A Stochastic Approach to Count RNA Molecules Using DNA Sequencing Methods

  • Boris Hollas
  • Rainer Schuler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2812)


Estimating the number of congeneric mRNA molecules in a preparation is an essential task in DNA technology and biochemistry. However, DNA sequencing methods can only distinguish molecules with different sequences or of different lengths. Recently, it was shown that it is possible to combine RNA molecules with short DNA molecules (tags) such that, with high probability, any two RNA molecules are combined with tags having different sequences. For this technique, we propose a statistical estimator and a confidence interval to determine the number of mRNA molecules in a preparation.

In a second approach, the mRNA molecules are lengthened by attaching a random number of linker oligonucleotides. The original number of mRNA molecules is then determined by the number of different lengths obtained from the experiment. We also give estimator and confidence interval for this method.

Both methods can be implemented using recent as well as established methods from DNA technology. The methods can also be applied to a larger number of molecules without the need to exhaust the complete preparation. The computation of estimators and confidence intervals can be accomplished by dynamic programming.


Stochastic Approach Oligonucleotide Sequence Unknown Number mRNA Molecule Massively Parallel Signature Sequencing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Braich, R.S., Chelyapof, N., Johnson, C., Rothemund, P.W.K., Adleman, L.M.: Solution of a 20-variable 3-SAT problem on a DNA computer. Science 96, 478–479 (2002)Google Scholar
  2. 2.
    Brenner, S., Johnson, M., Bridgham, J., Golda, G., Lloyd, D.H., Johnson, D., Luo, S., McCurdy, S., Foy, M., Ewan, M., Roth, R., George, D., Eletr, S., Albrecht, G., Vermaas, E., Williams, S.R., Moon, K., Burcham, T., Pallas, M., DuBridge, R.B., Kirchner, J., Fearon, K., Mao, J., Corcoran, K.: Gene expression analysis by massively parallel signature sequencing (MPSS) on microbead arrays. Nature Biotechnology 18, 630–634 (2000)CrossRefGoogle Scholar
  3. 3.
    Brenner, S., Williams, S.R., Vermaas, E.H., Storck, T., Moon, K., McCollum, C., Mao, J., Luo, S., Kirchner, J., Eletr, S., DuBridge, R.B., Burcham, T., Albrecht, G.: In vitro cloning of complex mixtures of dna on microbeads: physical separation of differentially expressed cDNA’s. Proc. Natl. Acad. Sci. USA 97, 1665–1670 (2000)CrossRefGoogle Scholar
  4. 4.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. McGraw Hill, New York (1990)zbMATHGoogle Scholar
  5. 5.
    Feller, W.: An Introduction to Probability Theory and Its Applications, vol. II. Wiley, Chichester (1971)zbMATHGoogle Scholar
  6. 6.
    Graham, R., Knuth, D., Patashnik, O.: Concrete Mathematics. Addison-Wesley, Reading (1998)Google Scholar
  7. 7.
    Hug, H., Schuler, R.: Measurement of the number of molecules of a single mRNA species in a complex mRNA preparation. Journal of Theoretical Biology 221(4), 615–624 (2003)CrossRefGoogle Scholar
  8. 8.
    Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1999)Google Scholar
  9. 9.
    Sanger, F., Nicklen, S., Coulson, A.R.: DNA sequencing with chain-terminating inhibitors. Proc. Natl. Acad. Sci. USA 74, 5463–5467 (1977)CrossRefGoogle Scholar
  10. 10.
    Tyagi, S.: Taking consensus of mRNA populations with microbeads. S. Nat. Biotechnol 18, 597–598 (2000)CrossRefGoogle Scholar
  11. 11.
    Wilks, S.: Mathematical Statistics, 2nd edn. Wiley, Chichester (1963)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Boris Hollas
    • 1
  • Rainer Schuler
    • 1
  1. 1.Abteilung Theoretische InformatikUniversität UlmUlmGermany

Personalised recommendations