Designability , thermodynamic stability , and

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be \protein-like", heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We nd two criteria which, together, guarantee that a sequence will be \protein like": i) the ground state is a highly designable stucture, i. e. the native structure is the ground state of a large number of sequences, and ii) the sequence has a large =? ratio, being the average energy separation between the ground state and the excited compact conformations, and ? the dispersion in energy of excited compact conformations. These two criteria are not incompatible since, on average, sequences whose ground states are highly designable structures have large =? values. These two criteria require knowledge only of the compact-state spectrum. These claims are substantiated by the study of 45 sequences, with various values of =? and various degrees of designability, by means of a Borst-Kalos-Lebowitz algorithm, and the Ferrenberg-Swendsen histogram optimization method. Finally, we report on the reasons for slow folding. A comparison between a very slow folding sequence, an average folding one and a fast folding one suggests that slow folding originates from a proliferation of nearly compact low-energy conformations, not present for fast folders.