Hydrodynamic description of protein folding: the decrease of the probability fluxes as an indicator of transition states in two-state folders.

Using hydrodynamic description of protein folding, the process of the first-passage folding of ubiquitin has been studied. Since a large number of folding trajectories were required to obtain converged folding flows, a coarse-grained representation of the protein in the form of a C-bead Gō-model was employed, and discrete molecular dynamics was used to perform simulations. It has been found that the free energy surface has a maximum width in the transition state region, so that the densities of folding flows (probability fluxes) decrease to minimum when the system passes through the transition state. There are indications that the increasing number of different protein conformations in the transition state region compared with those in the neighboring regions of semi-compact and native-like states is responsible for the present phenomena. It has also been shown that if the free energy is projected onto a single reaction coordinate, the low populations of the transition states can be compensated by the increasing number of states, which can lead to a considerable decrease or even disappearance of the free energy barrier in the transition state.