A number of investigators, including Jernigan and Covell at NIH, Dill's group at UCSF, and Shahknovich's group at Harvard, have studied cubic lattice models of the dynamic folding of a chain of residues. Usually the set of allowed moves consist of wiggles (ends only), planar flips of a residue between one of two possible states where the chain makes a bend, and crankshaft moves in 3-space. An energy matrix is used to give the energy of contact between residues not adjacent on the chain. The metropolis algorithm is used to search for a lowest energy state. When the lowest energy state is found the chain has folded successfully. One of the desirable properties of the cubic lattice model as here described is the fact that it is not difficult to give examples of chains of length 27 or more that can be successfully folded in this way. While the cubic lattice model has been an interesting model in which to examine the folding problem and has led to some insights, it is not a very realistic model for actual proteins. For this reason we have undertaken a study of the cubic lattice model in an attempt to understand its dynamics, the give and take between energy and entropy, with the purpose of uncovering if possible some general principles that might lead to more realistic models of folding. It has been proposed that one should try to find parameter's for the model which maximize Tf/Tg (Bryngelson, et al.) or Tf/T(theta) (Camacho & Thirumalai). Of the three transition temperatures mentioned here we have found only Tf to be helpful. Tg is difficult to obtain with sufficient accuracy to be useful and T(theta) has not proved to be useful in prediction thus far. We have developed a method of mapping the free energy surface by unfolding a molecule at Tf. While this does not give a complete picture of the free energy surface it does provide a picture that is very useful for adjusting the parameters of the model. By use of the Miyazawa & Jernigan energy matrix we have been able to adjust the parameters of a sequence 125 residues long so as to obtain folding in reasonable times for a large fraction of the trials. A manuscript is in preparation.
