Title: Numerical solutions of a master equation for protein folding kinetics

Authors: Yiming Li

Addresses: Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan

Abstract: 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.

Keywords: protein folding; kinetics; master equation; numerical methods; eigenvalues; transition matrix; QR; Arnoldi; Jacobi-Davidson; bioinformatics research; bioinformatics applications; high performance computing.

DOI: 10.1504/IJBRA.2006.011040

International Journal of Bioinformatics Research and Applications, 2006 Vol.2 No.4, pp.420 - 429

Published online: 05 Oct 2006 *

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