FACTORS GOVERNING THE FOLDABILITY OF PROTEINS

We use a three-dimensional lattice model of proteins to investigate sy stematically the global properties of the polypeptide chains that dete rmine the folding to the native conformation starting from an ensemble of denatured conformations. In the coarse-grained description, the po lypeptide chain is modeled as a heteropolymer consisting of N beads co nfined to the vertices of a simple cubic lattice. The interactions bet ween the beads are taken from a random gaussian distribution of energi es, with a mean value B-o < 0 that corresponds to the overall average hydrophobic interaction energy. We studied 56 sequences all with a uni que ground state (native conformation) covering two values of N (15 an d 27) and two values of B-o. The smaller value of \B-o\ was chosen so that the average fraction of hydrophobic residues corresponds to that found in natural proteins. The higher value of \B-o\ was selected with the expectation that only the fully compact conformations would contr ibute to the thermodynamic behavior. For N = 15 the entire conformatio n space (compact as well as noncompact structures) can be exhaustively enumerated so that the thermodynamic properties can be exactly comput ed at all temperatures. The thermodynamic properties for the 27-mer ch ain were calculated using the slow cooling technique together with sta ndard Monte Carlo simulations. The kinetics of approach to the native state for all the sequences was obtained using Monte Carlo simulations . For all sequences we find that there are two intrinsic characteristi c temperatures, namely, T-e and T-f. At the temperature T-e the polype ptide chain makes a transition to a collapsed structure, while at T-f the chain undergoes a transition to the native conformation. We show t hat foldability of sequences can be characterized entirely in terms of these two temperatures. It is shown that fast folding sequences have small values of sigma = (T-e - T-f/T-e whereas slow folders have large r values of a (the range of a is 0 < sigma < 1). The calculated values of the folding times correlate extremely well with a. An increase in a from 0.1 to 0.7 can result in an increase of 5-6 orders of magnitude s in folding times. In contrast, we demonstrate that there is no usefu l correlation between folding times and the energy gap between the nat ive conformation and the first excited state at any N for any value of B-o. In particular, in the parameter space of the model, many sequenc es with varying energy gaps, all with roughly the same folding time, c an be easily engineered. Folding sequences in this model, therefore, c an be classified based solely on the value of sigma. Fast folders have small values of sigma (typically less than about 0.1), moderate folde rs have values of sigma in the approximate range between 0.1 and 0.6, while for slow folders sigma exceeds 0.6. The precise boundary between these categories depends crucially on N and on the model. The range o f sigma for fast folders decreases with the length of the chain. At te mperatures close to T-f fast folders reach the native conformation via a native conformation nucleation collapse mechanism without forming a ny detectable intermediates, whereas only a fraction of molecule Phi(T ) reaches the native conformation by this process for moderate folders . The remaining fraction reaches the native state via three-stage mult ipathway process. For slow folders Phi(T)) is close to zero at all tem peratures. The simultaneous requirement of native state stability and kinetic accessibility can be achieved at high enough temperatures for those sequences with small values of sigma. The utility of these resul ts for de novo design of proteins is briefly discussed. (C) 1996 Wiley -Liss, Inc.