By means of Monte Carlo simulation, we investigated the equilibrium be
tween folded and unfolded states of lattice model proteins. The amino
acid sequences were designed to have pronounced energy minimum target
conformations of different length and shape. For short fully compact (
36-mer) proteins, the all-or-none transition from the unfolded state t
o the native state was observed. This was not always the case for long
er proteins. Among 12 designed sequences with the native structure of
a fully compact 48-mer, a simple all-or-none transition was observed i
n only three cases. For the other nine sequences, three states of beha
vior - the native, denatured, and intermediate states - were found. Th
e contiguous part of the native structure (domain) was conserved in th
e intermediate state, whereas the remaining part was completely unfold
ed and structureless. These parts melted separately from each other.