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Secondary Structure Ensemble Analysis via Community Detection

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Using Mathematics to Understand Biological Complexity

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 22))

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Abstract

We explored the extent to which graph algorithms for community detection can improve the mining of structural information from the predicted Boltzmann/Gibbs ensemble for the biological objects known as RNA secondary structures. As described, a new computational pipeline was developed, implemented, and tested against the prior method RNAStructProfiling. Since the new approach was judged to provide more structural information in 75% of the test cases, this proof-of-principle analysis supports efforts to improve the data mining of RNA secondary structure ensembles.

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Notes

  1. 1.

    https://rna.urmc.rochester.edu/RNAstructure.html

  2. 2.

    https://github.com/gtDMMB/ipam-wbio-scripts

  3. 3.

    The results in this manuscript use a new version of profiling which is still under development and will be made available at https://github.com/gtDMMB/RNAStructProfiling.

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Acknowledgements

The work described herein was initiated during the Collaborative Workshop for Women in Mathematical Biology hosted by the Institute for Pure and Applied Mathematics at the University of California, Los Angeles in June 2019. Funding for the workshop was provided by IPAM, the Association for Women in Mathematics’ NSF ADVANCE “Career Advancement for Women Through Research-Focused Networks” (NSF-HRD 1500481) and the Society for Industrial and Applied Mathematics. The authors thank the organizers of the IPAM-WBIO workshop (Rebecca Segal, Blerta Shtylla, and Suzanne Sindi) for facilitating this research.

The authors thank the anonymous reviewers whose comments significantly improved the paper.

This research of Huijing Du was supported in part by NSF-DMS 1853636; of Margherita Maria Ferrari by the NSF-Simons Southeast Center for Mathematics and Biology (SCMB) through NSF-DMS 1764406 and Simons Foundation SFARI 594594; of Christine Heitsch by NIH R01GM126554; of Forrest Hurley by GBMF4560 (to Sullivan) and NSF-DMS 1344199 (to Heitsch); of Christine Mennicke by an NSF GRFP; of Blair D. Sullivan by the Gordon & Betty Moore Foundation’s Data-Driven Discovery Initiative under Grant GBMF4560; and of Bin Xu by the Robert and Sara Lumpkins Endowment for Postdoctoral Fellows in Applied and Computational Mathematics and Statistics at the University of Notre Dame.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA

    Huijing Du

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, USA

    Margherita Maria Ferrari

  3. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA

    Christine Heitsch

  4. North Carolina State University, Raleigh, NC, USA

    Forrest Hurley

  5. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Christine V. Mennicke

  6. School of Computing, University of Utah, Salt Lake City, UT, USA

    Blair D. Sullivan

  7. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA

    Bin Xu

Authors
  1. Huijing Du
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  2. Margherita Maria Ferrari
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  3. Christine Heitsch
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  4. Forrest Hurley
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  5. Christine V. Mennicke
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  6. Blair D. Sullivan
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  7. Bin Xu
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Corresponding author

Correspondence to Christine Heitsch .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, USA

    Rebecca Segal

  2. Department of Mathematics, Pomona College, Claremont, CA, USA

    Blerta Shtylla

  3. Department of Applied Mathematics, University of California, Merced, CA, USA

    Suzanne Sindi

Appendix

Appendix

Two data files (Figs. 9 and 10) are included to supplement the examples presented and discussed in Sect. 4.5. The files begin by listing the RNA sequence analyzed and the CH index for this partition, which had the largest proportional increase. Recall that the (dis)similarity measure is the frequency-weighted symmetric difference and the community detection is performed by the GMC graph algorithm.

The clusters of the partition are listed by decreasing total frequency. Each one is first described by a “Summary” which lists a cluster label (‘partition id’) and its total frequency mass, followed by the list of helix classes appearing in the union of the the cluster elements. This Summary is followed by a list of all the extended profiles in the cluster, also sorted by decreasing frequency. Each extended profile is specified by the cluster label, its frequency in the sample (‘multiplicity’), and the set of helix classes particular to this extended profile.

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Du, H. et al. (2021). Secondary Structure Ensemble Analysis via Community Detection. In: Segal, R., Shtylla, B., Sindi, S. (eds) Using Mathematics to Understand Biological Complexity. Association for Women in Mathematics Series, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-57129-0_4

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