Meeting Review: Diffuse X-Ray Scattering to Model Protein Motions

Abstract

Problems in biology increasingly need models of protein flexibility to understand and control protein function. At the same time, as they improve, crystallographic methods are marching closer to the limits of what can be learned from Bragg data in isolation. It is thus inevitable that mainstream protein crystallography will turn to diffuse scattering to model protein motions and improve crystallographic models. The time is ripe to make it happen.

Researchers recently gathered in Berkeley, California to assess the state of the art of diffuse X-ray scattering and the potential for using it as an experimental probe of protein motions. The workshop entitled “Can Diffuse X-Ray Scattering Reveal Protein Dynamics?” was hosted by the Advanced Light Source User Meeting on October 9, 2013. It consisted of nine presentations that addressed topics such as data collection and integration; modeling and simulation; and dissemination of data and methods. This meeting report summarizes our current perspective on the field, informed by the deliberations of the workshop.¹

In traditional protein crystallography, the Bragg peak measurements are used to derive the mean unit cell electron density, which is used for building and validating single structural models. By contrast, the diffuse scattering, which lies between (and under) the Bragg peaks, contains rich information about the two-point correlations of the electron density fluctuations (Amorós and Amorós, 1968; Guinier, 1963; James, 1948; Warren, 1969; Welberry, 2004; Willis and Pryor, 1975; Wooster, 1962; Zachariasen, 1945).Diffuse scattering is potentially a powerful constraint for modeling protein motions as, unlike the Bragg peaks, it contains information about which atoms move together.

Although diffuse scattering is an established technique in materials science, its use in protein crystallography so far has been confined to a relatively small number of pioneering studies (Caspar et al., 1988; Chacko and Phillips, 1992; Clarage et al., 1992; Clarage et al., 1995; Doucet and Benoit, 1987; Glover et al., 1991; Héry et al., 1998; Kolatkar et al., 1994; Meinhold et al., 2007; Meinhold and Smith, 2005a, b, 2007; Mizuguchi et al., 1994; Moore, 2009; Phillips et al., 1980; Riccardi et al., 2010; Wall et al., 1997a; Wall et al., 1997b). The motivation for increasing the use of diffuse scattering in protein crystallography is now strong. Crystallography is producing increasingly sophisticated and detailed models of protein motions such as translation-libration-screw (TLS) models (Chaudhry et al., 2004) and contact network models (van den Bedem et al., 2013). Whereas the Bragg data cannot distinguish among different models that yield similar mean electron density, diffuse scattering can distinguish models by their correlated motions. Diffuse scattering therefore might be developed into a powerful tool for modeling crystalline protein motions. Indeed, Peter Moore has argued, in Structure (Moore, 2009), that diffuse scattering should be used to test TLS models; and Mark Wilson (Wilson, 2013) has noted that diffuse scattering could be used to develop and validate more detailed contact network (van den Bedem et al., 2013) or ensemble models (Burnley et al., 2012).

Increasing the use diffuse scattering in protein crystallography naturally presents some challenges. These challenges can be overcome (and should be met) by appropriate efforts. Progress is needed on several fronts.

Data collection

Data collection procedures and equipment for precise measurement of diffuse scattering must become widespread in protein crystallography. The considerations are similar to those for small-angle scattering, which places similar emphasis on the elimination of systematic background noise. Previously successful procedures have been documented and are compatible with traditional crystallography experiments (Wall, 2009). Charge-coupled-device (CCD) detectors at synchrotrons (Walter et al., 1995) have been successfully used to collect full three-dimensional diffuse scattering data sets (Wall et al., 1997b). The negligibly small point spread function and higher dynamic range of pixel array detectors (PADs) (Gruner, 2012) are now enabling improved data collection compared to CCDs, especially to resolve fine scale features in the neighborhood of Bragg peaks. Simultaneous Bragg and diffuse scattering data already have been collected from protein crystals using a PAD based PILATUS detector (Andrew Van Benschoten and J.S.F., unpublished), and the meeting participants noted the importance of the temperature dependence of diffuse features as an important future direction.

