Abstract
A model of the cell cycle, incorporating a deterministic cell-size monitor and a probabilistic component, is investigated. Steady-state distributions for cell size and generation time are calculated and shown to be globally asymptotically stable. These distributions are used to calculate various statistical quantities, which are then compared to known experimental data. Finally, the results are compared to distributions calculated from a Monte-Carlo simulation of the model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Diekmann, O., Heijmans, H. J. A. M., Thieme, H. R.: On the stability of the cell size distribution. J. Math. Biol. 19, 227–248 (1984)
Fantes, P. A.: Control of cell size and cycle time in Schizosaccharomyces pombe. J. Cell Sci. 24, 51–67 (1977)
Green, P. J.: A ‘random transition’ in the cell cycle? Nature 285, 116 (1980)
Hannsgen, K. B., Tyson, J. J.: Stability of the steady-state size distribution in a model of cell growth and division. J. Math. Biol. 22, 293–301 (1985)
Heijmans, H. J. A. M.: On the stable size distribution of populations reproducing by fission into two unequal parts. Math. Biosci. 72, 19–50 (1984)
John, P. C. L.: The cell cycle. London: Cambridge University Press 1981
Koch, A. L.: Does the variability of the cell cycle result from one or many chance events? Nature 286, 80–82 (1980)
Koch, A. L., Schaechter, M.: A model for statistics of the cell division process. J. Gen. Microbiol. 29, 435–454 (1962)
Kubitschek, H. E.: Normal distribution of cell generation rate. Exp. Cell Res. 26, 439–450 (1962)
Lasota, A., Yorke, J. A.: Exact dynamical systems and the Frobenius-Perron operator. Trans. Am. Math. Soc. 273, 375–384 (1982)
Lasota, A., Mackey, M. C.: Globally asymptotic properties of proliferating cell populations. J. Math. Biol. 19, 43–62 (1984)
Lord, P. G., Wheals, A. E.: Variability in individual cell cycles of Saccharomyces cerevisiae. J. Cell Sci. 50, 361–376 (1981)
Minor, P. D., Smith, J. A.: Explanation of degree of correlation of sibling generation times in animal cells. Nature 248, 241–243 (1974)
Mitchison, J. M.: The timing of cell cycle events. In: Little, M., Paweletz, N., Petzelt, C., Ponstingl, H., Schroeter, D., Zimmerman, H.-P. (eds.) Mitosis: Facts and questions, pp. 1–13. Berlin Heidelberg New York: Springer 1977
Nurse, P.: Cell cycle control—both deterministic and probabilistic? Nature 286, 9–10 (1980)
Nurse, P., Streiblova, E.: The microbial cell cycle. Boca Raton, Florida: CRC Press 1984
Painter, P., Marr, A. G.: Inequality of mean interdivision time and doubling time. J. Gen. Microbiol. 48, 155–159 (1967)
Painter, P. R., Marr, A. G.: Mathematics of microbial populations. Ann. Rev. Microbiol. 22, 519–548 (1968)
Powell, E. O.: Growth rate and generation time of bacteria, with special reference to continuous culture. J. Gen. Microbiol. 15, 492–511 (1956)
Powell, E. O.: A note on Koch and Schaechter's hypothesis about growth and fission of bacteria. J. Gen. Microbiol. 37, 231–249 (1964)
Schaechter, M., Williamson, J. P., Hood, J. R., Koch, A. L.: Growth, cell and nuclear divisions in some bacteria. J. Gen. Microbiol. 29, 421–434 (1962)
Shields, R.: Further evidence for a random transition in the cell cycle. Nature 273, 755–758 (1978)
Shields, R.: Transition probability and the regulation of the cell cycle. In: Jiminez de Asua, L., Levi-Montalcini, R., Shields, R., Iacobelli, S. (eds.) Control mechanisms in animal cells, pp. 157–164. New York: Raven Press 1980
Shields, R., Smith, J. A.: Cells regulate their proliferation through alterations in transition probability. J. Cell. Physiol. 91, 345–355 (1977)
Shields, R., Brooks, R. F., Riddle, P. N., Capellaro, D. F., Delia, D.: Cell size, cell cycle and transition probability in mouse fibroblasts. Cell 15, 469–474 (1978)
Shilo, B., Shilo, V., Simchen, G.: Cell-cycle initiation in yeast follows first-order kinetics. Nature 264, 767–770 (1976); see also Nature 267, 648–649 (1977)
Smith, J. A., Martin, L.: Do cells cycle? Proc. Natl. Acad. Sci. USA 70, 1263–1270 (1973)
Tyson, J. J., Hannsgen, K. B.: Analysis of a deterministic/probabilistic model of the cell division cycle. In: Rotenberg, M. (ed.) Biomathematics and cell kinetics, pp. 167–176. Amsterdam: Elsevier/North Holland 1981
Tyson, J. J., Hannsgen, K. B.: The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions. J. Theor. Biol. 113, 29–62 (1985)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tyson, J.J., Hannsgen, K.B. Cell growth and division: a deterministic/probabilistic model of the cell cycle. J. Math. Biology 23, 231–246 (1986). https://doi.org/10.1007/BF00276959
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00276959