Abstract
A mathematical model for the random process of repeated cell division and recombination in two nonoverlapping genetic intervals is formulated and investigated. From this model, a test for statistical independence of recombination in the two intervals and a method of estimating the rate of double recombination are developed. Crossing over in both intervals, crossing over in one and gene conversion in the other, and gene conversion in both are treated. For markers on the same chromosome, all possible arrangements of the loci relative to the centromere are considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Armitage, P.: The statistical theory of bacterial populations subject to to mutation. J. Roy. Stat. Soc. B. 14, 1–40 (1952)
Bailey, N. T. J.: The elements of stochastic processes. New York: Wiley 1964
Bartlett, M. S.: An introduction to stochastic processes. Cambridge: Cambridge University Press 1955
Bickel, P. J., Doksum, K. A.: Mathematical statistics. San Francisco: Holden-Day 1977
Catecheside, D. G.: The genetics of recombination. Baltimore: University Park Press 1977
Christianson, M. L.: Mitotic crossing-over as an important mechanism of floral sectoring in Tradescantia. Mutat. Res. 28, 389–395 (1975)
Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. II. New York: Interscience 1962
Crump, K. S., Hoel, D. G.: Mathematical models for estimating mutation rates in cell populations. Biometrika 61, 237–252 (1974)
Esposito, M. S.: Evidence that spontaneous mitotic recombination occurs at the two-strand stage. Proc. Natl. Acad. Sci. USA 75, 4436–4440 (1978)
Esposito, M. S., Wagstaff, J. E.: Mechanisms of mitotic recombination. In: Strathern, J. N., Jones, E. W., Broach, J. R. (eds.): The molecular biology of the yeast Saccharomyces: life cycle and inheritance, pp. 341–370. Cold Spring Harbor, N.Y.: Cold Spring Harbor Laboratory 1981
Fabre, F.: Induced intragenic recombination in yeast can occur during the G1 mitotic phase. Nature 272, 797–798 (1978)
Fabre, F., Roman, H.: Genetic evidence for inducibility of recombination competence in yeast. Proc. Natl. Acad. Sci. USA 74, 1667–1671 (1977)
Festa, R. S., Meadows, A. T., Boshes, R. A.: Leukemia in a black child with Bloom's syndrome. Cancer 44, 1507–1510 (1979)
Gautschi, W., Cahill, W. F.: Exponential integral and related functions. In: Abramowitz, M., Stegun, I. A. (eds.): Handbook of mathematical functions, pp. 227–251. Washington: National Bureau of Standards 1964
Golin, J. G.: Dissertation, The University of Chicago, Chicago, 1979
Grüneberg, H.: The case for somatic crossing over in the mouse. Genet. Res. 7, 58–75 (1966)
Hartwell, L. H., Unger, M. W.: Unequal division in Saccharomyces cerevisiae and its implications for the control of cell division. J. Cell Biol. 75, 422–435 (1977)
Hawthorne, D. C., Leupold, U.: Suppressor mutations in yeast. Curr. Top. Microbiol. Immunol. 64, 1–47 (1974)
Holliday, R.: The mechanism of gene conversion in fungi. Genet. Res. 5, 282–304 (1964)
Hurst, D. D., Fogel, S.: Mitotic recombination and heteroallelic repair in Saccharomyces cerevisiae. Genetics 50, 435–458 (1964)
Käfer, E.: Meiotic and mitotic recombination in Aspergillus and its chromosomal aberrations. Adv. Genet. 19 33–131 (1977)
Katz, E. R., Kao, V.: Evidence for mitotic recombination in the cellular slime mold Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 71, 4025–4026 (1974)
Kunz, B. A., Haynes, R. H.: Phenomenology and genetic control of mitotic recombination in yeast. Ann. Rev. Genet. 15, 57–89 (1981)
Lea, D. E., Coulson, C. A.: The distribution of the numbers of mutants in bacterial populations. J. Genet. 49, 264–285 (1949)
Luria, S. E., Delbrück, M.: Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28, 491–511 (1943)
Malone, R. E., Golin, J. G., Esposito, M. S.: Mitotic versus meiotic recombination in Saccharomyces cerevisiae. Curr. Genet. 1, 241–248 (1980)
Meselson, M. S., Radding, C. M.: A general model for genetic recombination. Proc. Natl. Acad. Sci. USA 72, 358–361 (1975)
Minet, M., Grossenbacher-Grunder, A.-M., Thuriaux, P.: The origin of a centromere effect on mitotic recombination. Curr. Genet. 2, 53–60 (1980)
Montelone, B. A., Prakash, S., Prakash, L.: Spontaneous mitotic recombination in mms8−1, an allele of the CDC9 gene of Saccharomyces cerevisiae. J. Bact. 147, 517–525 (1981)
Moore, C. W., Sherman, F.: Role of DNA sequences in genetic recombination in the iso-1 -cytochrome-c gene of yeast. I. Discrepancies between physical distances and genetic distances determined by five mapping procedures. Genetics 79, 397–418 (1975)
Nakai, S., Mortimer, R. K.: Studies of the genetic mechanism of radiation-induced mitotic segregation in yeast. Molec. Gen. Genet. 103, 329–338 (1969)
Nöthiger, R., Dübendorfer, A.: Somatic crossing-over in the housefly. Molec. Gen. Genet. 112, 9–13 (1971)
Peizer, D. B., Pratt, J. W.: A normal approximation for binomial, F, beta, and other common related tail probabilities. I. J. Amer. Stat. Assoc. 63, 1416–1456 (1968)
Prakash, S., Prakash, L., Burke, W., Montelone, B. A.: Effects of the RAD52 gene on recombination in Saccharomyces cerevisiae. Genetics 94, 31–50 (1980)
Roman, H.: Studies of gene mutation in Saccharomyces. Cold Spring Harbor Symp. Quant. Biol. 21, 175–183 (1956)
Roman, H., Jacob, F.: A comparison of spontaneous and ultraviolet-induced allelic recombination with reference to the recombination of outside markers. Cold Spring Harbor Symp. Quant. Biol. 23, 155–160 (1958)
Stern, C.: Somatic crossing over and segregation in Drosophila melanogaster. Genetics 21, 625–730 (1936)
Tan, W. Y.: On distribution theories for the number of mutants in cell populations. Soc. Ind. Appl. Math. J. Appl. Math. 42, 719–730 (1982)
Vig, B. K., Paddock, E. F.: Studies on the expression of somatic crossing over in Glycene max L. Theor. Appl. Genet. 40, 316–321 (1970)
Wheals, A. E.: Size-control models of Saccharomyces cerevisiae cell proliferation. Molec. Cellul. Biol. 2, 361–368 (1982)
Wildenberg, J.: The relation of mitotic recombination to DNA replication in yeast pedigrees. Genetics 66, 291–304 (1970)
Author information
Authors and Affiliations
Additional information
Supported by National Science Foundation Grant DEB81-03530.
Rights and permissions
About this article
Cite this article
Nagylaki, T. Double recombinants in mitosis. J. Math. Biology 19, 13–42 (1984). https://doi.org/10.1007/BF00275929
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00275929