ψ j φ j+1 Motif position

Transcription

1 1.0 % Occupancy ψ i-1 φ i ψ j φ j+1 ψ k-1 Motif position φ Supplementary Figure 1 Residue profiles for the positions in the β-sheet motif. Residue types as percentages for the six positions in the β-sheet motif. The positions correspond to those given in the main text. Shown in yellow; nonpolar residues (AVLIMFW), in green; polar residues (STNQCY), in red; acidic residues (ED) and in blue; basic residues (KRH).

2 Supplementary Figure 2 Correlation analysis for structural ensembles of homologous proteins. The structures are shown with the minimal motifs that behave as predicted from the model β-sheets are coloured red. Graphical summaries of the correlations coefficients (ρ) for the two highest and single lowest scoring motifs as well as the average for all motifs in the structure. Sampling overlap shows the overlap of the first PCA components from MD simulations or transition pathways with the ensembles of homologous proteins.

3 Supplementary Figure 3 Correlations caused by first 10 primary modes of motion in β-sheets calculated using ENM. Graphical summaries of the correlations coefficients (ρ) for the first 10 normal modes are shown for six representative strands from the 14 stranded synthetic β-sheet.

4 Supplementary Figure 4 Correlations caused by first 10 primary modes of motion in β-sheets calculated using the all atom molecular mechanics force field CHARMM27. Graphical summaries of the correlations coefficients (ρ) for the first 10 normal modes are shown for six representative strands from the 14 stranded synthetic β-sheet.

5 Motif Score 15 Mad2 spindle checkpoint protein (190) 1s2h 1go4 Adaptor protein p14 (91) 1szv 1vet Oligopeptide-binding protein (517) 1rkm 2rkm Diaminopimelic acid dehydrogenase (320) 3dap 1dap NF-kappa B (273) 1ram 1lei Supplementary Figure 5 Correlations caused by the transitions between states. β-sheets rich proteins are coloured blue and green to distinguish the two states and β- sheets with minimal motifs that behave as predicted from the model β-sheets are coloured red. The structures are coloured according to the motif score which has a maximum value of 15 and indicates that the β-sheets moves in a correlated way as predicted from the PDB and the PCA analysis. The probability of observing the red highlighted regions that correspond to values >10 and have a random probability of less than 0.06 under independence.

6 a b c k >0.5 k j+1 j -0.1 circular -0.3 i Adaptor protein p14 (91) 1szv 1vet NF-kappa B (273) 1ram 1lei i-1 i-1 i j j+1 k-1 k <-0.5 Supplementary Figure 6 Long-range correlations caused by transitions. β-sheets rich proteins are coloured blue and green to distinguish the two states and β- sheets with minimal motifs that behave as predicted from the model β-sheets are coloured red (a and b). The structures are coloured according to the motif score which has a maximum value of 15 and indicates that the β-sheets moves in a correlated way as predicted from the PDB and the PCA analysis. The probability of observing the red highlighted regions that correspond to values >10 and have a random probability of less than 0.06 under independence. A graphical summary (c) of the averaged correlations is show.

7 Supplementary Table 1 Means, standard deviations, and circular variances of the dihedral angles in the β-sheet motif. Dihedral angle* Mean angle ( ) Standard Circular Variance** deviation ( ) ψ i φ i ψ j φ j ψ k φ k *The dihedral angle positions correspond to those given in the main text. **The circular variance takes values between zero and one, where low values indicate a unique angle, with tight clustering around the mean.

8 Supplementary Table 2 Structure-specific correlation analysis for the minimal motif. PDB code Nres Fold Total Motifs 1PCA sig 1NMA Sig 5PCA sig 5NMA Sig 1a4h layer sandwich cbs 137 beta barrel cpn 208 sandwich d2u 184 beta barrel g7n 131 beta barrel gbg 214 sandwich gnd 430 2/3-layer sandwiches gof blade propeller icx layer sandwich ifc 131 beta barrel ij9 196 sandwich msc layer sandwich mvg 125 beta barrel ngl 179 beta barrel nkg 508 distorted sandwiches p6p 125 beta barrel plr 258 Box wp blade propeller yfq blade propeller axf 385 1/2-layer sandwiches axg 385 1/2-layer sandwiches ayh 214 sandwich bvo 385 1/2-layer sandwiches cbr 136 beta barrel Nres the total number of residues in the structure. Fold the fold definition for the structure. Total Motifs the number of motifs that exist in the structure 1PCA sig. the number of motifs with motif scores > 10 for the ensemble of structures generated with Brownian dynamics using just the first PCA component. 1NMA sig. the number of motifs with motif scores > 10 for the ensemble of structures generated with Brownian dynamics using just the first NMA mode. 5PCA sig. the number of motifs with motif scores > 10 for the ensemble of structures generated with Brownian dynamics using just the first five PCA components. 5NMA sig. the number of motifs with motif scores > 10 for the ensemble of structures generated with Brownian dynamics using just the first five NMA modes.

9 Supplementary Table 3 Conformational transitions structure pairs. Open/Closed Nres rmsd Name Total Motifs Sig Strands/Nres Major motif Θ bend Θ twist (MD) 1szv/1vet Adaptor protein p /35 163±8 º 155±10 º 1s2h/1go Mad2 spindle /55 170±6 º checkpoint protein 130±6 º 1ramB/1leiA NF-kappa B 5 2 4/34 170±5 º 146±8 º 3dapA/1dapB Diaminopimelic 4 3 3/34 162±4 º acid dehydrogenase 155±5 º 1rkm/2krm Oligopeptidebinding 7 4 3/36 160±5 º protein 150±7 º λ bend λ twist (MD) Å K bend K twist (MD) kcal.mol -1.Å bend twist 5º 10º 12º 2º 3º 1º 4º 2º 3º 10º Overlap, O 10 Deformation energy, E 10 kcal.mol -1 kcal.mol -1.res Nres the total number of residues in the structure. rmsd root mean square deviation (Å) between open and closed conformations. Fold the fold definition for the structure. Total Motifs the number of motifs that exist in the structure. Sig the number of β-motifs that have motif scores > 10 for the ensemble of structures. Strands/Nres - Number of strands and residues in the major β-sheet motif displaying correlated motions θ twist / θ bend - Bending and twisting angles in MD simulations for the major β-motif present in the structure (see definition above) λ twist / λ bend - Bending and twisting eigenvalues (Å 2 ) in MD simulations for the major β-motif present in the structure Κ twist / K bend - Bending and twisting stiffness constants (kcal.mol -1.Å -2 ) in MD simulations for the major β-motif present in the structure twist / bend - Change in bending and twisting angles associated to the conformational change for the major β-motif present in the structure between open and closed conformations O 10 Overlap of the X-ray transition with MD first 10 PCA modes (Eq.10) for the deformation of the major β-motif along the transition coordinate. E 10 Elastic energy (kcal.mol -1, kcal.mol -1.res -1, Eq.13) for the deformation of the primary β-motif along them to approach to the target structure.