Automatic Identification of Metastable Conformations via Self-Organized Neural Networks

As has been shown recently, the identification of metastable chemical conformations leads to a Perron cluster eigenvalue problem for a reversible Markov operator. Naive discretization of this operator would suffer from combinatorial explosion. As a first remedy, a pre-identification of essential degrees of freedom out of the set of torsion angles had been applied up to now. The present paper suggests a different approach based on neural networks: its idea is to discretize the Markov operator via self-organizing box maps. The thus obtained box decomposition then serves as a prerequisite for the subsequent Perron cluster analysis. Moreover, this approach also permits exploitation of additional structure within embedded simulations. As it turns out, the new method is fully automatic and efficient also in the treatment of biomolecules. This is exemplified by numerical results.

[1]  Marc M. Van Hulle,et al.  Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization , 2000 .

[2]  Michael Dellnitz,et al.  Computation of Essential Molecular Dynamics by Subdivision Techniques , 1996, Computational Molecular Dynamics.

[3]  T. Halgren.  Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94 , 1996, J. Comput. Chem..

[4]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[5]  P. Deuflharda,et al.  Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains , 2000 .

[6]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[7]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[8]  P. Deuflhard,et al.  Hierarchical Uncoupling-Coupling of Metastable Conformations , 2002 .

[9]  Marc M. Van Hulle,et al.  Faithful representations with topographic maps , 1999, Neural Networks.

[10]  H. Berendsen,et al.  Essential dynamics of proteins , 1993, Proteins.

[11]  N. Fisher,et al.  Statistical Analysis of Circular Data , 1993 .

[12]  Benedict Leimkuhler,et al.  Computational Molecular Dynamics: Challenges, Methods, Ideas , 1999, Computational Molecular Dynamics.

[13]  Thomas A. Halgren,et al.  Merck molecular force field. IV. conformational energies and geometries for MMFF94 , 1996, J. Comput. Chem..

[14]  Teuvo Kohonen,et al.  Comparison of SOM Point Densities Based on Different Criteria , 1999, Neural Computation.

[15]  An Uncoupling-Coupling Technique for Markov Chain Monte Carlo Methods , 2000 .

[16]  Hybrid Monte Carlo with adaptive temperature in mixed‐canonical ensemble: Efficient conformational analysis of RNA , 1998 .

[17]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[18]  Alexander Fischer,et al.  Hybrid Monte Carlo with adaptive temperature in mixed-canonical ensemble: Efficient conformational analysis of RNA , 1998, J. Comput. Chem..

[19]  P. Deuflhard,et al.  Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains , 2000 .

[20]  Dimitrios Gunopulos,et al.  Automatic subspace clustering of high dimensional data for data mining applications , 1998, SIGMOD '98.

[21]  C. Schütte.  Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules , 1999 .

[22]  Wilhelm Huisinga,et al.  Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification , 1999 .

[23]  P. Sopp.  Cluster analysis. , 1996, Veterinary immunology and immunopathology.

[24]  Peter Deuflhard,et al.  Adaptive hierarchical cluster analysis by Self-Organizing Box Maps , 2000 .

[25]  P. Deuflhard,et al.  A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo , 1999 .