Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T06:04:34.907Z Has data issue: false hasContentIssue false
  • English
  • Français

A new stochastic model of microsatellite evolution

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Richard Durrett  and
Semyon Kruglyak
Richard Durrett*
Affiliation:
Cornell University
Semyon Kruglyak*
Affiliation:
University of Southern California
*
∗Postal address: Department of Mathematics, 528 Mallott Hall, Cornell University, Ithaca, NY 14853, USA. Email address: rtd1@cornell.edu
∗∗Postal address: 293 Denney Research Building, University of Southern California, Los Angeles, CA 90089, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce a continuous-time Markov chain model for the evolution of microsatellites, simple sequence repeats in DNA. We prove the existence of a unique stationary distribution for our model, and fit the model to data from approximately 106 base pairs of DNA from fruit flies, mice, and humans. The slippage rates from the best fit for our model are consistent with experimental findings.

Keywords

Microsatellite evolutionMarkov chain model

MSC classification

Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 621 - 631
Copyright
Copyright © Applied Probability Trust 1999 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amos, W., Saucer, S., Feakes, R., and Rubinsztein, D. (1996). Microsatellites show mutational bias and heterozygote instability. Nature Genet. 13, 390–391.CrossRefGoogle ScholarPubMed
Ashley, C. T., and Warren, S. T. (1995). Trinucleotide repeat expansion and human disease. Ann. Rev. Genet. 29, 703–728.CrossRefGoogle ScholarPubMed
Bell, G., and Jurka, J. (1997). The length distribution of perfect dimer repetitive DNA is consistent with its evolution by an unbiased single step mutation process. J. Mol. Evol. 44, 414–421.CrossRefGoogle ScholarPubMed
Dallas, J. (1992). Estimation of microsatellite mutation rates in recombinant inbred strains of mouse. Mammalian Genome 3, 452–456.CrossRefGoogle ScholarPubMed
Dietrich, W., Katz, H., Lincoln, S. E., Shin, H. S., Friedman, J., Dracopoli, N. C., and Lander, E. S. (1992). A genetic map of the mouse suitable for typing interspecific crosses. Genetics 131, 423–447.CrossRefGoogle Scholar
DiRienzo, A., Peterson, A. C., Garza, J. C., Valdes, A. M., Slatkin, M., and Freimer, N. B. (1994). Mutational processes of simple sequence repeat loci in human populations. Proc. Nat. Acad. Sci. USA 91, 3166–3170.CrossRefGoogle Scholar
Feldman, M. W., Bergman, A., Pollock, D. D., and Goldstein, D. B. (1997). Microsatellite genetic distances with range constraints: Analytic description and problems of estimation. Genetics 145, 207–216.CrossRefGoogle ScholarPubMed
Garza, J. C., Slatkin, M., and Freimer, N. B. (1995). Microsatellite allele frequencies in humans and chimpanzees, with implications for constraints on allele size. Mol. Biol. Evol. 12, 594–603.Google ScholarPubMed
Goldstein, D. B., Ruiz-Linares, A., Cavalli-Sforza, L. L., and Feldman, M. W. (1995). An evaluation of genetic distances for use with microsatellite loci. Genetics 139, 463–471.CrossRefGoogle ScholarPubMed
Goldstein, D. B., Ruiz-Linares, A., Cavalli-Sforza, L. L., and Feldman, M. W. (1995). Genetic absolute dating based on microsatellites and modern human origins. Proc. Nat. Acad. Sci. 92, 6723–6727.CrossRefGoogle Scholar
Hudson, R. R. (1990). Gene genealogies and the coalescent process. Oxford Surveys in Evolutionary Biology, Vol. 7, ed. Futuyama, D. J. and Antonovics, J. OUP, Oxford, pp. 1–44.Google Scholar
Kimmel, M., and Chakraborty, R. (1996). Measures of variation at DNA repeat loci under a general stepwise mutation model. Theoret. Popul. Biol. 39, 30–48.Google Scholar
Levinson, G., and Gutman, G. A. (1987). Slipped–strand mispairing: a major mechanism for DNA sequence evolution. Mol. Biol. Evol. 4, 203–221.Google Scholar
