Recovering a Representative Conformational Ensemble from Underdetermined Macromolecular Structural Data

Abstract

Structural analysis of proteins and nucleic acids is complicated by their inherent flexibility, conferred, for example, by linkers between their contiguous domains. Therefore, the macromolecule needs to be represented by an ensemble of conformations instead of a single conformation. Determining this ensemble is challenging because the experimental data are a convoluted average of contributions from multiple conformations. As the number of the ensemble degrees of freedom generally greatly exceeds the number of independent observables, directly deconvolving experimental data into a representative ensemble is an ill-posed problem. Recent developments in sparse approximations and compressive sensing have demonstrated that useful information can be recovered from underdetermined (ill-posed) systems of linear equations by using sparsity regularization. Inspired by these advances, we designed Sparse Ensemble Selection (SES) method for recovering multiple conformations from a limited number of observations. SES is more general and accurate than previously published minimum-ensemble methods, and we use it to obtain representative conformational ensembles of Lys48-linked di-ubiquitin, characterized by the residual dipolar coupling data measured at several pH conditions. These representative ensembles are validated against NMR chemical shift perturbation data and compared to maximum-entropy results. The SES method reproduced and quantified the previously observed pH dependence of the major conformation of Lys48-linked di-ubiquitin, and revealed lesser-populated conformations that are pre-organized for binding known di-ubiquitin receptors, thus providing insights into possible mechanisms of receptor recognition by polyubiquitin. SES is applicable to any experimental observables that can be expressed as a weighted linear combination of data for individual states.

Prion Protein—Antibody Complexes Characterized by Chromatography-Coupled Small-Angle X-Ray Scattering

“…We overcame the challenge of the resulting overfitting by computing ensembles of multi-state models that fit the data, using MultiFoXS (see Materials and Methods), and highlighting only the conserved features of these ensembles. Other similar approaches include EOM (62,63), MaxOcc (64)(65)(66)(67), ASTEROIDS (68)(69)(70), SES (71), and EROS (72). A parsimonious explanation of the SAXS profiles for each of the recPrP and recPrP-Fab-P samples is provided by the open and closed states, corresponding to the two R g peaks that were conserved for N-state models (for N ¼ 2 .…”

Identification of productive and futile encounters in an electron transfer protein complex

“…This important issue has been widely studied, and a variety of methodologies has been developed by different groups (38)(39)(40)(41) to extract information (i.e., plausible conformational ensembles) from such conformationally averaged data (reviewed in ref. 42).…”

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

“…The large number of experimental data from NMR on the geometry of unfolded polypeptide ensembles together with the knowledge on the covalent structure of the polypeptide chain provide powerful input for computer models of representative ensembles of the unfolded state. Typically, ensembles containing tens of thousands of conformers are simulated in an unrestrained manner and reduced by various methods (23)(24)(25)(26) to smaller-size ensembles that satisfy the measured parameters. As an alternative, we have recently used restrained ensemble structure calculations (27) to create minimal-size ensembles of urea-denatured ubiquitin (76 aa) that satisfy a very high number of 419 RDC and 253 PRE restraints obtained by NMR (21).…”