# Classification of Polymer Structures by Graph Theory

Patra, SM and Vishveshwara, S (1999) Classification of Polymer Structures by Graph Theory. In: International Journal of Quantum Chemistry, 71 (4). pp. 349-356.

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## Abstract

Compact polymers such as proteins obtain their unique conformation by appropriate nonbonded interactions among their monomer residues. Innumerable nonnative compact conformations are also possible, and it is essential to distinguish the native from the nonnative conformations. Toward this goal we have used graph-theoretic methods to classify polymer structures formed by noncovalent interactions. All compact structures on a $4 \times 4$ two dimensional lattice and a few conformations on $3 \times 3 \times 3$ cubic lattice have been investigated. The 69 compact conformations in $4 \times 4$ two dimensional lattice are classified into 12 groups based on the highest eigenvalue and eigenvector. The complex graphs obtained for polymers in a $3 \times 3 \times 3$ lattice space are analyzed. Their eigenvalues and eigenvector components are correlated with the branching structure and the center of the graph. The method has application in classifying real polymers such as proteins into their substructures, cluster, and domains.

Item Type: Journal Article The copyright belongs to John Wiley & Sons, Inc. Polymer conformation;Nonbonded interaction;Graph theory;Eigenvalues;Eigenvectors;Lattice model Division of Biological Sciences > Molecular Biophysics Unit 11 Jun 2006 19 Sep 2010 04:29 http://eprints.iisc.ernet.in/id/eprint/7578