Journal of Molecular Biology
Backrub-Like Backbone Simulation Recapitulates Natural Protein Conformational Variability and Improves Mutant Side-Chain Prediction
Introduction
Proteins undergo conformational fluctuations in response to thermal energy, binding events, and mutation. Understanding and predicting such excursions around the native state of a protein is a key challenge in computational molecular biology. Side-chain sampling1 has been shown to be an extremely useful first-order method for predicting small-scale conformational change. Successful applications include protein–protein docking,2, 3 total redesign of protein sequences,4, 5 and redesign of both protein–protein6 and protein–DNA7 interfaces. However, one key approximation made by many of these applications is keeping the backbone structure fixed. In actual proteins the backbone often undergoes subtle shifts in response to binding events8 or sequence changes.9 Successfully capturing such near-native shifts is thus important for many docking and design applications.
Numerous methods have been developed to take backbone flexibility into account for both the whole protein and local subsections. Molecular dynamics is currently one of the most pervasive methods. However, in the absence of a steep energy gradient, dynamics depend on random thermal velocities and a long sequence of time steps to sample motions as simple as a rotamer change. Monte Carlo minimization of backbone torsion angles10, 11, 12 has also been very successful, but can result in highly nonlocal displacements of the protein backbone and becomes increasingly less efficient with greater protein size. Insertion of peptide fragments has been used for de novo protein structure prediction13 and loop prediction,14 but causes similar propagating changes. Several nonlocal sampling techniques have been applied to protein design including random torsion angle sampling15 and more correlated methods such as fragment insertion,16 parameterized coiled coils,17 and normal mode analysis.18 These methods make use of patterns commonly observed in protein structures or a harmonic approximation of intra-protein interactions to increase backbone sampling efficiency. Other methods have addressed the problem of making local perturbations using heuristics to iteratively optimize backbone torsion angles until distortions of covalent geometry are minimized,19, 20, 21 but those techniques sometimes leave strained chain junctions that must be relaxed with other algorithms. Another method, called wriggling,22 was developed to make partially local moves in which groups of four torsion angles are changed simultaneously to minimize the displacement of distant atoms.
Deformations of protein backbones are truly local only if all consecutive atoms beyond the perturbed region remain fixed. Several local methods exist, the first being introduced by Go and Scheraga23 with numerous subsequent refinements and adaptations.24, 25, 26, 27 These methods involve making a random prerotation of one or more backbone angles followed by solving a geometric constraint equation for six other backbone degrees of freedom to maintain the locality of the move. Several of the methods incorporated bond angle sampling, either as part of the prerotation24, 27 or as part of both the prerotation and the solved constraint equation.26 The latter work also biased the prerotations towards less perburbed backbone conformations. The implementation of these methods is more complex than other common techniques like rotamer sampling. Another drawback is that such loop closure methods are biased towards proposing moves that satisfy bonded, geometric constraints, whose multiple free rotation axes can lead to radically different conformations, often with substantial steric clashes and unsatisfied hydrogen bonds. Those nonbonded factors are particularly relevant in highly packed protein cores and interfaces.
The work described here, instead of being motivated by geometric constraints, derives its motional model from conformational variations observed in high-resolution (≤ 1 Å) crystal structures.28 The fluctuations observed in the crystal lattice motivated Davis et al. to create a simple model, called Backrub, for subtle backbone shifts using just three residues.28 The core idea in this work is to use that type of motion, observed in nature, to computationally sample backbone configurations in a generalized scheme. A similar move set was recently described29 in the context of a simplified energy function. Here, we investigate the utility of the backrub move to sample conformations in the context of the Rosetta all-atom force field. Rosetta has been successfully used for protein–protein docking,3 protein–ligand docking,30 redesign of protein cores,16 design of new protein interface specificities,6 and de novo prediction of small protein structures.31 As an initial test, we recapitulate the backbone/side-chain correlations observed in the same high-resolution structures that inspired the Backrub model. We go on to show that backrub backbone flexibility improves side-chain modeling of point mutations. Finally, as a demonstration of the method's potential, we present a proof-of-concept simulation showing efficient sampling of the opening and closing of triosephosphate isomerase (TIM) loop 6. Our results indicate that the backbone sampling method described here captures a sizable fraction of the subtle conformational variability found in folded proteins.
Section snippets
Results
We implemented the backrub sampling protocol inspired by motion observed in protein structures28 (see Fig. 1, Fig. 2, and Materials and Methods) and evaluated it using three different tests: First, we sought to determine whether the motional model, combined with an all-atom force field, could recapitulate the variation seen in occurrences of a backrub motion in high-resolution crystal structures. Secondly, we test whether backrub sampling can improve the accuracy of modeling small backbone and
Discussion
We have shown that the backrub sampling method is useful for sampling small, high-resolution conformational fluctuations as well as a larger, functionally relevant conformational change. In addition to capturing the structural variability of single sequences, generalized backrub sampling also improves modeling of changes to protein structures upon point mutation. While many of the backbone movements are less than 1 Å, they can result in significant displacements of the attached side chains. In
Generalized backrub move
The backrub move (Fig. 1) is applied to an internal protein segment two or more residues long and consists of a geometric rotation by a random angle, τ, about an axis defined by the flanking Cα atoms. The move simultaneously changes six internal backbone degrees of freedom in the protein, namely the ϕ and ψ angles at both pivot points and the N–Cα–C bond angle, α, at both pivots. (Variable names follow the conventions of Betancourt29 instead of Davis et al.,28 which uses τ for the N–Cα–C bond
Acknowledgements
The authors thank Andrew Bordner for providing a text version of the point mutant benchmark. Greg Friedland gave helpful feedback about the backrub sampling code and method. Jerome Nilmeier provided useful discussions about detailed balance. Matt Jacobson gave valuable feedback as co-advisor of C.A.S. Christopher McClendon, Libusha Kelly, and Ian Davis provided useful comments about the manuscript. C.A.S. was supported by NIH training grant GM067547, the Department of Defense Graduate Research
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