Identification of Metastabilities in Monomolecular Conformation Kinetics

作者: Susanna Kube , Marcus Weber

DOI:

关键词: Statistical physicsPotential energy surfaceDegrees of freedom (physics and chemistry)Dihedral anglePointwiseEigenvalues and eigenvectorsCombinatoricsTransfer operatorMatrix (mathematics)Boltzmann distributionMathematics

摘要: The identification of metastable conformations molecules plays an important role in computational drug design. One main difficulty is the fact that underlying dynamic processes take place high dimensional spaces. Although restriction degrees freedom to a few dihedral angles significantly reduces complexity problem, existing algorithms are time-consuming. They mainly based on approximation of transfer operator by extensive sampling states according to Boltzmann distribution and short-time Hamiltonian dynamics simulations. We present method which can identify without complete distribution. Our algorithm on local transition rates uses only pointwise information about potential energy surface. In order apply cluster PCCA+, we compute eigenvectors rate matrix Jacobi-Davidson method. Interpolation techniques applied approximate thermodynamical weights clusters. concluding example illustrates our approach for epigallocatechine, molecule be described seven angles.

参考文章(21)
Ch. Schütte, W. Huisinga, P. Deuflhard, Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. pp. 191- 223 ,(2001) , 10.1007/978-3-642-56589-2_9
R. B. Bapat, T. E. S. Raghavan, Nonnegative Matrices and Applications ,(1997)
Gerard L. G. Sleijpen, Fred W. Wubs, Exploiting Multilevel Preconditioning Techniques in Eigenvalue Computations SIAM Journal on Scientific Computing. ,vol. 25, pp. 1249- 1272 ,(2003) , 10.1137/S1064827599361059
Diederik R. Fokkema, Gerard L. G. Sleijpen, Henk A. Van der Vorst, Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils SIAM Journal on Scientific Computing. ,vol. 20, pp. 94- 125 ,(1998) , 10.1137/S1064827596300073
Michael T Wolfinger, W Andreas Svrcek-Seiler, Christoph Flamm, Ivo L Hofacker, Peter F Stadler, Efficient computation of RNA folding dynamics Journal of Physics A. ,vol. 37, pp. 4731- 4741 ,(2004) , 10.1088/0305-4470/37/17/005
Peter Deuflhard, Marcus Weber, Robust Perron cluster analysis in conformation dynamics Linear Algebra and its Applications. ,vol. 398, pp. 161- 184 ,(2005) , 10.1016/J.LAA.2004.10.026
Ch Schütte, A Fischer, W Huisinga, P Deuflhard, A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo Journal of Computational Physics. ,vol. 151, pp. 146- 168 ,(1999) , 10.1006/JCPH.1999.6231
William J. Stewart, Wei Wu, Numerical Experiments with Iteration and Aggregation for Markov Chains Informs Journal on Computing. ,vol. 4, pp. 336- 350 ,(1992) , 10.1287/IJOC.4.3.336
Gerard L. G. Sleijpen, Henk A. Van der Vorst, A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems SIAM Journal on Matrix Analysis and Applications. ,vol. 17, pp. 401- 425 ,(1996) , 10.1137/S0895479894270427