Transition probability cell cycle model. Part I - Balanced growth

Journal of Theoretical Biology

Volumn 185, Issue 1, 1997, Pages 55-67

  Cain, Scott J ^a   Chau, Pao C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CELL CYCLE; CELL GROWTH; CELL POPULATION; MITOSIS; PRIORITY JOURNAL; STATISTICAL MODEL;

EID: 0031557381     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0289     Document Type: Article

References (40)

1. BERTUZZI, A., GANDOLFI, A. & VITELLI, R. (1986). A regularization procedure for estimating cell kinetic parameters from flow cytometry data. Math. Biosci. 82, 63-85.
2. BROOKS, R. F., BENNETT, D. C. & SMITH, J. A. (1980). Mammalian cell cycles need two random transitions. Cell 19, 493-504.
3. o-phase in the cell cycle. Cell Tissue Kinet. 3, 321-334.
4. COLLINS, J. F. & RICHMOND, M. H. (1962). Rate of growth of Bacillus cereus between divisions. J. Gen. Microbiol. 28, 15-33.
5. DIBROV, D. F., ZHABOTINSKY, A. M., NEYFAKH, Y. A., ORLOVA, M. P. & CHURIKOVA, L. I. (1985). Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivity of therapy. Math. Biosci. 73, 1-31.
6. FREDRICKSON, A. G., RAMKRISHNA, D. & TSUCHIYA, H. M. (1967). Statistics and dynamics of procaryotic cell populations. Math. Biosci. 1, 327-374.
7. GUIGUET, M., KUPIEC, J.-J. & VALLERON, A.-J. (1984). A systematic study of the variability of cell cycle phase durations in experimental mammalian systems. In: Cell Cycle Clocks (L. N. Edmunds, Jr., ed.) pp. 97-111. New York: Marcel Dekker.
8. HANNSGEN, K. B., TYSON, J. J. & WATSON, L. T. (1985). Steady-state size distributions in probabilistic models of the cell division cycle. SIAM J. Appl. Math. 45, 523-540.
9. HIRSCH, H. R. (1983). Influence of the existence of a resting state on the probability of cell division in culture. J. theor. Biol. 100, 399-410.
10. HIRSCH, H. R. (1984). Influence of the existence of a resting state on the decay of synchronization in cell culture. J. theor. Biol. 111, 61-79.
11. KIMMEL, M., TRAGANOS, F. & DARZYNKIEWICZ, Z. (1983). Do all daughter cells enter the "indeterminate" ("A") state of the cell cycle? Analysis of stathmokinetic experiments on L1210 cells. Cytometry 4, 191-201.
12. KIMMEL, M., DARZYNKIEWICZ, Z., ARINO, O. & TRAGANOS, F. (1984). Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis. J. theor. Biol. 110, 637-664.
13. 1 phase of the cell cycle. Computers Math. Applic. 18, 907-917.
14. KUBBIES, M., SCHINDLER, D., HOEHN, H. & RABINOVITCH, P. S. (1985). Cell cycle kinetics by BrdU-Hoechst flow cytometry: An alternative to the differential metaphase labelling technique. Cell Tissue Kinet. 18, 551-562.
15. MURPHY, J. S., LANDSBERGER, F. R., KIKUCHI, T. & TAMM, I. (1984). Occurrence of cell division is not exponentially distributed: differences in the generation times of sister cells can be derived from the theory of survival of populations. Proc. Natl. Acad. Sci. U.S.A. 81, 2379-2383.
16. RABINOVITCH, P. S. (1983). Regulation of human fibroblast growth rate by both noncycling cell fraction transition probability is shown by growth in 5-bromodeoxyuridine followed by Hoechst 33258 flow cytometry. Proc. Natl. Acad. Sci. U.S.A. 80, 2951-2955.
17. RAMKRISHNA, D. (1979). Statistical models of cell populations. Adv. Biochem. Eng. 11, 1-48.
18. RAMKRISHNA, D. (1985). The status of population balances. Rev. Chem. Eng. 3, 49-95.
