Universality and diversity of folding mechanics for three-helix bundle proteins -- Yang et al. 105 (3): 895 Data Supplement - HTML Page - index.htslp -- Proceedings of the National Academy of Sciences

Yang et al. 10.1073/pnas.0707284105.

Supporting Information

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SI Figure 5

Fig. 5. Clustering results with various rmsd cutoffs, d_c, for protein A (A) and Villin (B). Clusters that consist of >10 structures are shown for clarity. In all cases, structures in the cluster with the highest average connectivity, <k> show very low average rmsd values, <rmsd>, from the experimental structure. The cluster with the second highest <k> is composed of mirror images.

SI Figure 6

Fig. 6. Relaxation behavior of the total energy rmsd(t) and E(t) for protein A and Villin, at T » 300 K. Fits to double-exponential curves (red curves) are good in all four cases. Relaxation times t_slow and t_fast for each curve are given in the plots.

SI Figure 7

Fig. 7. A schematic view explaining the concept of a structural graph and flux, F. Each node (colored ovals) represents a single conformation, and edges (solid lines) are drawn between structurally similar conformations (as determined by the criterion d < d_c, where d is a similarity measure). Different colors indicate conformations from different trajectories, and wavy lines indicate the direction of time t. A collection of nodes that are linked by edges (either directly or in several steps) belong to the same cluster. To determine the kinetic significance of a cluster, we use the concept of flux, F, which is defined as the fraction of all trajectories that pass although a cluster. Therefore, because all conformation will fold into the native state, this cluster will have F = 1 (rightmost cluster). Other clusters with F = 1, through which all trajectories have to pass, can be interpreted as obligatory intermediate states.

SI Figure 8

Fig. 8. Structural superimpositions of all TSE structures obtained by p_fold analysis for protein A (Left) and Villin (Right). The H1-H2 hairpin is formed in TSE for both proteins. The average total helicity calculated from the whole chain, as measured by the criterion of Kabsch and Sander (6), is 81% and 65% for protein A and Villin, respectively. The average size of the ensembles, <R_g>, is 14.2 Å for protein A and 10.3 Å for Villin.

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Fig. 9. Experimental F values of different types of mutations for protein A. Our calculation method based on the number of contacts only in wide-type can be regarded as WT®Gly mutation. It is surprising to see that this method can reproduce experimental F values for other types of mutations.

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Fig. 10. Computational counterpart of FRET signal distributions for protein A. The probability distribution of end-to-end distances, 1/r⁶, in the native and unfolded states, respectively. r is determined as the Ca-Ca distance between residues 10 and 56 (numbering as in PDB ID code 1BDD). The native state is composed of the set of 147 lowest-E conformations of the respective 147 trajectories used to study folding of protein A. The unfolded ensemble is composed of all snapshot taken at times t < 20 million MC steps excluding the initial configurations.

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Fig. 11. Simulated F values where the cutoff of 2 Å was used for being folded instead of 3 Å. The numbers of TSEs are 65 and 109 for protein A and Villin, respectively. Note that comparable results could be obtained regardless of the cutoff values. (For protein A, |F^exp - F^sim| = 0.14 on average.)

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Simulation. Protein A (1BDD) and Villin (1VII) were chosen as model proteins. Unstructured tails were truncated (residues 1-9; 57-60) for protein A, and W64 was mutated to A64 and a hydrophobic residue at the end, F76 was truncated for Villin. Starting from different random coil configurations, 2,000 independent Monte Carlo simulation for each protein were conducted at for 10⁸ steps. The melting temperature for protein A, , was obtained from simulations at different temperatures (data not shown), whereas the experimental melting temperature is 346 K (1). The MC temperature thus corresponds to . Global and local moves were used for backbone rotation (2). To keep the detailed balance condition, a knowledge-based move (2, 3) was not used, and the local move set was modified (4, 5) (see below). For each trajectory, snapshots were stored at every 10⁶ MC step and the energy minimum structure was recorded at the end of simulation.

The Side-Chain Torsional Angle Energy.
The side-chain torsional angle energy (J.S.Y., P. S. Kutchukian, and E.I.S., unpublished results) was obtained from the same database as our previous study (2) by

[S1]

where and are the number of observations in the jth bin of a side-chain torsional angle cs of residue A_i and total number of observances subtracted by for a triplet consisting of A_i-1, A_i, and A_i+1, respectively. The bin width was 30° and the value of was chosen to make the net interaction zero.