Journal of Mathematical Biology

, Volume 69, Issue 1, pp 39–54 | Cite as

Distributions of positive signals in pyrosequencing

  • Yong Kong


Pyrosequencing is one of the important next-generation sequencing technologies. We derive the distribution of the number of positive signals in pyrograms of this sequencing technology as a function of flow cycle numbers and nucleotide probabilities of the target sequences. As for the distribution of sequence length, we also derive the distribution of positive signals for the fixed flow cycle model. Explicit formulas are derived for the mean and variance of the distributions. A simple result for the mean of the distribution is that the mean number of positive signals in a pyrogram is approximately twice the number of flow cycles, regardless of nucleotide probabilities. The statistical distributions will be useful for instrument and software development for pyrosequencing and other related platforms.

Mathematics Subject Classification

05A15 60C05 92B05 92D20 



This work was supported in part by the Clinical and Translational Science Award UL1 RR024139 from the National Center for Research Resources, National Institutes of Health.


  1. Balakrishnan N, Koutras MV (2002) Runs and Scans with Applications. Wiley, New YorkzbMATHGoogle Scholar
  2. Flajolet P, Sedgewick R (2009) Analytic combinatorics. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
  3. Kong Y (2006) Distribution of runs and longest runs: a new generating function approach. J Am Stat Assoc 101:1253–1263CrossRefzbMATHGoogle Scholar
  4. Kong Y (2009) Statistical distributions of pyrosequencing. J Comput Biol 16:31–42. doi: 10.1089/cmb.2008.0106 CrossRefMathSciNetGoogle Scholar
  5. Kong Y (2009) Statistical distributions of sequencing by synthesis with probabilistic nucleotide incorporation. J Comput Biol 16:817–827. doi: 10.1089/cmb.2008.0215 CrossRefMathSciNetGoogle Scholar
  6. Kong Y (2012) Length distribution of sequencing by synthesis: fixed flow cycle model. J Math Biol. doi: 10.1007/s00285-012-0556-3
  7. Kong Y (2013) Distributions of runs revisited. Commun Stat Theory Methods (To appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Molecular Biophysics and Biochemistry, W.M. Keck Foundation Biotechnology Resource LaboratoryYale UniversityNew HavenUSA

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