Structure determination of symmetric homo‐oligomers by a complete search of symmetry configuration space, using NMR restraints and van der Waals packing

Abstract

Structural studies of symmetric homo-oligomers provide mechanistic insights into their roles in essential biological processes, including cell signaling and cellular regulation. This paper presents a novel algorithm for homo-oligomeric structure determination, given the subunit structure, that is both complete, in that it evaluates all possible conformations, and data-driven, in that it evaluates conformations separately for consistency with experimental data and for quality of packing. Completeness ensures that the algorithm does not miss the native conformation, and being data-driven enables it to assess the structural precision possible from data alone. Our algorithm performs a branch-and-bound search in the symmetry configuration space, the space of symmetry axis parameters (positions and orientations) defining all possible C n homo-oligomeric complexes for a given subunit structure. It eliminates those symmetry axes inconsistent with intersubunit nuclear Overhauser effect (NOE) distance restraints and then identifies conformations representing any consistent, well-packed structure to within a user-defined similarity level.For the human phospholamban pentamer in dodecylphosphocholine micelles, using the structure of one subunit determined from a subset of the experimental NMR data, our algorithm identifies a diverse set of complex structures consistent with the nine intersubunit NOE restraints. The distribution of determined structures provides an objective characterization of structural uncertainty: backbone RMSD to the previously determined structure ranges from 1.07 to 8.85 Å , and variance in backbone atomic coordinates is an average of 12.32 Å 2 . Incorporating vdW packing reduces structural diversity to a maximum backbone RMSD of 6.24 Å and an average backbone variance of 6.80 Å 2 . By comparing data consistency and packing quality under different assumptions of oligomeric number, our algorithm identifies the pentamer as the most likely oligomeric state of phospholamban, demonstrating that it is possible to determine the oligomeric number directly from NMR data. Additional tests on a number of homo-oligomers, from dimer to heptamer, similarly demonstrate the power of our method to provide unbiased determination and evaluation of homo-oligomeric complex structures.

Structure determination of helical filaments by solid-state NMR spectroscopy

“…4C). Existing grid-based methods are limited to symmetric oligomers with point symmetries (29)(30)(31). To accommodate helical symmetries, we therefore based our grid-search on a previously proposed approach for efficient modeling of symmetric oligomers from NMR data for any given fixed symmetry (32).…”

NMR Structural Inference of Symmetric Homo-Oligomers

“…, r n g (each specifying an atomic pair and allowed distances). We assume here that the oligomeric number has also been previously determined (e.g., from ultracentrifugation), but see our previous work (Potluri et al, 2006) for a discussion of how to score possible oligomeric states based on how well the restraints fit as well as empirical energy functions. If we fix the position of the initial subunit structure, then the homo-oligomeric complex structure is completely specified by the symmetry axis (Fig.…”

“…The line representing the symmetry axis can be specified by the position where it intersects the xy plane at (x, y), relative to the fixed subunit at the origin, and its orientation (y, f), relative to the major axis of the fixed subunit which we orient along the z-axis. Thus, all possible axes belong to a SCS, S 2 · R 2 (Potluri et al, 2006), with orientations from the two-sphere S 2 and translations from the xy plane R 2 (Fig. 2a).…”

“…We build upon our earlier work on searching symmetry configuration spaces (Potluri et al, 2006(Potluri et al, , 2007, but this article represents a significant extension in order to support inference and compute error bounds, which account for experimental noise and uncertainty. Our algorithmic approach, hierarchical subdivision with error guarantees, stands in contrast to sampling techniques, such as the replica-exchange MCMC algorithm employed by Nilges and co-workers (Rieping et al, 2005b, Habeck et al, 2005, which may under-sample the high-dimensional and very rugged posterior distribution of a monomer, and does not characterize (or place bounds on) the error in inferred quantities.…”

Symmetry versus Asymmetry in the Molecules of Life: Homomeric Protein Assemblies

“…Very interesting algorithm for determination of the oligomeric number for symmetrical homomer is based on search of symmetry configuration space using NMR restrains and van der Waals packing. This approach was tested on a number of homomeric assemblies ranging from dimers to heptamers [46]. …”