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Discrete model of transition between order and static chaos in peptides and polymers

Makaruk H.

Archives of Mechanics

2006

Vol. 58, nr 4-5

381-391

Biological function of a peptide or properties of a polymer material depend on chemical composition of a macromolecule and on its geometry. A mechanistic model is considered to investigate the factors changing a geometrically ordered macromolecule into a geometrically chaotic one, assuming no chemical change. 2D and 3D examples show how a small change in interaction between parts of a macromolecule can transform an ordered geometry of the (bio) polymer into a chaotic one. It is mathematically interesting that the systems obey the difference equations, which in the continuum limit lead to differential equations with well-behaving (non-chaotic) solutions, while in certain cases behavior of the difference equations seems to be chaotic.