Many theories have been proposed for the statistical mechanics of protein folding, typically derived from theories for less structured systems, such as random heteropolymers, diffusion-nucleation, random energies, or spin glasses. While these have certainly captured some important features of the physical chemistry of real proteins, such as cooperativity of folding and rapid folding from the random coil state, their derivation requires making some broad assumptions about the average behavior of polypeptides. In fact, the proteins of biological relevance consists of apparently very rare, moderately long amino acid sequences that permit the chain to fold rapidly- to a unique complicated native conformation, which depends greatly on the sequence. This suggests that theories focussing on average properties of long-chain heteropolymers may be over-generalizing and neglecting the important features of rare sequences folding to rare conformations. On the other hand, neither nature nor computer has sufficient time to exhaustively explore all conformations and all sequences for even small proteins. The idea here is to simply an otherwise realistic representation of polypeptides by reducing chain length, number of conformation states per residue, and choices of amino acid types until all sequences and all conformations can be exhaustively enumerated. By varying these parameters in the computationally feasible range, general conclusions can be detected and extrapolated to parameter values corresponding to real proteins. Since this model is so different from most theories, it is able to test their assumptions and conclusions about protein folding, such as the nature of the energy landscape and order parameters to describe the progress toward the native state. Questions to be addressed include: is there a general way to describe the folding of all proteins, or do some proceed by a recognizable pathway while others have innumerable routes? Can this model reproduce and explain the currently available experimental results on folding mechanisms and intermediates for certain particular proteins.
