FOLDING MODEL PROTEINS USING KINETIC AND THERMODYNAMIC ANNEALING OF THE CLASSICAL DENSITY DISTRIBUTION

The folding of several model proteins is studied using three optimizat ion algorithms which are based on the simulated annealing of an approx imation to the classical density distribution. These methods are deriv ed from the approximate solution of equations of motion for the time o r temperature evolution of the density distribution. Therefore, it is of interest to analyze not only the resulting lowest energy molecular conformations but also the folding mechanism followed during the annea ling runs. The results are compared with classical simulated annealing based on molecular dynamics and the diffusion equation method of Sche raga and coworkers. The model proteins studied are 22-mers and a 46-me r based on a three-letter code used by Honeycutt and Thirumalai. The p otential models the basic properties of attractive interactions betwee n hydrophobic residues, to encourage the formation of a hydrophobic co re, and the propensity of hydrophilic residues to be found at the prot ein surface. Analysis of the thermodynamically dominant structures dur ing annealing reveals a collapse transition at high temperature follow ed by a strong folding transition to the native state at lower tempera tures. This general mechanism has been seen previously in simulations of similar model proteins and predicted on the basis of mean field the ories of heteropolymers. We find that the probability of success in fi nding the set of lowest energy native states is strongly correlated wi th the energy separation between the native (and native-like) and non- native states. Our optimization algorithms are effective in finding th ose low-energy structures which correspond to the global energy minimu m fold. The results indicate that dynamical phase space simulated anne aling methods may have an advantage over configuration space based sea rch for complex fold topologies.