Parsimony in Protein Conformational Change

Abstract

Summary Protein conformational change is analyzed by finding the minimalist backbone torsion angle rotations that superpose crystal structures within experimental error. Of several approaches to enforcing parsimony during flexible least-squares superposition, an ℓ1-norm restraint provided greatest consistency with independent indications of flexibility from NMR 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.

The Sampling of Conformational Dynamics in Ambient-Temperature Crystal Structures of Arginine Kinase

“…Hinges identified from comparison of the crystal structures were broadly consistent with sites of NMR relaxation exchange that could be indicating intrinsic conformational fluctuation (Chapman et al, 2015; Davulcu et al, 2009). Furthermore, NMR residual dipolar couplings indicated that the average substrate-free solution structure is somewhat intermediate between the two crystal structures (Niu et al, 2011).…”

“…The effects of local changes upon ADP alignment were examined by comparing the ambient temperature ADPs not just to the differences in atomic positions (Table 2), but to the changes in the form I TSA structure when it was superposed onto the substrate-free structure. Superposition was either flexible, using parsimoniously restrained changes to backbone dihedrals (smoothing out local changes), or constrained as rigid groups, using the TLS groupings (Chapman et al, 2015). Improvement in ADP alignment was modest, 1° and 2° respectively for the flexible and rigid-group superpositions.…”

“…For arginine kinase, TLS-constrained ADPs show similar directionality (<dot product> = 0.93), but the mean square displacements are 2.4-fold larger at ambient vs. cryo - temperature. Directional correlations between ADPs and coordinate shifts, that can be calculated with the program Superpose (Chapman et al, 2015), fall short of levels needed to predict conformational change. However, when analyzed alongside ligand-bound and unbound structures, ADPs can provide insights into the mechanisms with which conformational change is effected.…”

“…Superimpositions were by minimization of a least-squares residual difference between backbone and C β atoms using Superpose (Chapman et al, 2015). For rigid group analysis, an overall superposition was followed by refinement of the orientation and position of the five rigid groups defined during earlier analysis of the effects of substrate-binding (Niu et al, 2011).…”

“…For rigid group analysis, an overall superposition was followed by refinement of the orientation and position of the five rigid groups defined during earlier analysis of the effects of substrate-binding (Niu et al, 2011). Flexible superposition was by adjustment of the backbone dihedral angles φ, ψ to minimize the sum of the above residual and an L 1 -norm parsimony restraint to limit the magnitude and number of changed dihedrals (Chapman et al, 2015). The weight for the parsimony restraint was where the cross-validated R free (Brünger, 1992) was minimized or approached its asymptotic value, when structure amplitudes for the flexibly superimposed model plus TSA components were compared to the test set reflections for the target structure.…”