Abstract
Studies on the development of cell populations are often based on results of the theory of stochastic birth- and death-processes (continuous or discrete (seee.g. references inVogel, Niewisch &Matioli (1969), in some cases, “death” may be interpreted not as actual death of the cell bute.g. as a recruitment of the cell considered into another cell compartment, etc.). It is usually assumed that the conditions for the development are homogeneous,i.e. that the probabilities of births and deaths are independent on the time. However, in most situations, this assumption is not fulfilled (owing to the maturation and differentiation of cells, changes of the microenvironment, inducing factors, etc.). Then it is necessary to study the development of cell populations under non-homogeneous conditions. In this paper, some properties of appropriate birth- and death-processes under nonhomogeneous conditions are studied; formulae given in section 4 permit calculation of some characteristics describing the cell population size distribution at individual discrete epochs (at individual generations) during the development of the cell population considered.
Similar content being viewed by others
References
Jílek, M. (1973). On a non-homogeneous birth- and death-process.-Biometr. Zeitschrift15, p. 485–494.
Jílek, M. (1974). Note on a branching process (contribution to a theory of the immune response).-In: Progress in Statistics, p. 365–371.-Amsterdam, North Holland Publ. Comp.
Jílek, M. &J. Šterzl (1970). A model of differentiation of immunologically competent cells.-In: Developmental aspects of antibody formation and structure, Proceedings of a Symposium, held in Prague and Slapy on June 1–7, 1969, p. 963–981.-Prague, Academia.
Jílek, M. &J. Šterzl (1971). Modelling of the immune processes.-In: Morphological and functional aspects of immunity.-New York, Plenum Publishing Corp., p. 333–349.
Jílek, M. &J. Šterzl (1973). On a theory of the immune response.-In: Trans. 6th Prague conference on information theory, statistical decision functions, random processes.-Prague, Academia, p. 275–289.
Kendall, M. G. &A. Stuart (1963). The advanced theory of statistics, vol. 1, 2nd ed.-London, Charles Griffin & Comp., xii + 433 pp.
Rényi, A. (1970). Probability theory.-Budapest, Akadémiai Kiadó, 666 pp.
Sevastyanov, B. A. (1971). Branching processes (in Russian).-Moskva, Nauka, 436 pp.
Vogel, H., H. Niewisch &G. Matioli (1969). Stochastic development of stem cells.-J. theoret. Biol.22, p. 249–270.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jílek, M. Stochastic development of cell populations under non-homogeneous conditions. Acta Biotheor 24, 108–119 (1975). https://doi.org/10.1007/BF01556998
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01556998