Multi-state design of flexible proteins predicts sequences optimal for conformational change
Fig 2
Metrics used to quantify conformational flexibility.
(A) Illustration of maximum RMSD100, the metric used to quantify large-scale, or global, conformational flexibility. For simplicity, we only represent RMSD on a two-dimensional plane, where the x and y axes represent the difference in distance of cartesian space if two conformations were superimposed onto the same coordinate system. Each protein conformation of identical sequence is represented as a circle, and is separated by some distance vector evaluated as the RMSD100 of two conformations. The maximum RMSD100 describes the greatest pairwise RMSD100 within an ensemble. (B) Illustration of dihedral angle ϕ and φ variation used to calculate dihedral angle RMSD (RMSDda). Orientation of atoms is color-coded and corresponds to the diagram drawn at the bottom of the panel. RMSDda is illustrated as the range of dotted lines, corresponding to the deviation in relative orientation of the third and fourth atoms. (C) Explanation of contact proximity deviation. Two conformations of the same protein are depicted in the left, with two residues, outlined in cyan or orange, shown in their respective positions. These two residues are magnified (top right) in their local side chain environment in Conformation A on the top and Conformation B on the bottom. Contact residues in Conformation A are colored yellow. If the same contacts are maintained in Conformation B, contact residues remain colored yellow in the bottom two boxes. If new contacts are made, contact residues are colored in purple. Even though the cyan residue changes slightly in its relative orientation between conformations, the same contacts are maintained so that the degree of conformational flexibility is relatively low in comparison to the heptad trimer refolding, and would have a low contact proximity deviation score. In contrast, the orange residue completely rearranges its local side chain contacts between conformations as a result of the large conformational rearrangement, and would have a high contact proximity deviation score. (D) Explanation of contact proximity deviation. We assigned a score to each Cβ–Cβ distance by applying a soft-bounded, continuously differentiable function that accounts for the proximity of two side chains and approximates the likelihood of two side chains forming a contact, illustrated in the top left of Panel D. We then calculated the deviation of each Cβ–Cβ distance across an ensemble as shown in the matrix, with low deviation scores in white and high scores in black. The contact proximity deviation score represents the sum of all Cβ–Cβ proximity deviations a single residue undergoes within an ensemble, as shown in the bottom row separated from the matrix.