  Recent advances in coarse-grained lattice and off-lattice protein models are
reviewed. The sequence dependence of thermodynamical folding properties are
investigated and evidence for non-randomness of the binary sequences of good
folders are discussed. Similar patterns for non-randomness are found for real
proteins. Dynamical parameter MC methods, such as the tempering and
multisequence algorithms, are essential in order to obtain these results. Also,
a new MC method for design, the inverse of folding, is presented. Here, one
maximizes conditional probabilities rather than minimizing energies. By
construction, this method ensures that the designed sequences represent good
folders thermodynamically.
