High-Resolution Modeling of Protein Structures Based on Flexible Fitting of Low-Resolution Structural Data

Abstract

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained C_α-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

Introduction

The biological functions of many biomolecules involve multiple conformational states and dynamic transitions in between. Despite rapid progress in structural biology, it remains highly difficult to directly solve all conformational states of biomolecules by high-resolution structural determination protocols such as X-ray crystallography and nuclear magnetic resonance spectroscopy. As attractive alternatives, low-resolution structure-determining techniques, including cryo-electron microscopy (cryo-EM) and small angle solution X-ray scattering (SAXS) are widely used. Cryo-EM constructs three-dimensional electron density maps for large biomolecular complexes at near/subnanometer resolutions based on a large number of two-dimensional images (Chiu et al., 2005, Saibil, 2000). SAXS measures orientationally averaged X-ray scattering intensity for biomolecules in solution which contains information about the size and shape of the biomolecules (Koch et al., 2003, Mertens and Svergun, 2010, Putnam et al., 2007). These low-resolution techniques alone cannot generate unique high-resolution structural models with atomistic details. However, they offer highly informative constraints for generating and selecting high-resolution structural models using computational methods (Esquivel-Rodriguez and Kihara, 2013, Fabiola and Chapman, 2005, Lindert et al., 2009). One viable venue of utilizing such constraints is “flexible fitting” (Flores, 2014, Lopez-Blanco and Chacon, 2013, Pandurangan et al., 2014, Wriggers and Birmanns, 2001), which flexibly deforms an initial protein structure to fit the given low-resolution data from cryo-EM or SAXS. An alternative venue is “rigid-body fitting” (Arai et al., 2004, Bernado et al., 2007, Bernado et al., 2009, Bernado et al., 2008, Rawat et al., 2003, Shiozawa et al., 2009, Volkmann et al., 2000, Wendt et al., 2001) which divides a protein complex into multiple domains and then fits them separately as rigid bodies. The rigid-body fitting methods depend on a subjective and error-prone partition of a biomolecule into rigid domains and ignore coupled motions between domains which may be functionally important. The success of the flexible fitting methods requires careful validation of the fitted models to avoid overfitting of the low-resolution data (Falkner and Schroder, 2013, Vashisth et al., 2013). This is particularly important for SAXS data which contains much less structural information than cryo-EM maps and there is additional contribution from hydration shell near the surface of biomolecules.

The flexibility of biomolecules can be simulated by various computational methods at different levels of details. Molecular dynamics (MD) simulation is, in principle, able to describe the dynamics of biomolecules under physiological conditions (i.e., in the presence of water and ions) with atomic details, which makes it a method of choice for flexible fitting (Li & Frank, 2007). Recently, several MD-based methods have been introduced for cryo-EM fitting with full flexibility. The common strategy of these methods is to bias the MD simulation toward a conformation that optimally fits the cryo-EM data by using a biasing potential function (Caulfield and Harvey, 2007, Chan et al., 2012, Noda et al., 2006, Orzechowski and Tama, 2008, Trabuco et al., 2008, Trabuco et al., 2009, Wu et al., 2013). The application of these methods, however, has been limited by the high-computational cost of running MD simulations for large biomolecular systems.

As an efficient alternative, the flexibility of biomolecules can be analyzed by coarse-grained models where a group of atoms are represented by a coarse-grained bead (Tozzini, 2005). For example, the elastic network model (ENM) (Atilgan et al., 2001, Hinsen, 1998, Tama and Sanejouand, 2001) represents a protein structure as a network of C_α atoms with neighboring ones connected by springs with a uniform force constant (Tirion, 1996). The ENM has been successfully used to assist the fitting of cryo-EM and X-ray data (Schroder et al., 2007, Schroder et al., 2010, Tan et al., 2008). In particular, ENM-based normal mode analysis (NMA) has been widely utilized to flexibly fit high-resolution structures to low-resolution structural data (Delarue and Dumas, 2004, Falke et al., 2005, Gorba et al., 2008, Hinsen et al., 2005, Mitra et al., 2005, Suhre et al., 2006, Tama et al., 2004a, Tama et al., 2004b, Tama et al., 2006), or satisfy a few pair wise distance constraints (Zheng and Brooks, 2005, Zheng and Brooks, 2006). Despite great success, the ENM/NMA-based flexible fitting methods are limited in accuracy because they usually only use a few low-frequency normal modes solved from ENM, which are less accurate for describing small local conformational changes (like rearrangement of helices inside a densely packed region) than large global ones (like domain motions) (Tama & Sanejouand, 2001). Indeed, it was found that many (> 20) normal modes are needed to accurately describe several observed conformational changes in proteins (Petrone & Pande, 2006).

Recently, to achieve both accuracy and efficiency in the flexible fitting of cryo-EM (Zheng, 2011) and SAXS (Zheng & Tekpinar, 2011) data, we have developed a coarse-grained method based on a modified form of the ENM (named mENM) that combines the harmonic interactions for maintaining pseudo-bonds and secondary structures, and the anharmonic interactions between nonbonded residues to allow them to move apart readily. As a result, mENM allows large global structural changes without distorting local structures. Our method is based on minimization of a pseudo-energy which linearly combines various terms of the mENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions (see Section 2). Our minimization-based implementation has two advantages: (a) unlike some previous flexible fitting efforts using the lowest few normal modes (Tama et al., 2004a, Tama et al., 2004b), our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. (b) It is efficiently implemented using the Newton–Raphson algorithm based on a sparse linear-equation solver (Chen, Davis, Hager, & Rajamanickam, 2008) which is significantly faster than NMA.

In this chapter, we will describe the methodological details of our flexible fitting method (see Section 2), and demonstrate its usage by applying it to the test case of adenylate kinase using simulated EM/SAXS data (see Section 3). Please refer to our papers (Zheng, 2011, Zheng and Tekpinar, 2011) for more test cases with both simulated and experimental data.