Molecular Fragment Replacement Approach to Protein Structure Determination by Chemical Shift and Dipolar Homology Database Mining

Abstract

A novel approach is described for determining backbone structures of proteins that is based on finding fragments in the protein data bank (PDB). For each fragment in the target protein, usually chosen to be 7–10 residues in length, PDB fragments are selected that best fit to experimentally determined one-bond heteronuclear dipolar couplings and that show agreement between chemical shifts predicted for the PDB fragment and experimental values for the target fragment. These fragments are subsequently refined by simulated annealing to improve agreement with the experimental data. If the lowest-energy refined fragments form a unique structural cluster, this structure is accepted and side chains are added on the basis of a conformational database potential. The sequential backbone assembly process extends the chain by translating an accepted fragment onto it. For several small proteins, with extensive sets of dipolar couplings measured in two alignment media, a unique final structure is obtained that agrees well with structures previously solved by conventional methods. With less dipolar input data, large, oriented fragments of each protein are obtained, but their relative positioning requires either a small set of translationally restraining nuclear Overhauser enhancements (NOEs) or a protocol that optimizes burial of hydrophobic groups and pairing of β-strands.

Introduction

With the completion of the sequencing of the human and many other genomes and the availability of an abundance of protein sequence data, there is a strong demand for rapid determination of tertiary protein structures. There are two main experimental avenues toward obtaining atomic resolution protein structures: X-ray crystallography and solution state nuclear magnetic resonance (NMR) spectroscopy. The process of structure determination by X-ray crystallography is already quite streamlined due to the availability of robotics for optimizing crystallization conditions, high-intensity synchrotron radiation sources, and standardized, semiautomated analysis software. Structure determination by NMR spectroscopy on the other hand is still a time-consuming and labor-intensive process with a turnaround time typically on the order of several months, which additionally requires ¹⁵N, ¹³C, and, for larger proteins, ²H isotopic enrichment. Usually, an NMR structure determination project proceeds in several stages: assignment of backbone resonances using pairs of now standard triple-resonance experiments, assignment of side chain resonances using ¹³C-, ¹H- or ¹⁵N-mediated TOCSY- and COSY-type experiments, followed by assignment of NOE cross-peaks, and structure calculation.

The introduction of facile methods for weakly aligning proteins relative to the magnetic field now also allows measurement of residual dipolar couplings (RDCs). In favorable cases, the alignment necessary for a nonvanishing dipolar interaction can be imposed on the solute macromolecules directly by the magnetic field (Bothner-by 1985, Kung 1995, Tjandra 1996, Tolman 1995), but more commonly an anisotropic aqueous medium is used. Many such media are now available, including lyotropic liquid crystalline solutions of phospholipid bicelles (Tjandra and Bax, 1997), Pf1, fd, or TM phage particles (Clore 1998b, Hansen 1998), cellulose crystallites (Fleming et al., 2000), and polyethylene glycol (Ruckert and Otting, 2000) or cetylpyridinium halide-based bilayers (Barrientos 2000, Prosser 1998). Anisotropically compressed, low-density polyacrylamide gels (Chou 2001a, Ishii 2001, Meier 2002, Sass 2000, Tycko 2000, Ulmer 2003) and suspensions of magnetically oriented purple membrane fragments (Koenig 1999, Sass 1999) also have proven useful for this purpose.

RDCs are global parameters in the sense that they restrain the orientations of the corresponding dipolar interaction vectors all relative to a single reference frame, often referred to as the principal axis frame of the alignment tensor. In this respect, they differ in nature from NOEs and dihedral restraints derived from J couplings, which report on atomic positions relative to one another. Besides improving local geometry (Chou 2001b, Tjandra 1997), RDCs have been shown to be highly useful for determining the relative orientation of individual domains in multisubunit proteins, nucleic acids, and their complexes (Braddock 2001, Clore 2000, Lukavsky 2003).

In the principal frame of the alignment tensor, the dipolar coupling is given by

$$\text{D}{}_{\mathrm{ij}}\text{(θ,φ) = D}{}_{\mathrm{<mtext>a</mtext>}}\text{[(3}\text{cos}{}^2\text{θ}{}_{\mathrm{ij}}\text{-1) +}\text{3}\text{2}\text{R}\text{sin}{}^2\text{θ}{}_{\mathrm{ij}}\text{cos}{}^2\text{φ}{}_{\mathrm{ij}}\text{]}$$

where θ and φ are the polar angles of the dipolar interaction vector, r_ij, in the alignment frame; D_a is the magnitude of the alignment tensor, which includes constants related to the magnetogyric ratio and internuclear distance of nuclei i and j, and R is the rhombicity of the alignment tensor (Bax et al., 2001). Clearly, with a single experimental D_ij(θ,φ) value, and two variable parameters, in general an infinite number of (θ,φ) solutions exist. This degeneracy may be partly lifted if RDCs in a different alignment medium and with a different, independent alignment tensor are available (Ramirez and Bax, 1998). However, even in this case, a vector orientation can never be distinguished from its inverse because both orientations lead to the same dipolar coupling. Only once the “handedness” of a local element of structure that involves several dipolar interactions in at least two alignment frames is known, can the absolute orientation of such a fragment and thereby of its vectors be determined (Al-Hashimi et al., 2000). As a consequence, when attempting to build a full protein structure that simultaneously satisfies Eq. (1) for all dipolar interactions, the number of false minima scales exponentially with this number of couplings. Solving this problem by means of a “brute force” simulated annealing or Monte Carlo program on a full protein has proven very difficult. However, when first assembling local substructures, this problem is no longer intractible, and a number of recently proposed approaches rely on this principle (Andrec 2001, Delaglio 2000, Hus 2000, Rohl 2002).

