It is hard to construct theories for the folding of globular proteins
because they are large and complicated molecules having enormous numbe
rs of nonnative conformations and having native states that are compli
cated to describe. Statistical mechanical theories of protein folding
are constructed around major simplifying assumptions about the energy
as a function of conformation and/or simplifications of the representa
tion of the polypeptide chain, such as one point per residue on a cubi
c lattice. It is not clear how the results of these theories are affec
ted by their various simplifications. Here we take a very different si
mplification approach where the chain is accurately represented and th
e energy of each conformation is calculated by a not unreasonable empi
rical function, However, the set of amino acid sequences and allowed c
onformations is so restricted that it becomes computationally feasible
to examine them all. Hence we are able to calculate melting curves fo
r thermal denaturation as well as the detailed kinetic pathway of refo
lding, Such calculations are based on a novel representation of the co
nformations as points in an abstract la-dimensional Euclidean conforma
tion space. Fast folding sequences have relatively high melting temper
atures, native structures with relatively low energies, small kinetic
barriers between local minima, and relatively many conformations in th
e global energy minimum's watershed. In contrast to other folding theo
ries, these models show no necessary relationship between fast folding
and an overall funnel shape to the energy surface, or a large energy
gap between the native and the lowest nonnative structure, or the dept
h of the native energy minimum compared to the roughness of the energy
landscape, (C) 1998 Wiley-Liss, Inc.