Integrating protein structural dynamics and evolutionary analysis with Bio3D
 Lars Skjærven^{1, 2}Email author,
 XinQiu Yao^{3},
 Guido Scarabelli^{3} and
 Barry J Grant^{3}Email author
DOI: 10.1186/s1285901403996
© Skjærven et al.; licensee BioMed Central. 2014
Received: 7 October 2014
Accepted: 26 November 2014
Published: 10 December 2014
Abstract
Background
Popular bioinformatics approaches for studying protein functional dynamics include comparisons of crystallographic structures, molecular dynamics simulations and normal mode analysis. However, determining how observed displacements and predicted motions from these traditionally separate analyses relate to each other, as well as to the evolution of sequence, structure and function within large protein families, remains a considerable challenge. This is in part due to the general lack of tools that integrate information of molecular structure, dynamics and evolution.
Results
Here, we describe the integration of new methodologies for evolutionary sequence, structure and simulation analysis into the Bio3D package. This major update includes unique highthroughput normal mode analysis for examining and contrasting the dynamics of related proteins with nonidentical sequences and structures, as well as new methods for quantifying dynamical couplings and their residuewise dissection from correlation network analysis. These new methodologies are integrated with major biomolecular databases as well as established methods for evolutionary sequence and comparative structural analysis. New functionality for directly comparing results derived from normal modes, molecular dynamics and principal component analysis of heterogeneous experimental structure distributions is also included. We demonstrate these integrated capabilities with example applications to dihydrofolate reductase and heterotrimeric Gprotein families along with a discussion of the mechanistic insight provided in each case.
Conclusions
The integration of structural dynamics and evolutionary analysis in Bio3D enables researchers to go beyond a prediction of single protein dynamics to investigate dynamical features across large protein families. The Bio3D package is distributed with full source code and extensive documentation as a platform independent R package under a GPL2 license from http://thegrantlab.org/bio3d/.
Keywords
Protein structure Protein dynamics Allostery Normal mode analysis Molecular dynamics Principal component analysis EvolutionBackground
The internal motions and intrinsic dynamics of proteins have increasingly been recognized as essential for protein function and activity [1],[2]. Notable examples include the dynamic rearrangements that facilitate many enzyme turnover events [3]; the force producing structural changes of motor proteins [4]; and the conformational and allosteric mechanisms that modulate protein associations in many signal transduction cascades [5],[6]. Dissecting these functional motions typically relies on the accumulation and comparison of multiple highresolution structures for a given protein. The rapidly increasing availability of such data is precipitating the need for new approaches that integrate knowledge of molecular structure, dynamics and evolution in functional analysis. In addition to multiple structure comparisons, computational methods including molecular dynamics (MD) and normal mode analysis (NMA) have emerged as popular approaches for characterizing protein dynamics and flexibility [7][9]. However, the general lack of tools that integrate these traditionally separate analyses with methods for sequence and structural analysis represents a practical bottleneck for the systematic study of the evolution of functional motions in large protein families and superfamilies.
Current software solutions lack much of the flexibility needed for comparative studies of large heterogeneous structural datasets. For example, popular web servers for NMA typically operate on single structures and do not permit highthroughput calculations [10][12]. Software libraries such as the Molecular Modeling ToolKit (MMTK) [13] and the packages ProDy [14] and MAVEN [15] provide more advanced calculation options but generally lack direct functionality for the quantitative comparison of dynamic features of nonidentical structures and sequences. These limitations complicate the assessment of functional motions in an evolutionary context. The Bio3D package [16] now provides these essential components thus greatly facilitating the study of evolutionarily related ensembles and their functional dynamics. Here, using selected case studies, we demonstrate the integration of versatile new ensemble NMA approaches and correlation network analysis facilities with enhanced interactive tools for extracting mechanistic information from molecular sequences, crystallographic structural ensembles and MD trajectories. This major update to the Bio3D package includes extensive functionality to analyze and visualize protein dynamics from both experiment and simulation, together with tools for systematic retrieval and analysis of publicly available sequence and structural data.