Our present approach represents a much improved and more stable version of the molecular fragment replacement (MFR) method described earlier, which derived backbone torsion angles from searching the PDB for seven-residue peptide fragments that fit experimental dipolar couplings in a fragment of the target protein (Delaglio et al., 2000). In the original procedure, a starting model was first built using these backbone torsion angles and subsequently refined by optimizing agreement between this model and the full set of dipolar couplings. Although the method results in reasonable structures, provided that a nearly complete set of dipolar coupling is available, convergence to a satisfactory final structure and accuracy of its local details remain limited by the quality of the fragments of the original search. However, in favorable cases, substantial regions of a protein can be assembled from such data, even in cases in which all dipolar couplings and assignments are derived from a single experiment (Zweckstetter and Bax, 2001).

Our MFR approach is related to work by Annila et al. (1999), who proposed to use dipolar couplings for finding structurally homologous proteins in the PDB. Instead of searching for complete proteins, the MFR program searches the PDB for structural homology for only 7–10 residues at a time. The idea of using small substructures from a database of representative protein structures as “templates” for building a structure was pioneered by Jones and co-workers and has been very successful in X-ray crystallography (Jones and Thirup, 1986). The approach has also been applied to solving structures on the basis of NOEs, where it searches a database for substructures compatible with the experimental NOEs (Kraulis and Jones, 1987). However, because only short and medium range NOEs can be used in the search process, obtaining the correct tertiary fold remains very difficult with such a method. Other approaches relying on database substructures have also been described in recent years. Work by the Baker group (Rohl and Baker, 2002) relies on selecting a large number of database fragments that are roughly compatible with the experimental parameters measured for the corresponding target fragment and then using efficient Monte Carlo methods to assemble these fragment into a common structure with reasonable packing properties, where the fragments retain an orientation needed to satisfy dipolar coupling restraints. A method proposed by Andrec et al. (2001) is similar in spirit to our own MFR method but uses “postprocessing” to distinguish correct from incorrect fragments by comparing them with the overlapping region of an adjacent fragment. Using a so-called bounded-tree search, self-consistent sets of overlapping fragments can be identified relatively rapidly, resulting in a backbone structure.

A different approach to building complete protein backbone structures from dipolar couplings, which does not rely on a database for finding suitable substructures, has been proposed by Hus 2000, Giesen 2003. It is conceptually somewhat similar to approaches pursued in determining polypeptide structure on the basis of ¹⁵N–¹H dipolar couplings derived from solid-state NMR measurements (Brenneman 1990, Marassi 1998, Nishimura 2002, Wu 1995) and conducts a systematic search in Cartesian space when adding a peptide plane to the chain. The approach requires a very complete set of dipolar couplings when applied de novo, but it has other applications too. For example, it was shown to be particularly powerful for pinpointing the precise structural differences in the backbone at the active site of a 27-kDa enzyme [methionine sulfoxide reductase (MsrA) from Erwinia chrysanthemi] and its Escherichia coli homologue, for which an X-ray structure was available (Beraud et al., 2002). Conceptually, Hus' method shares features with a method devised by Mueller et al. (2000), which determines the (usually 4-fold degenerate) peptide plane orientations compatible with experimental dipolar couplings prior to finding a chain compatible with these orientations. Finally, Fowler et al. (2000) demonstrated it is feasible to get information on the fold from ¹⁵N–¹H^N, ¹H^N–¹H^N, and ¹H^N–¹H^α couplings without the need for ¹³C enrichment.

Our improved MFR approach, which we refer to as MFR+, represents a much more versatile and stable version of the original MFR method. The method differs from all previous database substructure methods by introduction of an intermediate step where the fragments are refined with respect to the experimental observables (shifts, couplings, and possibly short and medium range NOEs or torsion angle restraints) prior to their final selection and incorporation into a structure. It also utilizes the unique advantage of dipolar tensor parameters to maintain reasonable orientations for each fragment at all stages of the substructure assembly. The user has complete freedom to specify weighting factors used and to define the minimal criteria for deeming a selection to be “reliable.” With the default settings, and with dipolar couplings available from two different media, the program can rapidly generate backbone structures for the proteins ubiquitin and GB3 that are considerably less than 1 Å from their true structure. With less experimental data, accurate partial structures can be obtained, which subsequently can be used to assemble the structure either manually or by using docking algorithms (Clore 2000, Clore 2003).