Data integration

Methods for diffuse scattering data integration must be extended and combined with Bragg integration in the standard crystallography toolkit. Two complementary approaches can be exploited. One approach, adopted by Lunus software ((Wall, 2009), http://lunus.sf.net), is to collect diffuse scattering measurements on a three-dimensional reciprocal space lattice, the structure of which is identical to a Bragg lattice. An advantage of this approach is that it enables the existing infrastructure in crystallography to be maximally leveraged, from data indexing (a preliminary pipeline using LABELIT (Sauter et al., 2004) and CCTBX (Grosse-Kunstleve et al., 2002) was demonstrated at the workshop) to model building, validation, refinement, and tools for computing model inputs such as structure factors (such as are available in the PHENIX software suite (Adams et al., 2010), http://www.phenix-online.org/). It also can be adapted to measure small-scale, streaked diffuse features, by constructing a lattice with a finer sampling of reciprocal space (Wall et al., 1997a).A challenge shared with traditional methods is the need to separate the diffuse from the Bragg intensity; in this sense, better modeling of the diffuse scattering can potentially improve Bragg peak integration. A second approach is to use the diffraction images themselves to constrain models of the protein crystal. This approach is inspired by the EVAL15 method ((Schreurs et al., 2010), http://www.crystal.chem.uu.nl/distr/eval/) in which a physical model of the crystal is refined using highly detailed Bragg peak profiles obtained from diffraction images. An advantage of this approach is that it enables model building using the primary data and eliminates the need for separating the Bragg and diffuse intensity. A challenge is the additional computational cost, which can potentially be overcome by taking advantage of GPUs or other advanced computing architectures.

Model building and refinement

New model building and refinement tools must be developed for diffuse scattering. Many diffuse scattering studies have addressed the forward problem of calculating a simulated diffraction image or three-dimensional diffuse lattice from a model of correlated motions and comparing it to experimental data. The forward problem has been a useful paradigm for validating correlated motions predicted from molecular dynamics (MD) simulations (Clarage et al., 1995; Doucet and Benoit, 1987; Faure et al., 1994; Héry et al., 1998; Meinhold and Smith, 2005a, 2007) and normal mode analysis (Meinhold et al., 2007; Mizuguchi et al., 1994; Riccardi et al., 2010), and we expect it to be useful for validating predicted correlations from TLS models, contact networks, and other independently developed models. To fully realize its potential, however, diffuse scattering should also be developed as a tool for solving the inverse problem of deriving models of correlated motions from the data. One important advance would be to derive atom pair coupled displacement parameters (i.e., the off-diagonal elements of the covariance matrix of atomic displacements) from diffuse scattering data. Initial steps have been taken by using individual diffraction images (Caspar et al., 1988; Chacko and Phillips, 1992; Clarage et al., 1992) or three-dimensional diffuse scattering data (Wall et al., 1997a; Wall et al., 1997b) to model homogeneous elastic or liquid-like correlated motions in the crystal.

Molecular dynamics simulations

One especially important challenge in model building is the derivation of ensemble models from MD simulations. This approach has been revisited over the years as advances in computers and algorithms have enabled longer simulations of larger systems and deeper sampling of conformational ensembles. Early MD simulations of single molecules of lysozyme (Faure et al., 1994) and myoglobin (Clarage et al., 1995) yielded ensemble models that did not accurately reproduce diffuse scattering data. Clarage et al. traced the problem to inadequate sampling of the conformational ensemble, leading to lack of convergence of the covariance matrix of atomic displacements (the lysozyme simulation was 600 ps duration and myoglobin was 500 ps). Later 1 ns simulations of a single P2₁2₁2₁ lysozyme unit cell (Héry et al., 1998) and 10 ns simulations of a single P4₁ Staphylococcal nuclease unit cell (Meinhold and Smith, 2005b) showed improved agreement with the data but did not yet show complete convergence. Longer MD simulations of Staph. nuclease (M.E.W., unpublished) indicate that convergence now is within reach even for models consisting of multiple unit cells, as might be important to accurately describe diffuse scattering data. Future avenues for achieving increased sampling include millisecond all-atom simulations (Dror et al., 2012), advanced sampling methods such as parallel tempering (Earl and Deem, 2005), and acceleration schemes such as Markov State Models (Pande et al., 2010).

Other challenges remain. For example, there are only a limited number of data sets available. This is now changing, with several groups ramping up their data collection efforts. Dissemination of data would be facilitated by establishing a resource where existing diffuse scattering data and models could be archived and made publicly available using standard formats. We are seeking advice from the Worldwide Protein Data Bank as how to best manage these data, including the development of data definitions for the PDBx/mmCIF dictionary.

Problems in biology increasingly need models of protein flexibility to understand and control protein function. At the same time, as they improve, crystallographic methods are marching closer to the limits of what can be learned from Bragg data in isolation. It is thus inevitable that mainstream protein crystallography will turn to diffuse scattering to model protein motions and improve crystallographic models. The time is ripe to make it happen.