Package overview and architecture
Bio3D version 2.0 now provides extensive functionality for highthroughput NMA of an ensemble of protein structures facilitating the study of evolutionary and comparative protein dynamics across protein families. The NMA module couples to major protein structure and sequence databases (PDB, PFAM, UniProt and NR) and associated search tools (including BLAST [17] and HMMER [18]). This enables the automated identification and analysis of related protein structures. Efficient elastic network model (ENM) NMA is implemented with multicore functionality to enable rapid calculation of modes even for large structural ensembles. Results of the ensemble NMA algorithm include aligned eigenvectors and mode fluctuations for the different structures in the ensemble. These can readily be analyzed and compared with a variety of implemented methodologies. This facilitates the prediction and identification of distinct patterns of flexibility among protein families or between different conformational states of the same protein. The user can perform ensemble NMA by providing a set of either PDB structures or RCSB PDB codes. Alternatively a single protein sequence or structure can be used to search the PDB for similar structures to analyze.
Implementation
Elastic network models
A unique collection of multiple ENM force fields is now provided within Bio3D. These include the popular anisotropic network model (ANM) [19], the associated parameterfree ANM [20], and a more sophisticated Calpha force field derived from fitting to the Amber94 allatom potential [21]. Also included is the REACH force field employing force constants derived from MD simulations [22], and a recent parameterization providing sequencespecific force constants obtained from an ensemble of 1500 NMR structures [23]. A convenient interface for the application of userdefined force fields is also provided enabling customized normal mode calculations, perturbation analysis, and other more advanced options as detailed online and in Additional file 1.
with units of k(r) given in kJ mol^{− 1} Å^{− 2}. The selection of different force fields is described in detail both online and in Additional file 1.
Ensemble NMA
where V is the matrix of eigenvectors and λ the associated eigenvalues.
Ensemble PCA
where i and j enumerate all 3 N Cartesian coordinates (N is the number of atoms), and 〈r〉 denotes the ensemble average. Projection of the distribution onto the subspace defined by the PCs with the largest eigenvalues provides a lowdimensional representation of the structures facilitating interconformer analysis.
Similarity measures
Multiple similarity measures have been implemented to provide an enhanced framework for the assessment and comparison of ensemble NMA and PCA. These measures also facilitate clustering of proteins based on their predicted modes of motion:
where ${\mathbf{v}}_{i}^{\mathrm{A}}$ and ${\mathbf{v}}_{j}^{\mathrm{B}}$ represent the ith and jth eigenvectors obtained from protein A and B, respectively. l is the number of modes to consider which is commonly chosen to be 10. The RMSIP measure varies between 0 (orthogonal) and 1 (identical directionality).
where Q is the matrix of the principal components of (C _{A} + C _{B})/2, Λ is diagonal matrix containing the corresponding eigenvalues, and q the number of modes needed to capture 90% of the variance of Q. The Bhattacharyya coefficient varies between 0 and 1, and equals to 1 if the covariance matrices (C _{A} and C _{B}) are identical.
where w _{ A } and w _{ B }w _{ B } are vectors of length N containing the fluctuation value (e.g. RMSF) for each atom in protein A and B, respectively.
PCA of crosscorrelation and covariance matrices
where Υ is a matrix containing the elements of the M correlation/covariance matrices (with one row per structure), B the eigenvectors and Γ the associated eigenvalues. Projection into the subspace defined by the largest eigenvectors enables clustering of the structures based on the largest variance within the crosscorrelation or covariance matrices.
All similarity measures described above can be utilized for clustering the ensemble of structures based on their normal modes. Various clustering algorithms are available, such as kmeans clustering, as well as hierarchical clustering using the Ward’s minimum variance method, or single, complete and average linkage. The application and comparison of the described similarity measures is presented in Additional file 2.
Force constants variance weighting
where S _{ ij } (the elements of matrix S) represents the variance of the distance between residues i and j in the ensemble, ŝ is the maximum of such variance for any pair of atoms, and φ is an optional scaling factor. The application of force constant weighting is presented in Additional file 1.
Identification of dynamic domains
