Figure 1.
Correlated motions couple the catalytic domain interface to the substrate-binding loop of Pin1's WW domain.
The WW domain is shown in cartoon and sticks, the catalytic domain as a surface, and the substrate in spheres. The structure shown is from PDB entry 1F8A. Only the WW domain was simulated; the catalytic domain is only shown for reference. (A) Hierarchical clustering of the mutual information between residues' torsions identifies several functionally important groups of residues. (B) Most residues in the red cluster lie in the catalytic domain interface and are correlated with residues in magenta cluster, which includes a number of key substrate-binding residues. All residues exhibiting slow motions in NMR experiments are in either the red or magenta clusters. (C) Mutual information between atoms complements torsional analysis and importantly captures correlated motions of secondary structure elements, highlighting correlated motions between the first
(residues 7–9) and Loop 1 (residues 10–16), between the first
and the second
(residues 17–21), and between the C-terminal part of Loop 2 and the beginning of the third
(residues 23–26) and the rest of the protein.
Figure 2.
Correlation obtained by producing exchange states out of clustering different numbers of macrostates for the 1,000 microstate MSM.
This plot reflects the dependence on the number of macrostates in our MSM model to achieve a maximum correlation (y-axis) and more statistically significant p-values. A MSM with 40 macrostates achieved the best partition that correlated significantly with experiment.
Figure 3.
Correlation of to
for a Markov State Model of apo Pin1-WW dynamics.
For the two data sets of different lengths, Extended 1 (1 ) and Extended 2 (30
), a statistically significant correlation was achieved for 40 macrostates. Bootstrapping was used to compute statistical error for the estimated
, the error bars are smaller than symbol size.
Figure 4.
Superposition of representative structures for the two macrostates (16 and 26) belonging to the Minor State.
Two different conformations of Loop 1 show a high degree of internal hydrogen bonds. The WW domain is shown in cartoon representation, with side chains in Loop 1 shown as sticks, and hydrogen bonds within Loop 1 are shown in dashes. Macrostate 16 is colored wheat and Macrostate 26 is colored light blue.
Figure 5.
Betweenness centrality based kinetic network for the simulation ensemble Extended 2.
In this kinetic network nodes represent macrostates, edge widths are proportional to their betweenness measure . If an edge is thicker then it means that this edge belongs to several shortest paths among pairs of macrostates. Node size depends on the macrostate population. A node colored blue is closer, in RMSD terms, to the Apo Pin1-WW conformation and a red node is closer to the Holo Pin-WW structure. Figure created using Cytoscape [52].
Figure 6.
Betweeness centrality based backbone network for the simulation ensemble Extended 1.
Macrostate 16 remains as the kinetic hub and states 38 and 9 are also conserved as the states with larger populations. Edge weights are proportional to betweenness centrality and node size is proportional to population. A node colored blue is closer, in RMSD terms, to the Apo Pin1-WW conformation and a red node is closer to the Holo Pin-WW structure.
Table 1.
Kullback-Leibler divergence between macrostates populations for the Extended 1 and Extended 2 simulation ensembles.
Table 2.
NOE violations for MSM Ensemble.
Figure 7.
Superposition of representative structures for all 40 macrostates shows diverse conformations of Loop 1.
The WW domain is shown in cartoon representation, with side chains in Loop 1 shown as sticks. Residues are colored in the same fashion as in Figure 1, i.e. according to cluster membership in the MutInf analysis.