Comparisons of experimental and computed protein anisotropic temperature factors

Yang, Lei; Song, Guang; Jernigan, Robert L.

doi:10.1002/prot.22328

Cited by 39 publications

(44 citation statements)

References 39 publications

(53 reference statements)

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“…Therefore, a perfect prediction would render both and as 0. From the Table 1, we see that neither pfANM nor ANM does well in this regard, for possible reasons that were discussed in (26). However, the point of interest here is that pfANM does slightly better than ANM.…”

Section: Anisotropic B-factor Predictionsmentioning

confidence: 78%

“…The experimental and calculated anisotropic B-factor tensors, which can be represented by ellipsoids, are compared [see (26) for details]. Specifically, the first and second anisotropies ( and ) of the experimental anisotropic B-factors are compared with those calculated from the models (pfANM or ANM).…”

Section: Anisotropic B-factor Predictionsmentioning

confidence: 99%

“…The mean and values in the third and fourth column describe how well the directions of the ellipsoids match between experiment and calculation. Specifically, is the angle between the longest axes of the ellipsoids (which represent the anisotropic B-factor tensors of experiment and calculation), and is the rotation angle required to align the second longest axes of the 2 ellipsoids once their longest axes are aligned (26). Therefore, a perfect prediction would render both and as 0.…”

Section: Anisotropic B-factor Predictionsmentioning

confidence: 99%

“…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%

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Protein elastic network models and the ranges of cooperativity

Yang

Song²,

Jernigan³

2009

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

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238

285

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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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Section: Anisotropic B-factor Predictionsmentioning

confidence: 78%

Section: Anisotropic B-factor Predictionsmentioning

confidence: 99%

Section: Anisotropic B-factor Predictionsmentioning

confidence: 99%

mentioning

confidence: 99%

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Protein elastic network models and the ranges of cooperativity

Yang

Song²,

Jernigan³

2009

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

Self Cite

238

285

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show abstract

“…As temperature factors can only provide information regarding the magnitude of the atomic fluctuations in most of the PDB data, it is generally problematic to compare the calculated and experimentally observed atomic fluctuations with respect to their directional properties. Such a comparison is possible for the PDB data with anisotropic temperature factors, and there is some literature that discusses this method (Atilgan et al 2001;Eyal et al 2007;Yang et al 2009;Hafner and Zheng 2011). However, we have not discussed this in our review.…”

Section: Fluctuation Of Atomsmentioning

confidence: 99%

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Wako

Endo

2017

Biophys Rev

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Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo-and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.

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Normal Mode Analysis Techniques in Structural Biology

López‐Blanco

Miyashita

Tama

et al. 2014

Encyclopedia of Life Sciences

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The dynamic simulation of macromolecular systems with biologically relevant sizes and time scales is critical for understanding macromolecular function. In this context, normal mode analysis (NMA) approximates the complex dynamical behaviour of a macromolecule as a simple set of harmonic oscillators vibrating around a given equilibrium conformation. This technique, originated from classical mechanics, was first applied to investigate the dynamical properties of small biological systems more than 30 years ago. During this time, a wealth of evidence has accumulated to support NMA as a successful tool for simulating macromolecular motions at extended length scales. Today, NMA combined with coarse‐grained representations has become an efficient alternative to molecular dynamics simulations for studying the slow and large‐amplitude motions of macromolecular machines. Interesting insights into these systems can be obtained very quickly with NMA to characterise their flexibility, to predict the directions of their collective conformational changes, or to help in the interpretation of experimental structural data. The recently developed methods and applications of NMA together with an introduction of the underlying theory will be briefly reviewed here. Key Concepts: NMA computes all motions around an equilibrium conformation (normal modes). Normal modes are orthogonal displacement vectors with an associated frequency. The collective functional motions of the macromolecules are well described by lowest frequency modes. NMA inexpensive and accurately simulates the slow and large‐amplitude motions of biomolecules, but local reorganisations and the absolute time scale or amplitude of the motions are poorly predicted. NMA can be used to characterise macromolecular flexibility, to predict the directions of collective conformational changes, and to interpret structural experimental data.

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Comparisons of experimental and computed protein anisotropic temperature factors

Cited by 39 publications

References 39 publications

Protein elastic network models and the ranges of cooperativity

Protein elastic network models and the ranges of cooperativity

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal Mode Analysis Techniques in Structural Biology

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