Schematic one-dimensional and 2D representations of a model free energy landscape. Although the reduced-dimensionality representation reproduces the correct number of minima and their energies, the connectivity of these states and their barriers are obscured in a single dimension.
(a) Probability distribution along the first PC as obtained from an 800 ns MD simulation of . Compared are three versions of PCA, the dPCA (full red line), a PCA that uses Cartesian coordinates (dotted blue line), and a PCA directly on the dihedral angles (dashed green line). (b) DPCA probability distributions along the PCs , , and . The size of the statistical error is similar to the line width of the plots.
2D representations of the free energy landscape of as obtained by dPCA: (a) , (b) , and (c) . The color coding in panels (d)–(f) illustrates some prominent conformational states which are described in Table I, visualized on the upper landscape.
The PCs of as obtained by the dPCA, characterized by (a) their cumulative fluctuations and (b) their normalized fluctuation autocorrelation functions. The latter is shown for the PCs (full line), (dashed line), and (dotted line). The size of the statistical error is similar to the line width of the plots.
Geometric and kinetic clusterings of the free energy landscape of . (a) Percentage of “geometrically good” clusters as a function of the number of clusters considered in means. (b) Percentage of metastable states (i.e., “kinetically good” clusters) as a function of the number of clusters.
Master equation results for the decay of (a) the most stable state 1 and (b) the least stable state 23, assuming lag times , 10, 100, 500, and 1000 ps (from left to right). The size of the statistical error is similar to the line width of the plots.
Visualization of the free energy landscape of . Shown are (a) a 2D cut along the first two components including transitions with transition probability between cluster centers, (b) a 2D principal coordinate representation where only transitions with probability are indicated (using a line width that is proportional to ), and (c) a disconnectivity graph of the system.
2D population maps (upper panels) and their one-dimensional projections (lower panels), where for empty fields. By projecting on the horizontal axis, the barrier between the right and left states (a) remains, (b) becomes higher, and (c) becomes smaller.
Conformational states of as obtained from a -means clustering on the 5D dPCA space. The states are characterized by the structure of their five inner amino acids ( for helical conformations and for extended or poly-L-proline II conformations), their population probability , and their metastability . The -means results for and in reduced space are compared to the results and of a direct clustering on the full-dimensional free energy landscape of . Statistical errors are for populations and for metastabilities.
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