Parsimony in Protein Conformational Change

Protein conformational change is analyzed by finding the minimalist backbone torsion angle rotations that superpose crystal structures within experimental error. Of several approaches for enforcing parsimony during flexible least-squares superposition, an ℓ(1)-norm restraint provided greatest consistency with independent indications of flexibility from nuclear magnetic resonance relaxation dispersion and chemical shift perturbation in arginine kinase and four previously studied systems. Crystallographic cross-validation shows that the dihedral parameterization describes conformational change more accurately than rigid-group approaches. The rotations that superpose the principal elements of structure constitute a small fraction of the raw (φ, ψ) differences that also reflect local conformation and experimental error. Substantial long-range displacements can be mediated by modest dihedral rotations, accommodated even within α helices and β sheets without disruption of hydrogen bonding at the hinges. Consistency between ligand-associated and intrinsic motions (in the unliganded state) implies that induced changes tend to follow low-barrier paths between conformational sub-states that are in intrinsic dynamic equilibrium.