Lamplighter model of a random copolymer adsorption on a line

• Published in: Condensed matter physics Vol. 17; no. 3; p. 33002
• Main Authors: Nazarov, L. I., Nechaev, S. K., Tamm, M. V.
• Format: Journal Article
• Language: English
• Published: Institute for Condensed Matter Physics 01.01.2014
• Subjects: heteropolymer folding; lamplighter random walk; local optimization; Physics; subdiffusive chemical reaction
• ISSN: 1607-324X
• DOI: 10.5488/CMP.17.33002

We present a model of an AB-diblock random copolymer sequential self-packaging with local quenched interactions on a one-dimensional infinite sticky substrate. It is assumed that the A-A and B-B contacts are favorable, while A-B are not. The position of a newly added monomer is selected in view of the local contact energy minimization. The model demonstrates a self-organization behavior with the nontrivial dependence of the total energy, $E$ (the number of unfavorable contacts), on the number of chain monomers, $N$: $E\sim N^{3/4}$ for quenched random equally probable distribution of A- and B-monomers along the chain. The model is treated by mapping it onto the "lamplighter" random walk and the diffusion-controlled chemical reaction of $X+X\to 0$ type with the subdiffusive motion of reagents.