Figure 1.
SSD algorithm applied to a synthetic funnel-like potential.
(A) 2D funnel-like potential. (B) A stochastic trajectory is translated into a CMN where 6 sets of nodes (corresponding to different color) are the result of the SSD algorithm. (C) Recovering the spatial coordinates, the stationary probabilities of each node are shown in color code. The 6 basins detected are represented as color striped regions. (D) A coarse-grained CMN is built where new nodes take the role of the basins.
Figure 2.
Hierarchies of the basins detected for the funnel-like potential.
(A) Free Energy hierarchy: based on the relative free-energy of the nodes. (B) Temporal hierarchy: number of basins defined by SSD for the different networks built by Eq. (7). The original basins merge in function of time. Both hierarchies reveals a coarse-grained behavior of two macro-states: and
.
Figure 3.
Free energy basins of the Alanine dipeptide.
(A) The dialanine dipeptide with the angles and
. (B) Plot of the CMN generated. The 6 sets of nodes (corresponding to different colors) are the result of the SSD algorithm. (C) Left: Ramachandran plot with the probability of occupation of the cells used to build the CMN. The boundaries of the free energy basins are shown in white. Right: the 6 basins represented as regions of different color. (Color code:
,
,
,
,
and
).
Table 1.
Relative free energies and Mean Escape Time of the basins defined by SSD.
Figure 4.
Dendogram based on the relative Free Energy of the CMN nodes.
Two sets of basins are clearly distinguished with a high free energy barrier in between: (,
,
,
) and (
,
). Note that
looks like the conformer with the largest dwell time, in agreement with data in Table 1.
Table 2.
Characteristic times for direct inter-basins transitions.
Figure 5.
Dendogram based on the temporal hierarchy of basins.
In around 100 ps the peptide finds the way to reach the global minimum, conformer , from any basin.