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Identification of Metastabilities in Monomolecular Conformation Kinetics

Please always quote using this URN: urn:nbn:de:0297-zib-8956
  • The identification of metastable conformations of molecules plays an important role in computational drug design. One main difficulty is the fact that the underlying dynamic processes take place in high dimensional spaces. Although the restriction of degrees of freedom to a few dihedral angles significantly reduces the complexity of the problem, the existing algorithms are time-consuming. They are based on the approximation of transition probabilities by an extensive sampling of states according to the Boltzmann distribution. We present a method which can identify metastable conformations without sampling the complete distribution. Our algorithm is based on local transition rates and uses only pointwise information about the potential energy surface. In order to apply the cluster algorithm PCCA+, we compute a few eigenvectors of the rate matrix by the Jacobi-Davidson method. Interpolation techniques are applied to approximate the thermodynamical weights of the clusters. The concluding example illustrates our approach for epigallocatechine, a molecule which can be described by seven dihedral angles.

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Author:Susanna Kube, Marcus Weber
Document Type:ZIB-Report
Tag:clustering; eigenvectors; metastable conformations; potential energy surface; transition rates
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A30 Chemical kinetics [See also 76V05, 92C45, 92E20]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B41 Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Exx Chemistry (For biochemistry, see 92C40) / 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
Date of first Publication:2005/12/29
Series (Serial Number):ZIB-Report (06-01)
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