A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers

An algorithm to enumerate all possible protein conformations verifying a set of distance constraints

BACKGROUND

The determination of protein structures satisfying distance constraints is an important problem in structural biology. Whereas the most common method currently employed is simulated annealing, there have been other methods previously proposed in the literature. Most of them, however, are designed to find one solution only.

RESULTS

In order to explore exhaustively the feasible conformational space, we propose here an interval Branch-and-Prune algorithm (iBP) to solve the Distance Geometry Problem (DGP) associated to protein structure determination. This algorithm is based on a discretization of the problem obtained by recursively constructing a search space having the structure of a tree, and by verifying whether the generated atomic positions are feasible or not by making use of pruning devices. The pruning devices used here are directly related to features of protein conformations.

CONCLUSIONS

We described the new algorithm iBP to generate protein conformations satisfying distance constraints, that would potentially allows a systematic exploration of the conformational space. The algorithm iBP has been applied on three α-helical peptides.

Systematic solution to homo-oligomeric structures determined by NMR

Protein structure determination by NMR has predominantly relied on simulated annealing-based conformational search for a converged fold using primarily distance constraints, including constraints derived from nuclear Overhauser effects, paramagnetic relaxation enhancement, and cysteine crosslinkings. Although there is no guarantee that the converged fold represents the global minimum of the conformational space, it is generally accepted that good convergence is synonymous to the global minimum. Here, we show such a criterion breaks down in the presence of large numbers of ambiguous constraints from NMR experiments on homo-oligomeric protein complexes. A systematic evaluation of the conformational solutions that satisfy the NMR constraints of a trimeric membrane protein, DAGK, reveals 9 distinct folds, including the reported NMR and crystal structures. This result highlights the fundamental limitation of global fold determination for homo-oligomeric proteins using ambiguous distance constraints and provides a systematic solution for exhaustive enumeration of all satisfying solutions.

Stoichiometries and affinities of interacting proteins from concentration series of solution scattering data: decomposition by least squares and quadratic optimization

In studying interacting proteins, complementary insights are provided by analyzing both the association model (the stoichiometry and affinity constants of the intermediate and final complexes) and the quaternary structure of the resulting complexes. Many current methods for analyzing protein interactions either give a binary answer to the question of association and no information about quaternary structure or at best provide only part of the complete picture. Presented here is a method to extract both types of information from X-ray or neutron scattering data for a series of equilibrium mixtures containing the initial components at different concentrations. The method determines the association pathway and constants, along with the scattering curves of the individual members of the mixture, so as to best explain the scattering data for the mixtures. The derived curves then enable reconstruction of the intermediate and final complexes. Using simulated solution scattering data for four hetero-oligomeric complexes with different structures, molecular weights and association models, it is demonstrated that this method accurately determines the simulated association model and scattering profiles for the initial components and complexes. Recognizing that experimental mixtures contain static contaminants and nonspecific complexes with the lowest affinities (inter-particle interference) as well as the desired specific complex(es), a new analytical method is also employed to extend this approach to evaluating the association models and scattering curves in the presence of static contaminants, testing both a nonparticipating monomer and a large homo-oligomeric aggregate. It is demonstrated that the method is robust to both random noise and systematic noise from such contaminants, and the treatment of nonspecific complexes is discussed. Finally, it is shown that this method is applicable over a large range of weak association constants typical of specific but transient protein-protein complexes.

Structure of an HIV-1-neutralizing antibody target, the lipid-bound gp41 envelope membrane proximal region trimer

The membrane proximal external region (MPER) of HIV-1 glycoprotein (gp) 41 is involved in viral-host cell membrane fusion. It contains short amino acid sequences that are binding sites for the HIV-1 broadly neutralizing antibodies 2F5, 4E10, and 10E8, making these binding sites important targets for HIV-1 vaccine development. We report a high-resolution structure of a designed MPER trimer assembled on a detergent micelle. The NMR solution structure of this trimeric domain, designated gp41-M-MAT, shows that the three MPER peptides each adopt symmetric α-helical conformations exposing the amino acid side chains of the antibody binding sites. The helices are closely associated at their N termini, bend between the 2F5 and 4E10 epitopes, and gradually separate toward the C termini, where they associate with the membrane. The mAbs 2F5 and 4E10 bind gp41-M-MAT with nanomolar affinities, consistent with the substantial exposure of their respective epitopes in the trimer structure. The traditional structure determination of gp41-M-MAT using the Xplor-NIH protocol was validated by independently determining the structure using the DISCO sparse-data protocol, which exploits geometric arrangement algorithms that guarantee to compute all structures and assignments that satisfy the data.

Crystal structure of the integral membrane diacylglycerol kinase

Diacylglycerol kinase catalyses the ATP-dependent phosphorylation of diacylglycerol to phosphatidic acid for use in shuttling water-soluble components to membrane-derived oligosaccharide and lipopolysaccharide in the cell envelope of Gram-negative bacteria. For half a century, this 121-residue kinase has served as a model for investigating membrane protein enzymology, folding, assembly and stability. Here we present crystal structures for three functional forms of this unique and paradigmatic kinase, one of which is wild type. These reveal a homo-trimeric enzyme with three transmembrane helices and an amino-terminal amphiphilic helix per monomer. Bound lipid substrate and docked ATP identify the putative active site that is of the composite, shared site type. The crystal structures rationalize extensive biochemical and biophysical data on the enzyme. They are, however, at variance with a published solution NMR model in that domain swapping, a key feature of the solution form, is not observed in the crystal structures.

Protein loop closure using orientational restraints from NMR data

Protein loops often play important roles in biological functions. Modeling loops accurately is crucial to determining the functional specificity of a protein. Despite the recent progress in loop prediction approaches, which led to a number of algorithms over the past decade, few rigorous algorithmic approaches exist to model protein loops using global orientational restraints, such as those obtained from residual dipolar coupling (RDC) data in solution nuclear magnetic resonance (NMR) spectroscopy. In this article, we present a novel, sparse data, RDC-based algorithm, which exploits the mathematical interplay between RDC-derived sphero-conics and protein kinematics, and formulates the loop structure determination problem as a system of low-degree polynomial equations that can be solved exactly, in closed-form. The polynomial roots, which encode the candidate conformations, are searched systematically, using provable pruning strategies that triage the vast majority of conformations, to enumerate or prune all possible loop conformations consistent with the data; therefore, completeness is ensured. Results on experimental RDC datasets for four proteins, including human ubiquitin, FF2, DinI, and GB3, demonstrate that our algorithm can compute loops with higher accuracy, a three- to six-fold improvement in backbone RMSD, versus those obtained by traditional structure determination protocols on the same data. Excellent results were also obtained on synthetic RDC datasets for protein loops of length 4, 8, and 12 used in previous studies. These results suggest that our algorithm can be successfully applied to determine protein loop conformations, and hence, will be useful in high-resolution protein backbone structure determination, including loops, from sparse NMR data. Proteins 2012. © 2011 Wiley Periodicals, Inc.

A geometric arrangement algorithm for structure determination of symmetric protein homo-oligomers from NOEs and RDCs

Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologically-relevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homo-oligomers present a unique challenge. Using X-filtered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homo-oligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, disco, runs in expected O(n²) time, where n is the number of distance restraints, potentially assigned ambiguously. disco is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli diacylglycerol kinase (DAGK) and a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G (GB1). In both cases, disco computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs. The entire protocol DISCO has been completely automated in a software package that is freely available and open-source at www.cs.duke.edu/donaldlab/software.php.