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Enumeration of protein structures by cut and join method

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  • Jørgen Ellegaard Andersen, University of Southern Denmark, Denmark
  • Hiroyuki Fuji, Osaka Institute of Technology, Japan
  • Yuki Koyanagi
We discuss the enumeration of protein diagrams by matrix model techniques. We construct a matrix model for the basic protein model, where the configuration of peptide units in a backbone is exclusively twisted or untwisted. An untwisted backbone models the backbone configuration in the $\alpha$-helix, while a twisted backbone models the configuration in the $\beta$-sheet. We prove that the partition function obeys the heat equation, which can also be expressed as a cut and join equation. We then extend the model by adding a simple propagator to represent a backbone bend or turn, that connect $\alpha$-helices and $\beta$-sheets. This generalises the matrix model to 3-matrix model, and we prove that it also obeys the heat equation. Finally bacbone end points, representing N- and C-termini, are added to the model. We prove that it again obeys the heat equation.
Original languageEnglish
Number of pages36
Publication statusIn preparation - 1 Feb 2021

    Research areas

  • Protein structure, Matrix model

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