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Redundant and Critical Noncovalent Interactions in Protein Rigid Cluster Analysis

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Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Abstract

A protein’s fold is held together by weak noncovalent interactions, known to break and form during naturally occurring fluctuations. Rigidity analysis leverages connectivity information about these interactions, calculated from PDB structural data, and computes a decomposition of the molecule into groups of atoms, called rigid clusters, that tend to remain together during such local motions. A crucial question in the application of this technique is how robust the results of rigidity analysis are to small variations in the noncovalent network. If any particular interaction within a cluster were to break, would the cluster remain rigid, would it “shatter” into many smaller clusters, or would the flexibility increase but only negligibly? In this chapter, we overview the mathematical principles underlying rigidity analysis, and propose a method for classifying the interactions which are redundant or critical for a computed cluster decomposition. We also measure the change in cluster size upon the interaction’s removal, which we refer to as its criticality value. In addition, we propose a new method for assigning scores to the rigid clusters based on the fraction of interactions that are redundant. We demonstrate this classification scheme on a data set of multiple conformations of 16 proteins. We have found that typically the dominant rigid clusters do not contain highly critical interactions, yet, when such interactions exist, they tend to be concentrated around the active site. In our case studies, we have found that removal of these interactions results in functionally relevant changes in rigidity. We present our results on the redundancy and presence of critical interactions on benchmarking data sets, with case studies on adenylate kinase, dihydrofolate reductase, DNA polymerase β, HIV-1 protease, and cytochrome-c. We also provide survey results on a larger data set of 150 proteins. These methods have been implemented in the KINARI-Redundancy server, publicly available from the KINARI-Web site (http://kinari.cs.umass.edu).

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Acknowledgements

The studies described in this chapter were funded by the National Institute of General Medical Sciences grant DMS-0714934 as part of the Joint Program in Mathematical Biology supported by the Directorate for Mathematical and Physical Sciences of the National Science Foundation and the National Institute of General Medical Sciences of the National Institutes of Health, and by the Mathematical Challenges grants NSF CCF-1016988 and DARPA to IS.

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Authors and Affiliations

  1. Department of Computer Science, University of Massachusetts Amherst, 140 Governors Drive, Amherst, MA, 01002, USA

    Naomi Fox & Ileana Streinu

  2. Department of Computer Science, Smith College, Northampton, MA, 01063, USA

    Ileana Streinu

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  1. Naomi Fox
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Correspondence to Ileana Streinu .

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Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

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Fox, N., Streinu, I. (2014). Redundant and Critical Noncovalent Interactions in Protein Rigid Cluster Analysis. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-40193-0_8

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