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A Polynomial Time Solution for Protein Chain Pair Simplification under the Discrete Fréchet Distance

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Bioinformatics Research and Applications (ISBRA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 7292))

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Abstract

The comparison and simplification of polygonal chains is an important and active topic in many areas of research. In the study of protein structure alignment and comparison, a lot of work has been done using RMSD as the distance measure. This method has certain drawbacks, and thus recently, the discrete Fréchet distance was applied to the problem of protein (backbone) structure alignment and comparison with promising results. Another important area within protein structure research is visualization, due to the number of nodes along each backbone. Protein chain backbones can have as many as 500~600 α-carbon atoms which constitute the vertices in the comparison. Even with an excellent alignment, the similarity of two polygonal chains can be very difficult to see visually unless the two chains are nearly identical. To address this issue, the chain pair simplification problem (CPS-3F) was proposed in 2008 to simultaneously simplify both chains with respect to each other under the discrete Fréchet distance. It is unknown whether CPS-3F is NP-complete, and so heuristic methods have been developed. Here, we first define a version of CPS-3F, denoted CPS-3F + , and prove that it is polynomially solvable by presenting a dynamic programming solution. Then we compare the CPS-3F +  solutions with previous empirical results, and further demonstrate some of the benefits of the simplified comparison. Finally, we discuss future work and implications along with a web-based software implementation, named FPACT (The Fréchet-based Protein Alignment & Comparison Tool), allowing users to align, simplify, and compare protein backbone chains using methods based on the discrete Fréchet distance.

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Authors and Affiliations

  1. Department of Computer Science, Montana State University, Bozeman, MT, 59717-3880, USA

    Tim Wylie & Binhai Zhu

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  1. Tim Wylie
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  2. Binhai Zhu
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Editor information

Editors and Affiliations

  1. Departments of Bioengineering and Electrical Engineering, University of Texas at Dallas, 75080, Richardson, TX, USA

    Leonidas Bleris

  2. Department of Computer Science and Engineering, University of Connecticut, 06269, Storrs, CT, USA

    Ion Măndoiu

  3. Department of Biological Sciences, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Russell Schwartz

  4. School of Information Science and Engineering, Central South University, 410083, Changsha, China

    Jianxin Wang

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© 2012 Springer-Verlag Berlin Heidelberg

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Wylie, T., Zhu, B. (2012). A Polynomial Time Solution for Protein Chain Pair Simplification under the Discrete Fréchet Distance. In: Bleris, L., Măndoiu, I., Schwartz, R., Wang, J. (eds) Bioinformatics Research and Applications. ISBRA 2012. Lecture Notes in Computer Science(), vol 7292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30191-9_27

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  • DOI: https://doi.org/10.1007/978-3-642-30191-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30190-2

  • Online ISBN: 978-3-642-30191-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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