Analysis and identification of dynamic domains, i.e. parts of the molecule that move as relatively rigid entities within a conformational ensemble, is made available through a new implementation of the GeoStaS algorithm previously presented as a standalone Java program [35]. The algorithm relies on the identification of the best pairwise superimposition of atomic trajectories based on rotation and translation in quaternion space. The resulting atomic movement similarity matrix provides a means for clustering the atoms in the system based on their respective similarity. This approach has the advantage of capturing the potential correlation in rotational motions of two atoms placed on opposite sites, which may otherwise be found to be anticorrelated in a standard crosscorrelation analysis. The application of GeoStaS is demonstrated in Additional files 1 and 2 for both single structure and ensemble NMA, as well as for ensembles of PDB structures and MD trajectories.
Correlation network analysis
Correlation network analysis can be employed to identify protein segments with correlated motions. In this approach, a weighted graph is constructed where each residue represents a node and the weight of the connection between nodes, i and j, represents their respective crosscorrelation value, c _{ ij }, expressed by either the Pearsonlike form [36], or the linear mutual information [37]. Here we propose an approach related to that introduced by Sethi et al. [38], but using multiple correlation matrices derived from the input ensemble instead of contact maps. Specifically, the correlation matrix (C) is calculated for each structure in the ensemble NMA. Then, edges are added for residue pairs with c _{ ij } ≥ c _{0} across all experimental structures, where c _{0} is a constant. In addition, edges are added for residues where c _{ ij } ≥ c _{0} for at least one of the structures and the CαCα distance, d _{ ij }, satisfies d _{ ij } ≤ 10 Å for at least 75% of all conformations. Edges weights are then calculated with − log(〈c _{ ij }〉), where 〈 ⋅ 〉 denotes the ensemble average. Girvan and Newman betweeness clustering [39] is then performed to generate aggregate nodal clusters, or communities, that are highly intraconnected but loosely interconnected. Visualization of the resulting network and community structures in both 2D and 3D along with additional clustering and analysis options are also provided. See Additional file 4 for a complete example of the integration of ensemble NMA with correlation network analysis.
Results and discussion
In this section we demonstrate the application of new Bio3D functionality for analyzing functional motions in two distinct protein systems. Further examples, along with executable code, are provided in Additional files 1, 2, 3 and 4.
Crossspecies analysis of DHFR
Dihydrofolate reductase (DHFR) plays a critical role in promoting cell growth and proliferation in all organisms by catalyzing the reaction of dihydrofolate to tetrahydrofolate, an essential precursor for thymidylate synthesis [40]. DHFR is a major target for several antibiotics and has been subject of extensive structural studies. There are currently more than 500 DHFR structures in the PDB including a multitude of liganded states from a number of species. Here we demonstrate the use of Bio3D to take full advantage of this large structural data set when performing NMA. We first focus on the E. coli. DHFR structures before proceeding to a cross species analysis of all available DHFR structures.
Heterotrimeric Gproteins
Applying ensemble NMA to heterotrimeric Gprotein αsubunits (Gα) reveals nucleotide dependent structural dynamic features of functional relevance. Gα undergoes cycles of nucleotidedependent conformational rearrangements to couple cell surface receptors to downstream effectors and signaling cascades that control diverse cellular processes. These process range from movement and division to differentiation and neuronal activity. Interaction with activated receptor promotes the exchange of GDP for GTP on Gα and its separation from its βγ subunit partners (Gβγ). Both isolated Gα and Gβγ can then interact and activate downstream effectors. GTP hydrolysis deactivates Gα, which reassociates with Gβγ effectively completing the cycle.
It has been suggested that the activation mechanism of Gα involves a large domain opening that facilitates GDP/GTP exchange [43],[44]. Applying NMA to a predicted open form of Gα [42], highlights the large flexibility of the helical domain and captures this opening closing motion (Figure 4A). Combining NMA results with correlation network analysis methods, as implemented in the cna() function, reveals dynamically coupled subdomains that may facilitate the allosteric coupling of receptor and nucleotide binding sites (Figure 4B and Additional file 4). In summary, this example demonstrates the potential of ensemble NMA for characterizing key structural dynamic mechanisms in G proteins and other biomolecular systems.
Related solutions and future developments
Related software for analysis of protein structural dynamics
MMTK 2.7  ProDy 1.5  MAVEN 1.2  WebNM@ 2.0  Bio3D 2.0  

