Conformations of Randomly Linked Polymers

Abstract

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean squared end to end distance growing as r^2 ~ M/N. A possible collapse transition (to a region of order unity) is related to percolation in a one dimensional model with long--ranged connections. A directed version of the model is also solved exactly. Based on these results, we conjecture that the typical size of a self-avoiding polymer is reduced by the links to R > (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.

6 pages, 3 Postscript figures, LaTeX

References in corpus (1)

• Statistical mechanics of macromolecular networks without replicas

Cited by in corpus (7)

• Physical descriptions of the bacterial nucleoid at large scales, and their biological implications
• A polymer model for the quantitative reconstruction of 3d chromosome architecture from Hi-C and GAM data
• Small-World Rouse Networks as models of cross-linked polymers
• Local Interactions and Protein Folding: A Model Study on the Square and Triangular Lattices
• Phase separation of polymer-bound particles induced by loop-mediated 1D effective long-range interactions
• A thermodynamic model for agglomeration of DNA-looping proteins
• Elastic properties of small-world spring networks