Figure 1. Illustration of the cut-based FEP [13].

(a) The high-dimensional free-energy surface is coarse-grained into nodes of the network. Two nodes are linked if the system proceeds from one to the other along the considered timeseries. The mean first passage time (mfpt) is calculated for each node analytically (see text). (b) For each value of mfpt the set A of all nodes with a lower mfpt value is defined. The free-energy of the barrier between the two states formed by the nodes in A and the remainder of the network B can be calculated by the number of transitions between nodes of either set [13]. (c) The cut-based FEP is a projection of the free-energy surface onto the relative partition function , which includes all pathways to the reference node. For each value of mfpt, the point is added to the FEP. The cut-based FEP projects the free-energy surface faithfully for all nodes to the left of the first barrier (basin 1). After the first barrier, two or more basins overlap (e.g., basins 2 and 3) if they have the same kinetic distance from the reference node.