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Whole Genome Amplification and Branching Processes

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Fengzhu Sun  and
Michael S. Waterman
Fengzhu Sun*
Affiliation:
Emory University
Michael S. Waterman*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Genetics, Emory University School of Medicine, Atlanta, GA 30329, USA.
∗∗ Postal address: Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113, USA.
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Abstract

Whole genome amplification is important for multipoint mapping by sperm or oocyte typing and genetic disease diagnosis. Polymerase chain reaction is not suitable for amplifying long DNA sequences. This paper studies a new technique, designated PEP-primer-extension-preamplification, for amplifying long DNA sequences using the theory of branching processes. A mathematical model for PEP is constructed and a closed formula for the expected target yield is obtained. A central limit theorem and a strong law of large numbers for the number of kth generation target sequences are proved.

Keywords

BRANCHING PROCESSESPEPCENTRAL LIMIT THEOREMSTRONG LAW OF LARGE NUMBERS

MSC classification

Secondary: 60J85: Applications of branching processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 629 - 668
Copyright
Copyright © Applied Probability Trust 1997 

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References

Arnheim, N. and Erlich, H. A. (1992) PCR strategy. Ann. Rev. Biochem. 61, 131–56.Google Scholar
Arnheim, N., Li, H. and Cui, X. (1990a) PCR analysis of DNA sequences in single cells: single sperm gene mapping and genetic disease diagnosis. Genomics 8, 415–419.CrossRefGoogle ScholarPubMed
Arnheim, N., White, T. and Rainey, W. E. (1990b) Application of PCR: organismal and population biology. BioScience 40, 174–82.CrossRefGoogle Scholar
Dear, P. H. and Cook, P. R. (1993) Happy mapping-linkage mapping using a physical analog of meiosis. Nucl. Acids Res. 21, 13–20.CrossRefGoogle ScholarPubMed
Durrett, R. (1991) Probability: Theory and Examples. Wadsworth and Brooks, New York.Google Scholar
Erlich, H. A. and Arnheim, N. (1992) Genetic analysis using the polymerase chain reaction. Ann. Rev. Genet. 26, 479–506.CrossRefGoogle ScholarPubMed
Grothues, D., Cantor, C. R. and Smith, C. L. (1993) PCR amplification of megabase DNA with tagged random primers (T-PCR). Nucl. Acids Res. 21, 1321–1322.CrossRefGoogle ScholarPubMed
Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
Jeffreys, A. J., Tamaki, K., Neil, D. L. and Monckton, D. G. (1991) Minisatellite repeat coding as a digital approach to DNA typing. Nature 354, 204–209.CrossRefGoogle ScholarPubMed
Kinzler, K. W. and Vogelstein, B. (1989) Whole genome PCR: Applications to the identification of sequences bound by gene regulatory proteins. Nucl. Acids Res. 17, 3645–3653.CrossRefGoogle Scholar
Krawczak, M., Reiss, J., Schmidtke, J. and Rosler, U. (1989) Polymerase chain reaction: replication errors and reliability of gene diagnosis. Nucl. Acids Res. 17, 2197–2201.CrossRefGoogle ScholarPubMed
Kristjansson, K., Chong, S. S., Van Den Veyver, I. B., Subramanian, S., Snabes, M. C. and Hughes, M. R. (1994) Preimplantation single-cell analyses of dystrophin gene deletions using whole genome amplification. Nature Genet. 6, 19–23.CrossRefGoogle ScholarPubMed
Ludecke, H., Senger, G., Claussen, U. and Horsthemke, B. (1989) Cloning defined regions of the human genome by microdissection of banded chromosomes and enzymatic amplification. Nature 338, 348–350.CrossRefGoogle ScholarPubMed
Mullís, K. B. and Faloona, F. A. (1987) Specific synthesis of DNA in vitro via a polymerase catalyzed chain reaction. Meth. Enzymol. 155, 335–51.CrossRefGoogle Scholar
Ross, S. M. (1971) Applied Probability Models with Optimization Applications. Holden-Day, New York.Google Scholar
Saiki, R., Scharf, S., Faloona, F., Mullís, K., Horn, G. T., Erlich, H. A. and Arnheim, N. (1985) Enzymatic amplification of ß-globin genomic sequences and restriction site analysis for diagnosis of sickle cell anemia. Science 230, 1350–54.CrossRefGoogle Scholar
Saiki, R., Gelfand, D. H., Stoffel, S., Scharf, S. J., Higuchi, R., Horn, G. T., Mullís, K. B. and Erlich, H. A. (1988) Primer-directed enzymatic amplification of DNA with a thermostable DNA polymerase. Science 239, 487–491.CrossRefGoogle ScholarPubMed
Sun, F. (1995) The polymerase chain reaction and branching processes. J. Comp. Bio. 2, 63–86.CrossRefGoogle ScholarPubMed
Sun, F., Arnheim, N. and Waterman, M. S. (1995) Whole genome amplification of single cells: mathematical analysis of PEP and tagged PCR. Nucl. Acids Res. 23, 3034–3040.CrossRefGoogle ScholarPubMed
Telenius, H., Carter, N. P., Bebb, C. E., Nordenskjold, M., Ponder, B. A. and Tunnacliffe, A. (1992) Degenerate oligonucleotide-primed PCR-general amplification of target DNA by a single degenerate primer. Genomics 13, 718–725.CrossRefGoogle ScholarPubMed
Weiss, G. and von Haeseler, A. (1995) Modeling the polymerase chain reaction. J. Comp. Bio. 2, 49–62.CrossRefGoogle ScholarPubMed
White, T. J., Arnheim, N. and Erlich, H. A. (1989) The polymerase chain reaction. Trends Genet. 5, 185–89.CrossRefGoogle ScholarPubMed
Zhang, L., Cui, X., Schmitt, K., Hubert, R., Navidi, W. and Arnheim, N. (1991) Whole genome amplification from a single cell: Implications for genetic analysis. Proc. Nat. Acad. Sci. 89, 5847–5851.CrossRefGoogle Scholar