Numerical solutions of a master equation for protein folding kinetics

Yi-Ming Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The numerical solution of a master equation involves the calculation of eigenpairs for the corresponding transition matrix. In this paper, we computationally study the folding rate for a kinetics problem of protein folding by solving a large-scale eigenvalue problem. Three numerical methods, the implicitly restarted Arnoldi, the Jacobi-Davidson, and the QR methods are applied to solve the corresponding large-scale eigenvalue problem of the transition matrix of the master equation. Comparison among three methods is performed in terms of the computational efficiency. It is found that the QR method demands tremendous computing resource when the length of sequence L > 10 due to the extremely large size of matrix and CPU time limitation. The Jacobi-Davidson method may encounter convergence issues, for some testing cases with L > 9. Among the three solution methods the implicitly restarted Arnoldi method is suitable for solving the problem. Numerical examples with various residues are investigated.

Original languageEnglish
Pages (from-to)420-429
Number of pages10
JournalInternational Journal of Bioinformatics Research and Applications
Issue number4
StatePublished - 2006


  • Arnoldi
  • Bioinformatics research and applications
  • Eigenvalues
  • Jacobi-Davidson
  • Kinetics
  • Master equation
  • Numerical method
  • Protein folding
  • QR
  • Transition matrix

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