Dependencies  Python, NumPy, ScientificPython  Python, NumPy, MatplotLib  Matlab Component Runtime (MCR)  Web browser  R, Muscle 
Reading and analysis of molecular sequences  No  Yes  No  No  Yes 
Reading and analysis of multiple molecular structures  No  Yes  Yes  Yes  Yes 
Reading and analysis of binary MD simulation trajectories  Yes  Yes  No  No  Yes 
Biomolecular database integration  No  PDB, PFAM^{a}  No^{b}  No^{b}  PDB, PFAM, UNIPROT, NR^{c} 
Energy minimization and MD  Yes  No  No  No  No 
Standard NMA  Yes  Yes  Yes  Yes  Yes 
Ensemble NMA across heterogeneous structures  No  No  No  Yes  Yes 
Forcefields for NMA  Calpha, ANM, Amber allatom  GNM/ANM, Custom  GNM/ANM, pANM, STM, nnANM, mcgANM, Custom^{d}  Calpha  Calpha, ANM, pfANM sdENM, REACH, Custom 
Ensemble PCA across heterogeneous structures  No  Yes  Identical structures only  No  Yes 
Correlation network analysis from NMA and MD  No  No  No  No  Yes 
Dynamic domain analysis  No  No  No  No  Yes 
Sequence alignment  No  No  No  No  Yes 
Structure alignment  Yes  Yes  No  No  Yes 
Advanced statistical analysis  No  No  No  No  Yes 
Permits both interactive and batch analysis  Yes  Yes  No  Yes  Yes 
Open source code available  Yes  Yes  Yes^{e}  No  Yes 
Multicore compatibility  Yes  No  No  No  Yes 
GUI  No  No^{f}  Yes  Webserver  No^{g} 
Current and future development of Bio3D (see: https://bitbucket.org/Grantlab/bio3d) includes implementation of additional 3D visualization functionality, enhanced compatibility with the AMBER package [47], and further parallelization and optimization of structural alignment methods using graphical processing units (GPUs). We also plan to develop a webinterface and API for ensemble NMA and PCA to make this functionality more widely accessible. Finally, we envisage the development of new tools for structural dynamic mapping of clinical variants from next generation sequencing data and integration with the Bioconductor project [48] and tools for analysis of various omics data.
Conclusion
Bio3D version 2.0 provides a versatile integrated environment for protein structural and evolutionary analysis with unique capabilities including highthroughput ensemble NMA for examining the dynamics of evolutionary related protein structures; a convenient interface for accessing multiple ENM force fields; and a direct integration with a large number of functions for sequence, structure and simulation analysis. The package is implemented in the R environment and thus couples to extensive graphical and statistical capabilities along with a powerful userfriendly interactive programming environment that, together with Bio3D, enables both exploratory structural bioinformatics analysis and automated batch analysis of large datasets.
Availability and requirements
Project name: Bio3D
Project home page: http://thegrantlab.org/bio3d
Operating system(s): Platform independent
Programming language: R
Other requirements: R > = 3.0.0
License: GPL2
Any restrictions to use by nonacademics: none
Additional files
Abbreviations
 CNA:

Correlation network analysis
 DHFR:

Dihydrofolate reductase
 ENM:

Elastic network model
 MD:

Molecular dynamics
 NMA:

Normal mode analysis
 PCA:

Principal component analysis
 RMSIP:

Root mean square inner product
Declarations
Acknowledgements
We thank Edvin Fuglebakk and Julia Romanowska (University of Bergen, Norway) as well as the Bio3D user community for valuable discussions and software testing. We acknowledge the University of Bergen (LS) and University of Michigan (XY, GS and BJG) for funding.
Authors’ Affiliations
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