Abstract.
We introduce and give a complete description of a new graph to be used for DNA sequencing questions. This graph has the advantage over the classical de Bruijn graph that it fully accounts for the double stranded nature of DNA, rather than dealing with single strands. Technically, our graph may be thought of as the quotient of the de Bruijn graph under the natural involution of sending a DNA strand to its complementary strand. However, this involution has fixed points, and this complicates the structure of the quotient graph which we have therefore modified herein.
As an application and motivating example, we give an efficient algorithm for constructing universal footprinting templates for n-mers. This problem may be formulated as the task of finding a shortest possible segment of DNA which contains every possible sequence of base pairs of some fixed length n. Previous work by Kwan et al has attacked this problem from a numerical point of view and generated minimal length universal footprinting templates for n=2, 3, 5, 7, together with unsubstantiated candidates for the case n=4. We show that their candidates for n=4 are indeed minimal length universal footprinting templates.
Similar content being viewed by others
References
Bollobas, B.: Graph Theory: an introductory course. Graduate Texts Math. 63, Springer-Verlag, New York, 1979
Fox, K.R., Waring, M.J.: High Resolution footprinting studies of drug-DNA complexes using chemical and enzymic probes. Meth. Enzymol. 340, 412–430 (2001)
Galas, D.J., Schmitz, A.: DNAase footprinting – Simple method for detection of protein – DNA binding specificity. Nucleic Acids Res. 5, 3157–3170 (1978)
Guille, M.J., Kneale, G.: Methods for the analysis of DNA-protein interactions. Molecular Biotechnology 8, 35–52 (1997)
Kwan, A.H.Y., Czolij, R., Mackay, J.P., Crossley, M.: Pentaprobe: a comprehensive sequence for the one-step detection of DNA-binding activities. Nucleic Acids Res. 31, e124 (2003)
Lavesa, M., Fox, K.R.: Preferred binding sites for [N-MeCys3,N-MeCys7]TANDEM determined using a universal footprinting substrate. Analytical Biochemistry 293, 246–250 (2001)
Pevzner, P., Tang, H., Waterman, M.S.: An Eulerian path approach to DNA fragment assembly. Proc. Nat. Acad. Sci. U.S.A. 98, 9748–9753 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Anderson, J., Fox, K. & Niblo, G. A fast algorithm for the construction of universal footprinting templates in DNA. J. Math. Biol. 52, 307–342 (2006). https://doi.org/10.1007/s00285-005-0357-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-005-0357-z