FROM COLLAPSE TO FREEZING IN RANDOM HETEROPOLYMERS

We consider a two-letter self-avoiding (square) lattice heteropolymer model of N-H (out of N) attracting sites. At zero temperature, permane nt links are formed leading to collapse structures for any fraction rh o(H) = N-H/N. The average chain size scales as R similar or equal to ( NF)-F-1/d(rho(H)) (d is the space dimension). As rho(H) --> 0, F(rho(H )) similar to rho(H)(zeta) with zeta = 1/d - nu = -1/4 for d = 2. More over, for 0 < rho(H) < 1, entropy per monomer approaches zero as N --> infinity (being finite for a homopolymer). An abrupt decrease in entr opy occurs at the phase boundary between the swollen (R similar to N-n u) and collapsed region. Scaling arguments predict different regimes d epending on the ensemble of crosslinks. Some implications to the prote in folding problem are discussed.