Li, W. H. (1997). Molecular Evolution. Sinauer Associates, Massachusetts, pp. 177–236.Google ScholarPubMed
McMurray, C. T. (1995). Mechanisms of DNA expansion. Chromosoma 104, 2–13.Google ScholarPubMed
Moran, P. A. P (1975). Wandering distributions and the electrophoretic profile. Theoret. Pop. Biol. 8, 318–330.CrossRefGoogle ScholarPubMed
Ohta, T., and Kimura, M. (1973). The model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a genetic population. Genet. Res. 22, 201–204.CrossRefGoogle Scholar
Petrukhin, K. E., Speer, M. C., Cayanis, E., DeFatima Bonaldo, M., Tantravahi, U., Soares, M. B., Fischer, S. G., Warburton, D., Gilliam, T. C., and Ott, J. (1993). A microsatellite genetic linkage map of human chromosome 13. Genomics 15, 76–85.CrossRefGoogle ScholarPubMed
Primmer, C. R., Ellegren, H., Saino, N., and Moller, A. P. (1996). Directional evolution in germline microsatellite mutations. Nature Genet. 13, 391–393.CrossRefGoogle ScholarPubMed
Pritchard, J. K., and Feldman, M. W. (1996). Statistics for microsatellite variation based on coalescence. Theoret. Popul. Biol. 50, 325–344.CrossRefGoogle ScholarPubMed
Schlotterer, C., and Tautz, D. (1992). Slippage synthesis of simple sequence DNA. Nucleic Acids Res. 20, 211–216.CrossRefGoogle ScholarPubMed
Schug, M. D., Wetterstrand, K., Gaudette, M., Lim, R., Hutter, C., and Aquadro, C. F. (1997). The distribution and frequency of microsatellite loci in Drosophila melanogaster. Submitted to Nucleic Acids research 1/29/97.Google Scholar
Schug, M. D., Hutter, C. M., Wetterstrand, K. A., Gaudette, M. S., Mackay, T. F. C., and Aquadro, C. F. (1998). The mutation rate of di- tri– and tetranucleotide repeats in Drosophila melanogaster. Mol. Biol. Evol. 15, 1751–1760.CrossRefGoogle ScholarPubMed
Shriver, M. D., Jin, L., Chakraborty, R., and Boerwinkle, E. (1993). VNTR allele frequency distributions under the stepwise mutation model: A computer simulation approach. Genetics 134, 983–993.CrossRefGoogle Scholar
Slatkin, M. (1995). A measure of population subdivision based on microsatellite allele frequencies. Genetics 139, 457–462.CrossRefGoogle ScholarPubMed
Slatkin, M. (1995) Hitchhiking and associative overdominance at a microsatellite locus. Mol. Biol. Evol. 12, 473–480.Google Scholar
Smith, G. P. (1973). Unequal crossover and the evolution of multigene families. Cold Spring Harbor Symp. Quant. Biol. 38, 507–513.CrossRefGoogle Scholar
Takezaki, N., and Nei, M. (1996). Genetic distances and reconstruction of phylogenetic trees from microsatellite DNA. Genetics 144, 389–399.CrossRefGoogle ScholarPubMed
Tavaré, S. (1984). Line-of-descent and genealogical processes and their application in population genetics models. Theoret. Pop. Biol. 26, 119–164.CrossRefGoogle ScholarPubMed
Valdes, A., Slatkin, M., and Freimer, N. B. (1993). Allele frequencies at microsatellite loci: the stepwise mutation model revisited. Genetics 133, 737–749.CrossRefGoogle ScholarPubMed
Weber, J. L., and Wong, C. (1993). Mutation of human short tandem repeats. Hum. Mol. Genet. 2, 1123–1128.CrossRefGoogle ScholarPubMed
Weissenbach, J., Gyapay, G., Dib, C., Vignal, A., Morissette, J., Millasseau, P., Vaysseix, G., and Lathrop, M. (1992). A second-generation linkage map of the human genome. Nature, 359, 794–801.CrossRefGoogle ScholarPubMed
Wetterstrand, K. S. (1997). Microsatellite polymorphism and divergence in worldwide populations of Drosophila Melanogaster and D. simulans. , Cornell University, Ithaca, NY.Google Scholar
Wierdl, M., Dominiska, M., and Petes, T. D. (1996). Microsatellite instability in yeast: dependence on the length of the microsatellite. Genetics, 146, 769–779.CrossRefGoogle Scholar
Zhivotovsky, L. A., Feldman, M. W., and Grishechkin, S. A. (1997). Biased mutations and microsatellite variation. Mol. Biol. Evol. 14, 926–933.CrossRefGoogle ScholarPubMed