SCALING OF FOLDING PROPERTIES IN GO MODELS OF PROTEINS

Marek Cieplak

Institute of Physics, Polish Academy of Sciences,
Al. Lotnikow 32/46, 02-668 Warsaw, Poland

Insights about scaling of folding properties of proteins
are obtained by studying folding in
heteropolymers described by Go-like Hamiltonians.
Both lattice and continuum space models are considered. In the
latter case, the monomer-monomer interactions correspond to the
Lennard-Jones potential. Several statistical ensembles of the
two- and three-dimensional target
native conformations are generated. Among them  are structures
which are maximally compact and those which are obtained
through quenching of homopolymers to compact states.
Characteristic folding times are found to grow as power
laws with the system size. The corresponding exponents are not universal.
The size related deterioration of foldability is found to be
consistent with the scaling behavior of the characteristic
temperatures: asymptotically, the folding temperature
becomes much lower than the temperature at which glassy kinetics
become important. The scaling properties of the Go-like models
of the protein structures stored in the Protein Data Bank
are similar to those obtained for the classes of the decoy
target structures.
Reaching a ground state of an Ising spin system is analogous to a protein
evolving into its native state. The "folding" properties of the spin
systems also deteriorate with the system size.