Network representation of conformational transitions between hidden intermediates of Rd-apocytochrome b₅₆₂

The folding kinetics of Rd-apocytochrome b₅₆₂ is two-state, but native-state hydrogen exchange experiments show that there are discrete partially unfolded (PUF) structures in equilibrium with the native state. These PUF structures are called hidden intermediates because they are not detected in kinetic experiments and they exist after the rate-limiting step. Structures of the mimics of hidden intermediates of Rd-apocytochrome b₅₆₂ are resolved by NMR. Based upon their relative stability and structural features, the folding mechanism was proposed to follow a specific pathway (unfolded → rate-limiting transition state → PUF1 → PUF2 → native). Investigating the roles of equilibrium PUF structures in folding kinetics and their interrelationship not only deepens our understanding of the details of folding mechanism but also provides guides in protein design and prevention of misfolding. We performed molecular dynamics simulations starting from a hidden intermediate and the native state of Rd-apocytochrome b₅₆₂ in explicit solvent, for a total of 37.18 μs mainly with Anton. We validated our simulations by detailed comparison with experimental data and other computations. We have verified that we sampled the post rate-limiting transition state region only. Markov state model was used to analyze the simulation results. We replace the specific pathway model with a network model. Transition-path theory was employed to calculate the net effective flux from the most unfolded state towards the most folded state in the network. The proposed sequential folding pathway via PUF1 then more stable, more native-like PUF2 is one of the routes in our network, but it is not dominant. The dominant path visits PUF2 without going through PUF1. There is also a route from PUF1 directly to the most folded state in the network without visiting PUF2. Our results indicate that the PUF states are not necessarily sequential in the folding. The major routes predicted in our network are testable by future experiments such as single molecule experiment.