From Collapse to Freezing in Random Heteropolymers

Details From Collapse to Freezing in Random Heteropolymers From Collapse to Freezing in Random Heteropolymers

1996-04-29

arxiv.org/abs/cond-mat/9604174v3

Physics

Condensed Matter

Statistical Mechanics

4 pages, Revtex, figs upon request. New interpretation and emphasis. Submitted to Europhys.Lett

Scientific paper

10.1209/epl/i1997-00197-2

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N_H (out ofN) attracting sites. At zero temperature, permanent links are formed leading to collapse structures for any fraction rho_H=N_H/N. The average chain size scales as R = N^{1/d}F(rho_H) (d is space dimension). As rho_H --> 0, F(rho_H) ~ rho_H^z with z={1/d-nu}=-1/4 for d=2. Moreover, for 0 < rho_H < 1, entropy approaches zero as N --> infty (being finite for a homopolymer). An abrupt decrease in entropy occurs at the phase boundary between the swollen (R ~ N^nu) and collapsed region. Scaling arguments predict different regimes depending on the ensemble of crosslinks. Some implications to the protein folding problem are discussed.

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