19. RAMKRISHNA, D., FREDRICKSON, A. G. & TSUCHIYA, H. M. (1967). Dynamics of microbial propagation: Models considering inhibitors and variable cell composition. Biotechnol. Bioeng. 9, 129-170.
20. ROBINSON, J. H., SMITH, J. A., TOTTY, N. F. & RIDDLE, P. N. (1976). Transition probability and the hormonal and density-dependent regulation of cell proliferation. Nature 262, 298-300.
21. RONNING, O. W. & SEGLEN, P. O. (1982). The relation between protein accumulation and cell cycle traverse of human NHIK 3025 cells in unbalanced growth. J. Cell. Physiol. 112, 19-26.
22. ROTENBERG, M. (1982). Theory of distributed quiescent state in the cell cycle. J. theor. Biol. 96, 495-509.
23. ROTENBERG, M. (1983). Transport theory for growing cell populations. J. theor. Biol. 103, 181-199.
24. RUBINOW, S. I. (1968). A maturity-time representation for cell populations. Biophys. J. 8, 1055-1073.
25. SAHAR, E., WAGE, M. L. & LATT, S. A. (1983). Maturation rates and transition probabilities of cycling cells. Cytometry 4, 202-210.
26. 1 exit kinetics in asynchronous L1210 cell cultures with the constant transition probability model. Cytometry 3, 196-200.
27. SHIELDS, R. (1978). Further evidence for a random transition in the cell cycle. Nature 273, 755-758.
28. SHIELDS, R., BROOKS, R. F., RIDDLE, P. N., CAPELLARO, D. F. & DELIA, D. (1978). Cell size, cell cycle and transition probability in mouse fibroblasts. Cell 15, 469-474.
29. SHIELDS, R. & SMITH, J. A. (1977). Cells regulate their proliferation through alterations in transition probability. J. Cell. Physiol. 91, 345-356.
30. SMITH, J. A. & MARTIN, L. (1973). Do cells cycle? Proc. Natl. Acad. Sci. U.S.A. 70, 1263-1267.
31. SMITH, J. A. & MARTIN, L. (1974). Regulation of cell proliferation. In: Cell Cycle Controls (Padilla, G. M., Cameron, I. L. & Zimmerman, A., eds) pp. 43-60. New York: Academic Press.
32. SVETINA, S. (1977). An extended transition probability model of the variability of cell generation times. Cell Tissue Kinet. 10, 575-581.
33. SVETINA, S. & ZEKS, B. (1978). Transition probability models of the cell cycle exhibiting the age distribution for cells in the indeterministic state of the cell cycle. In: Biomathematics and Cell Kinetics (Valleron, A.-J. & MacDonald, P. D. M., eds) pp. 71-82. New York: Elsevier.
34. TAKAHASHI, M. (1966). Theoretical basis for cell cycle analysis. I. Labelled mitosis wave method. J. theor. Biol. 13, 202-211.
35. TAKAHASHI, M., HOGG JR., J. D. & MENDELSOHN, M. L. (1971). The automatic analysis of FLM curves. Cell Tissue Kinet. 4, 505-518.
36. TALAVERA, A. & BASILICO, C. (1978). Requirements of BHK cells for the exit from different quiescent states. J. Cell. Physiol. 97, 429-439.
37. TRUCCO, E. (1965a). Mathematical models for cellular systems. The Von Foerster equation. Part I. Bull. Math. Biophy. 27, 285-304.
38. TRUCCO, E. (1965b). Mathematical models for cellular systems. The Von Foerster equation. Part II. Bull. Math. Biophy. 27, 449-471.
39. VAN ZOELEN, E. J. J., VAN DER SAAG, P. T. & DE LAAT, S. W. (1981). Family tree analysis of a transformed cell line and the transition probability model for the cell cycle. Exp. Cell Res. 131, 395-406.
40. WEBB, G. F. & GRABOSCH, A. (1987). Asynchronous exponential growth in transition probability models of the cell cycle. SIAM J. Math. Anal. 18, 897-908.