Folding with downhill behavior and low cooperativity of proteins

The downhill folding observed experimentally for a small protein BBL is studied using off-lattice Go-like model. Our simulations show that the downhill folding has low cooperativity and is barrierless, which is consistent with the experimental findings. As an example of comparison in detail, the two-state folding behavior of proteins, for example, protein CI2, is also simulated. By observing the formation of contacts between the residues for these two proteins, it is found that the physical origin of the downhill folding is due to the deficiency of nonlocal contacts which determine the folding cooperatively. From a statistics on contacts of the native structures of 17 well-studied proteins and the calculation of their cooperativity factors kappa(2) based on folding simulations, a strong correlation between the number of nonlocal contacts per residue N-N and the factors kappa(2) is obtained. Protein BBL with a value of N-N = 0.73 has the lowest cooperativity factor kappa(2) = 0.34 among all 17 proteins. A crossover around N-N(c) similar to 0.9 could be defined to separate the two-state folders and the downhill folder roughly. A protein would behave downhill folding when its N-N = N-N. For proteins with their N-N values are about (or slightly larger than) N-N, the folding behaves with low cooperativity and the barriers are small, showing a weak two-state behavior or a downhill-like behavior. Furthermore, simulations on mutants of a two-state folder show that a mutant becomes a downhill folder when its N-N is reduced to a value smaller than N-N(c). These could enable us to identify the downhill folding or the cooperative two-state folding behavior solely from the native structures of proteins.