Macromolecular docking restrained by a small angle X-ray scattering profile
Introduction
Many proteins are components of complexes, interacting with other proteins to deliver their functions, such as signal transduction, transport, and catalysis (Krogan et al., 2006, Robinson et al., 2007). Thus, structural description of protein complexes is important for understanding these processes. However, the number of solved complex structures remains relatively low, even while the number of experimentally solved single protein structures increases (Dutta and Berman, 2005). This gap can be bridged by hybrid or integrative methods (Alber et al., 2008, Alber et al., 2007, Steven and Baumeister, 2008). Integrative methods determine complex architectures by computationally combining information from different methods, such as X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy of component structures, electron microscopy of whole complexes, chemical cross-linking of components detected by mass spectrometry, and small angle X-ray scattering (SAXS) of complexes.
The computational docking problem, which aims to predict a binary complex starting from the structures of unbound components, has been studied for more than three decades (Katchalski-Katzir et al., 1992, Wodak and Janin, 1978). Docking methods can be classified into three classes based on the sampling algorithms (Ritchie, 2008, Vajda and Kozakov, 2009): global search methods using the fast Fourier transform (FFTs) (Eisenstein and Katchalski-Katzir, 2004) or geometric shape matching (Schneidman-Duhovny et al., 2003), medium-range Monte Carlo methods (Fernandez-Recio et al., 2003, Gray et al., 2003), and the restraint-guided methods (van Dijk et al., 2005). Each class of methods is suitable for a specific docking sub-problem. Global methods are required for an adequate coverage of the search space, medium-range methods are best for local search and refinement, and restraint-guided methods perform well when additional information is available and can be translated into spatial restraints.
Docking methods have been systematically and prospectively evaluated at Critical Assessment of PRedictions of Interactions (CAPRI), relying on target complexes without available structures at the time of prediction (Janin, 2005). It is clear that the state-of-the-art docking methods can successfully (within top 10 predictions) predict the complex structure of two components with limited conformational change upon binding (induced fit that involves rotations of a few side chains), a standard size interface area (change in solvent accessibility area upon complex formation is between 1400 and 2000 Å2), and significant hydrophobic interaction (solvation free energy of complex formation is less than −4 kcal/mol) (Vajda, 2005). Predictions can also be accurate if additional experimental information about the interaction is available, such as mutations and cross-linking that help identify binding site residues. However, docking methods still suffer from a relatively high rate of incorrect prediction, due to protein flexibility and lack of a reliable scoring function (Lensink et al., 2007, Mendez et al., 2003, Mendez et al., 2005).
SAXS measurement is emerging as a rapid and effective way for obtaining low-resolution (10–30 Å) structural information about macromolecular structures in solution (Petoukhov and Svergun, 2007, Putnam et al., 2007). The scattering curve resulting from the subtraction of the buffer from the sample, (SAXS profile, I(q)), is radially symmetric (isotropic) due to the randomly-oriented distribution of particles in solution. The profile can be converted into a radial distribution function of the molecule via a Fourier transform. Unlike electron microscopy, NMR spectroscopy, and X-ray crystallography, SAXS experiments can be performed under a wide variety of solution conditions, including near physiological conditions. The measurement is performed with ∼1.0 mg/ml of a macromolecular sample in a ∼15 μl volume, and usually takes only a few minutes on a well-equipped synchrotron beam line (Hura et al., 2009, Tsuruta and Irving, 2008).
Computational approaches for modeling a macromolecular structure based on its SAXS profile can be classified into ab initio and rigid body modeling methods (Putnam et al., 2007). On the one hand, the ab initio methods search for coarse shapes represented by dummy atoms (beads) that fit the experimental SAXS profile (Chacon et al., 1998, Svergun, 1999, Svergun et al., 2001). On the other hand, rigid body approaches search for an atomic model of the molecule with a computed SAXS profile that fits the experimental profile (Förster et al., 2008, Pelikan et al., 2009, Petoukhov and Svergun, 2005). Therefore, rigid body modeling can be used only if an approximate structure of the studied molecule or its components are available, as is the case in protein–protein docking.
There are several methods for rigid docking with a SAXS profile. DIMFOM, GLOBSYMM and SASREF (Petoukhov and Svergun, 2005) are based on the CRYSOL program (Svergun et al., 1995) for SAXS profile fitting with a simplified sampling algorithm, where the structure of one monomer is rolled over the surface of the other; however, no interface optimization is performed. In another method, the scoring function combines SAXS and simple interface complementarity terms, sampled by a local search method that requires a relatively accurate initial configuration (Förster et al., 2008); in the absence of the initial configuration, the method starts from 1000 random orientations. A number of analyses of specific biological systems relied on docking followed by filtering of models based on a fit to a SAXS profile (Covaceuszach et al., 2008, Filgueira de Azevedo et al., 2003, Sondermann et al., 2005).
Here, we present a hybrid approach that computes a model of a complex for two given component structures, by simultaneously satisfying physicochemical complementarity between the components as well as a fit to a SAXS profile. The SAXS profile allows to increase the configurational sampling precision and decrease the number of inaccurate models with good scores. Moreover, while docking methods optimize interface shape complementarity, a SAXS profile provides information about the global complex shape. In many cases, especially if the proteins are elongated, small changes in the interface can lead to large changes in the global complex shape. Therefore, it is necessary to increase the sampling resolution to sample the complex accurately in terms of its interface as well as global shape. We test the method on 124 cases with simulated SAXS profiles and six cases with experimental SAXS profiles. The hybrid approach significantly improves on molecular docking alone: When induced fit is less than 1.5 Å interface Cα RMSD and the fraction residues missing from the component structures is less than 3%, FoXSDock can find a model close to the native structure within the top 10 predictions in 77% of the cases; in comparison, docking alone succeeds in only 34% of the cases.
Section snippets
Method outline
The method presented here addresses the docking problem restrained by a SAXS profile: given two structures of molecules (referred to as a receptor and a ligand) and the SAXS profile of their complex, the goal is to find the complex structure; only minor conformational changes, such as side chain repacking, are explicitly modeled.
The docking protocol involves five steps (Fig. 1):
- (1)
Global search. Rigid docking is performed by a geometric shape-matching algorithm PatchDock, generating thousands of
Results
We begin by assessing the accuracy of the radius of gyration computed from a SAXS profile, followed by quantifying the match between an experimental SAXS profile and a SAXS profile computed for the native complex. Finally, we assess FoXSDock by its performance on the two benchmarks.
Overview
Three key points emerge from this study. First, incorporation of a SAXS profile into rigid docking requires increasing configurational sampling precision of docking. Second, a SAXS profile helps to achieve a significant improvement over a standard docking protocol. Third, while helpful, a SAXS profile still provides only limited information about the complex shape; thus, the accuracy of the scoring function for selecting near-native models is a major remaining problem. We discuss each of these
Acknowledgments
We thank Hiro Tsuruta, David Agard, Bill Weis, and Dmitry Svergun for discussions about SAXS, as well as Ben Webb and Daniel Russel for help with IMP. DSD has been funded by the Weizmann Institute Advancing Women in Science Postdoctoral Fellowship. We acknowledge support from NIH R01 GM083960, NIH U54 RR022220, NIH PN2 EY016525, and Rinat (Pfizer) Inc. SIBYLS beamline at Lawrence Berkeley National Laboratory is supported by the DOE program Integrated Diffraction Analysis Technologies (IDAT). We
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