kirkwood,et al.  Accumulation of defective mitochondria through delayed degradation of damaged organelles and its possible role in the ageing of post-mitotic and dividing cells. , 2000, Journal of theoretical biology.

[25]  M. Faddy,et al.  Accelerated disappearance of ovarian follicles in mid-life: implications for forecasting menopause. , 1992, Human reproduction.

[26]  M. C. Mackey,et al.  Cell kinetic status of haematopoietic stem cells , 2001, Cell proliferation.

[27]  M Kimmel,et al.  Stochastic models of telomere shortening. , 1999, Mathematical biosciences.

[28]  E. Blackburn,et al.  The rate of telomere sequence loss in human leukocytes varies with age. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[29]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[30]  C B Harley,et al.  Telomere end-replication problem and cell aging. , 1992, Journal of molecular biology.

[31]  E. Akin,et al.  How do the ovaries count , 1988 .

[32]  M. Faddy,et al.  Ovary and ovulation: A model conforming the decline in follicle numbers to the age of menopause in women , 1996 .

[33]  R. Miller.  Telomere diminution as a cause of immune failure in old age: an unfashionable demurral. , 2000, Biochemical Society transactions.

[34]  Leon Glass,et al.  Time delays, oscillations, and chaos in physiological control systems , 1988 .

[35]  T. Kirkwood,et al.  A network theory of ageing: the interactions of defective mitochondria, aberrant proteins, free radicals and scavengers in the ageing process. , 1996, Mutation research.

[36]  L. Lipsitz.  Age-related changes in the "complexity" of cardiovascular dynamics: A potential marker of vulnerability to disease. , 1995, Chaos.

[37]  I. Rubelj,et al.  Stochastic mechanism of cellular aging--abrupt telomere shortening as a model for stochastic nature of cellular aging. , 1999, Journal of theoretical biology.

[38]  U. Erikson,et al.  INTRAVENOUS UROGRAPHY IN HYPERTENSION , 1975, The Lancet.

[39]  N. Kopell.  We Got Rhythm: Dynamical Systems of the Nervous System , 1999 .

[40]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[41]  A. Kowald.  The mitochondrial theory of aging: Do damaged mitochondria accumulate by delayed degradation? , 1999, Experimental Gerontology.

[42]  R. Hodes.  Telomere Length, Aging, and Somatic Cell Turnover , 1999, The Journal of experimental medicine.

[43]  A. D. Grey.  A proposed refinement of the mitochondrial free radical theory of aging , 1997 .

[44]  M. Mackey,et al.  Dynamical Diseases , 1987, Annals of the New York Academy of Sciences.

[45]  C. D. Dunn.  Current concepts in erythropoiesis , 1983 .

[46]  O. Pereira-smith,et al.  Replicative Senescence: Implications for in Vivo Aging and Tumor Suppression , 1996, Science.

[47]  L. Glass,et al.  Understanding Nonlinear Dynamics , 1995 .

[48]  H. Kay.  HOW MANY CELL-GENERATIONS? , 1965, Lancet.