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Death and Life of a Cell Mathematic al Measure of Life of a Cell

Death and Life of a Cell Mathematic al Measure of Life of a Cell. Estimates of the Cell Population Doublings (PD) , Cell Generations (CG) and Cell Loss (CL) in the Cell Culture of the Human Diploid Fibroblast (HDF) Presentation by Saša Tkalec. References.

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Death and Life of a Cell Mathematic al Measure of Life of a Cell

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  1. Death and Life of a CellMathematical Measure of Life of a Cell Estimates of the Cell Population Doublings (PD),Cell Generations (CG) and Cell Loss (CL) in the Cell Culture of the Human Diploid Fibroblast (HDF) Presentation by Saša Tkalec

  2. References • Rubelj, Huzak, Brdar: Sudden Senescence Syndrome Plays a Major Role in Cell Culture Proliferation: Mechanisms of Ageing and Development 112 (1999): pg. 233-241 • Rubelj, Vondracek: Stochastic Mechanism of Cellular Ageing – Abrupt Telomere Shortening as a Model for Stochastic Nature of Cellular Ageing: Journal of Theoretical Biology 197 (1999): pg. 425-438

  3. Research CentersAmazing Cutting Edge Research • Institute Ruđer Bošković – Zagreb, Croatia • http://www.irb.hr/ • Department of Mathematics – University of Zagreb, Croatia • http://www.math.hr/

  4. Problem • Investigate the nature of ageing • What is ageing at the cellular level? • What are mechanisms of ageing? • How old can cells get? What is the best measure of ageing? • Can a reliable mathematical model describing ageing be produced?

  5. ATS – Abrupt Telomere Shortening Occurs either through DNA recombination or nuclease digestion at the subtelomeric/ telomeric border region of the chromosome GTS – Gradual Telomere Shortening Occurs during each cell division as a consequence of the inability of DNA polymerase to replicate the very ends of chromosomal DNA Concepts Related to Ageing1/3

  6. Concepts Related to Ageing2/3 • SSS– Sudden Senescence Syndrome • Result of shortening of one or more telomeres in the cell causing a sudden onset of cell senescence • This is manifested as a stochastic and abrupt transition of cells from the larger to the smaller proliferative pool and can cause cell cycle arrest within one cell division

  7. Concepts Related to Ageing3/3 • PD – Population Doublings – number of times / measure of cell culture doublings • CG – Cell Generations – number of generations of cells (in any one line) produced over some period • CL – Cell Loss – Number of newly non-dividing cells observed between any two measurements

  8. What is of interests to us? Number of Cell Generations Comprehensible estimate of Cell Loss Number of Cell Doublings Problems in reaching results? Differences in PD of diff. HDF (sub)cultures Implications in other estimates Little Bit of Mathematics Behind It All

  9. How to deal with this problem? • Ignore it  (not a very good solution) • Blame others  (better, but still not a solution) • Apathy  (common, but not a solution) • Join MASS(excellent first step!) • Expressing percentage of labeled nuclei as a function of percent of lifespan completed: this yields highly reproducible relationship

  10. To Start… 1/5 Let Nk be the total size of the culture, and Ck a number ofcells with the nuclei labeled, both after the kth measurement. Fraction of cells with their nuclei labeled after the kth measurement is Pk=Ck/Nk. The number of PDs that the culture obtains between k-1th and kth measurements is tk= log2 (Nk/Nk-1).

  11. To Continue2/5 Furthermore, number of non-dividing cells between the k-1th and kth measurements is Nk-Ck therefore the number of cells in the culture, which are to divide immediately after the k-1th measurement, is Nk-1 – (Nk – Ck).

  12. My 1st calculations  today! The number of newborn CG between the k-1th and kth measurement is k is no less then

  13. More Calculations… Consequently, the total number of CGs k obtained in the moment of kth measurement satisfies where tk = t1 + t2 + … tk is the total number of PDs after the kth measurement.

  14. Don’t ask questions here…Just read it! • Because there average measurements are not real measurements, it is not possible to determine formula (2) for lower bound of k. • Let us suppose that between k-1th and kth average measurement from Table A (use your imagination – no space for Table here)one had a sequence of m real but unknown measurements which gave a sequence of PD increments tk1, tk2, …, tkm and the constant ratio of nuclei labeled equal to Pk (real measurement understands that inequality 1 – (1 – Pk)  2 tkj > 0).

  15. Relax and enjoy these beautiful #s! Then

  16. Since the function  2 is convex and 0 < Pk < 1, it follows that

  17. Coming to MASS CASE 2002 Zagreb?! And this is equivalent to

  18. Interpretation? The lower bound in (4; previous) is the best possible because

  19. Graphs, Interpretations, Results

  20. If there are no questions… The End

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