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Combinatorics of Contacts in Protein Contact Maps

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Abstract

Contacts play a fundamental role in the study of protein structure and folding problems. The contact map of a protein can be represented by arranging its amino acids on a horizontal line and drawing an arc between two residues if they form a contact. In this paper, we are mainly concerned with the combinatorial enumeration of the arcs in m-regular linear stack, an elementary structure of the protein contact map, which was introduced by Chen et al. (J Comput Biol 21(12):915–935, 2014). We modify the generating function for m-regular linear stacks by introducing a new variable y regarding to the number of arcs and obtain an equation satisfied by the generating function for m-regular linear stacks with n vertices and k arcs. Consequently, we also derive an equation satisfied by the generating function of the overall number of arcs in m-regular linear stacks with n vertices.

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Acknowledgements

This work was supported by the 973 Project, the National Science Foundation of China, and the Natural Science Foundation of Tianjin City, China.

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  1. Center for Combinatorics, LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Qiang-Hui Guo & Lisa H. Sun

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  1. Qiang-Hui Guo
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  2. Lisa H. Sun
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Correspondence to Lisa H. Sun.

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Guo, QH., Sun, L.H. Combinatorics of Contacts in Protein Contact Maps. Bull Math Biol 80, 385–403 (2018). https://doi.org/10.1007/s11538-017-0380-4

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  • DOI: https://doi.org/10.1007/s11538-017-0380-4

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