Cubic lattice models for the dynamic folding of peptide chains provide insight into the folding process. Usually the set of allowed moves consist of wiggles, planar flips of a residue between one of two possible states, and crankshaft moves. An energy matrix is used to give the energy of contact between residues. The metropolis algorithm is used in an attempt to fold the chain into its lowest energy or native state. 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. Because the cubic lattice model is not a realistic model for actual proteins we have undertaken a study of the cubic lattice model in an attempt to understand its dynamics. The purpose is to uncover 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. We have therefore followed the strategy of determining Tf for a given set of parameters and then testing the speed of folding at this temperature. This seems to be quite successful at finding the best set of parameters for folding. We have examined several different energy matrices to see where the best folding occurs. We are now examining the relationship between the Boltzman probability of being in the native state for specific sequences and how this correlates with the speed of folding. We hope in this way to understand what thermodynamic state predictions may tell us about dynamics.
