Application of the Diffusion–Collision Model to the Folding of Three-helix Bundle Proteins

The diffusion–collision model has been successful in explaining many features of protein folding kinetics, particularly for helical proteins. In the model the folding reaction is described in terms of coupled chemical kinetic (Master) equations of coarse grained entities, called microdomains. Here, the diffusion–collision model is applied to compute the folding kinetics of four three-helix bundle proteins, all of which fold on a time scale of tens of microseconds and appear to have two-state folding. The native structure and the stability of the helical microdomains are used to determine the parameters of the model. The formulation allows computation of the overall rate and determination of the importance of kinetic intermediates. The proteins considered are the B domain of protein A (1BDC), the Engrailed Homeodomain (1ENH), the peripheral sub-unit-binding domain (1EBD C-chain) and the villin headpiece subdomain (1VII). The results for the folding time of protein A, the Engrailed Homeodomain, and 1EBD C-chain are in agreement with experiment, while 1VII is not stable in the present model. In the three proteins that are stable, two-state folding is predicted by the diffusion–collision model. This disagrees with published assertions that multistate kinetics would be obtained from the model. The contact order prediction agrees with experiment for protein A, but yields values that are a factor of 40, 30 and 15 too slow for 1ENH, 1EBD C-chain and 1VII. The effect of mutants on folding is described for protein A and it is demonstrated that significant intermediate concentrations (i.e. deviation from two-state folding) can occur if the stability of some of the helical microdomains is increased. A linear relationship between folding time and the length of the loop between helices B and C in protein A is demonstrated; this is not evident in the contact order description.