Harmonicity in slow protein dynamics

Hinsen, Konrad; Petrescu, Andrei‐Jose; Dellerue, Serge; Bellissent-Funel, Marie-Claire; Kneller, Gerald R.

doi:10.1016/s0301-0104(00)00222-6

Cited by 208 publications

(304 citation statements)

References 30 publications

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“…This means that the cohesiveness of protein structures is better represented by interactions decaying with the inverse square of the separation distances. In some ways this corresponds to others' findings where they used inverse 6th power springs (29,36) Improvements to the ENMs are critical for their use in developing mechanisms (50)(51)(52)(53). Previously springs of different strengths for different classes of interactions were not been found to improve the motions computed with ENMs (54).…”

Section: Discussionsupporting

confidence: 69%

“…In our parameter-free models, we use an inverse 2nd power (square distance) to model the spring constants. Past work had used an inverse 6th power spring (29,36) or a spring of exponential form (34)(35)(36)(37). However, our results show that our pfENM with inverse 2nd power springs clearly outperforms them all in B-factor predictions (see Table S1 and Table S2).…”

mentioning

confidence: 60%

“…One concern about this approach is that the results of such a fitting (or overfitting) may not have a real physical basis, even though the correlations achieved between experiment and prediction can be excellent. The Hinsen (34)(35)(36)(37) and the Phillips (29) groups have used a distancedependent force constant in their studies of protein dynamics. They proposed a force constant exhibiting an exponential decay over the distance between a pair of interacting atoms.…”

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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.

240

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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Section: Discussionsupporting

confidence: 69%

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confidence: 60%

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.

240

284

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“…Despite their coarse-grained nature, ENMs capture the overall geometry of proteins efficiently and modes from ENMs have been shown to be significantly accurate at reproducing experimental temperature factors for a number of crystal structures. 55–58 All the elastic network models and fluctuations were implemented using the ‘bio3d’ package 59 in R. We specifically used two variations of elastic network models implemented in the bio3d package: the anisotropic network model (ANM) 60 and the Hinsen’s network model 61 (referred to as HNM in this paper). In the ANM, all springs between residue i and j are assumed to have the same stiffness (spring constant ) whereas in the HNM, springs between sequentially adjacent C α atoms are represented as and those between non-adjacent C α atoms as where is the distance between residues and ; and and are constants as previously discussed.…”

Section: Methodsmentioning

confidence: 99%

“…In the ANM, all springs between residue i and j are assumed to have the same stiffness (spring constant ) whereas in the HNM, springs between sequentially adjacent C α atoms are represented as and those between non-adjacent C α atoms as where is the distance between residues and ; and and are constants as previously discussed. 61 In both models, the potential energy of the system is measured to be proportional to the sum of squares of displacements of the beads from their equilibrium positions. The hessian matrix of the double derivatives of the potential function is then constructed and eigen-decomposed to derive the modes and their frequencies (square root of the eigenvalues).…”

Section: Methodsmentioning

confidence: 99%

Prediction of methionine oxidation risk in monoclonal antibodies using a machine learning method

Sankar¹,

Hoi²,

Yuan

et al. 2018

mAbs

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Monoclonal antibodies (mAbs) have become a major class of protein therapeutics that target a spectrum of diseases ranging from cancers to infectious diseases. Similar to any protein molecule, mAbs are susceptible to chemical modifications during the manufacturing process, long-term storage, and in vivo circulation that can impair their potency. One such modification is the oxidation of methionine residues. Chemical modifications that occur in the complementarity-determining regions (CDRs) of mAbs can lead to the abrogation of antigen binding and reduce the drug’s potency and efficacy. Thus, it is highly desirable to identify and eliminate any chemically unstable residues in the CDRs during the therapeutic antibody discovery process. To provide increased throughput over experimental methods, we extracted features from the mAbs’ sequences, structures, and dynamics, used random forests to identify important features and develop a quantitative and highly predictive in silico methionine oxidation model.

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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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Harmonicity in slow protein dynamics

Cited by 208 publications

References 30 publications

Protein elastic network models and the ranges of cooperativity

Protein elastic network models and the ranges of cooperativity

Prediction of methionine oxidation risk in monoclonal antibodies using a machine learning method

Normal Mode Analysis Techniques in Structural Biology

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