Geometric properties of crumpled wires and the condensed non-solid packing state of very long molecular chains

Abstract

Geometric aspects associated with the hierarchical and heterogeneous packing of crumpled wires are reviewed. The recently discovered phenomenon of condensation of elastic energy of curvature in these structures is discussed, and new results are presented with emphasis on robust scaling laws. It is examined the possible relevance of these laws in the conformational properties of long molecular chains densely packaged in a non-solid state, as e.g. in the packing of DNA strands in chromosomes, or in virus capsids. In particular, mean field arguments are used to estimate the dependence of the number of loops in the dense non-solid packed three-dimensional configurations of a very long polymer strand as a function of the number of monomers or the chain length. ©2008 Sociedade Brasileira de Química.