Protein Structural Variation in Computational Models and Crystallographic Data

Kondrashov, D.A.; Wynsberghe, Adam W. Van; Bannen, Ryan M.; Cui, Qiang; Phillips, George N.

doi:10.1016/j.str.2006.12.006

Cited by 97 publications

(144 citation statements)

References 53 publications

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“…3-5, 16, 24, 37 It was shown that the GNM is about one order more efficient than most other approaches. 48 Improvements to these approaches have been developed for many aspects, including crystal periodicity and cofactor corrections, 17,21,22,35 and density -cluster rotational -translational blocking. 11 These approaches have been applied to the study of large proteins or protein complexes, such as, hemoglobin, 47 F1 ATPase, 10,50 chaperonin GroEL, 20, 49 viral capsids, 29,36 and ribosome.…”

Section: Introductionmentioning

confidence: 99%

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

Opron

Xia

Guo

2014

The Journal of Chemical Physics

242

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Protein structural fluctuation, typically measured by Debye-Waller factors, or B-factors, is a manifestation of protein flexibility, which strongly correlates to protein function. The flexibility-rigidity index (FRI) is a newly proposed method for the construction of atomic rigidity functions required in the theory of continuum elasticity with atomic rigidity, which is a new multiscale formalism for describing excessively large biomolecular systems. The FRI method analyzes protein rigidity and flexibility and is capable of predicting protein B-factors without resorting to matrix diagonalization. A fundamental assumption used in the FRI is that protein structures are uniquely determined by various internal and external interactions, while the protein functions, such as stability and flexibility, are solely determined by the structure. As such, one can predict protein flexibility without resorting to the protein interaction Hamiltonian. Consequently, bypassing the matrix diagonalization, the original FRI has a computational complexity of O(N 2 ). This work introduces a fast FRI (fFRI) algorithm for the flexibility analysis of large macromolecules. The proposed fFRI further reduces the computational complexity to O(N ). Additionally, we propose anisotropic FRI (aFRI) algorithms for the analysis of protein collective dynamics. The aFRI algorithms permit adaptive Hessian matrices, from a completely global 3N × 3N matrix to completely local 3 × 3 matrices. These 3 × 3 matrices, despite being calculated locally, also contain non-local correlation information. Eigenvectors obtained from the proposed aFRI algorithms are able to demonstrate collective motions. Moreover, we investigate the performance of FRI by employing four families of radial basis correlation functions. Both parameter optimized and parameter-free FRI methods are explored. Furthermore, we compare the accuracy and efficiency of FRI with some established approaches to flexibility analysis, namely, normal mode analysis and Gaussian network model (GNM). The accuracy of the FRI method is tested using four sets of proteins, three sets of relatively small-, medium-, and large-sized structures and an extended set of 365 proteins. A fifth set of proteins is used to compare the efficiency of the FRI, fFRI, aFRI, and GNM methods. Intensive validation and comparison indicate that the FRI, particularly the fFRI, is orders of magnitude more efficient and about 10% more accurate overall than some of the most popular methods in the field. The proposed fFRI is able to predict B-factors for α-carbons of the HIV virus capsid (313 236 residues) in less than 30 seconds on a single processor using only one core. Finally, we demonstrate the application of FRI and aFRI to protein domain analysis. © 2014 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

Opron

Xia

Guo

2014

The Journal of Chemical Physics

242

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“…Such lowenergy eigenvalues reflect the long-time behavior of the protein dynamics beyond the reach of MD simulations. 6,8,36,55,58 These approaches have been improved in many aspects including crystal periodicity corrections 28,34,35,54 and densitycluster rotational-translational blocking. 20 These methods are relatively inexpensive particularly in their coarse-grained settings.…”

Section: Introductionmentioning

confidence: 99%

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Xia

Opron

Guo

2013

The Journal of Chemical Physics

221

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The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the PoissonBoltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CE-WAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of O(N 2 ) at most, where N is the number of atoms or residues, in contrast to O(N 3 ) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

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“…The ENM for isotropic fluctuations is called the Gaussian network model (GNM) (23,24), where only the magnitudes of the fluctuations are considered. Its anisotropic counterpart, where the directions of the collective motions are also examined, is called the anisotropic network model (ANM) (25), and these can be compared with the experimental anisotropic temperature factors (26)(27)(28)(29), but generally these comparisons are worse than when atomic representations are used (30).…”

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confidence: 99%

Protein elastic network models and the ranges of cooperativity

Yang

Song²,

Jernigan³

2009

Proc. Natl. Acad. Sci. U.S.A.

238

284

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Elastic network models (ENMs) are entropic models that have demonstrated in many previous studies their abilities to capture overall the important internal motions, with comparisons having been made against crystallographic B-factors and NMR conformational variabilities. ENMs have become an increasingly important tool and have been widely used to comprehend protein dynamics, function, and even conformational changes. However, reliance upon an arbitrary cutoff distance to delimit the range of interactions has presented a drawback for these models, because the optimal cutoff values can differ somewhat from protein to protein and can lead to quirks such as some shuffling in the order of the normal modes when applied to structures that differ only slightly. Here, we have replaced the requirement for a cutoff distance and introduced the more physical concept of inverse power dependence for the interactions, with a set of elastic network models that are parameter-free, with the distance cutoff removed. For small fluctuations about the native forms, the power dependence is the inverse square, but for larger deformations, the power dependence may become inverse 6th or 7th power. These models maintain and enhance the simplicity and generality of the original ENMs, and at the same time yield better predictions of crystallographic B-factors (both isotropic and anisotropic) and of the directions of conformational transitions. Thus, these parameter-free ENMs can be models of choice whenever elastic network models are used.B factors ͉ conformational entropy P rotein dynamics can provide important insights into protein function. Most proteins carry out their functions through conformational changes of the structures. In X-ray structures, the information about thermal motions is provided by the Debye-Waller temperature factors or B-factors, which are proportional to the mean square fluctuations of atom positions in a crystal. Thus, accurate predictions of crystalline B-factors offer a good starting point for understanding the functional dynamics of proteins.A number of computational and statistical approaches has been proposed to predict protein B-factors from protein sequence (1-7), atomic coordinates (8-13), and electron density maps (14). The atomic coordinate-based methods such as molecular dynamics (MD) (15-18) and normal mode analysis (NMA) (19)(20)(21)(22) are computationally expensive, and thus, in the past decade, the elastic network model (ENM), with NMA, using a single parameter harmonic potential, usually coarse-grained, has been widely used for studying protein dynamics including B-factor predictions. The ENM for isotropic fluctuations is called the Gaussian network model (GNM) (23,24), where only the magnitudes of the fluctuations are considered. Its anisotropic counterpart, where the directions of the collective motions are also examined, is called the anisotropic network model (ANM) (25), and these can be compared with the experimental anisotropic temperature factors (26-29), but generally these comparisons are ...

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Protein Structural Variation in Computational Models and Crystallographic Data

Cited by 97 publications

References 53 publications

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Protein elastic network models and the ranges of cooperativity

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