A kinetic model for the internal motions of proteins: Diffusion between multiple harmonic wells

Amadei, Andrea; Groot, Bert L. de; Ceruso, Marc-Antoine; Paci, Maurizio; Nola, Alfredo Di; Berendsen, Herman J. C.

doi:10.1002/(sici)1097-0134(19990515)35:3<283::aid-prot2>3.3.co;2-i

Cited by 39 publications

(47 citation statements)

References 4 publications

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“…Comparison of the motions spanned by the first 10 eigenvectors from each simulation can be carried out by calculating the r.m.s.i.p. between the first 10 eigenvectors of each trajectory (Amadei et al 1999b) …”

Section: Methodsmentioning

confidence: 99%

Native-state dynamics of the ubiquitin family: implications for function and evolution

Marianayagam

Jackson

2005

J. R. Soc. Interface.

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Protein dynamics are integral to protein function. In recent years, the use of computer simulation to understand the molecular motions of proteins has become widespread. However, there are few such studies which compare the dynamics of proteins that are structurally and functionally related. In this study, we present native-state molecular dynamic simulations of four proteins which possess a ubiquitin-like fold. Three of these proteins are thought to have evolved from a common ancestral ubiquitin-like protein and have similarities in their function. A fourth protein, which is structurally homologous but which appears to have a different function, is also studied. Local fluctuations in the native state simulations are analysed, and conserved motions of the C-a backbone atoms are identified in residues which are important for function. In addition, the global dynamics of the proteins are analysed using the essential-dynamics method. This analysis reveals a slightly higher degree of conservation in dynamics for the three proteins which are functionally related. Both the global and local analyses illustrate how nature has optimized and conserved protein motions for specific biological activity within the ubiquitin family.

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Section: Methodsmentioning

confidence: 99%

Native-state dynamics of the ubiquitin family: implications for function and evolution

Marianayagam

Jackson

2005

J. R. Soc. Interface.

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“…These difficulties motivated the use of dimensionality reduction ͑in the form of quasiharmonic analysis or essential dynamics͒ as a successful approach for isolating lowfrequency motions and obtaining improved sampling of the phase space for MD and Monte Carlo approaches. [9][10][11][12][13][14][15][16][17] For example, by diagonalizing the covariance matrix of atomic displacements, it is often found that over 90% of the atomic motion in peptides or proteins is concentrated in correlated motions involving only 1%-5% of the degrees of freedom. 3,12,18,19 In addition to providing reduced complexity, an accurate representation for correlated molecular motions can aid in the interpretation of NMR and x-ray studies.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic dimensionality reduction for molecular structure analysis

Brown

Martin

Pollock

et al. 2008

The Journal of Chemical Physics

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Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation-a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a deterministic enumeration of ring conformations. We demonstrate a drastic improvement in dimensionality reduction with the use of nonlinear methods. We discuss the use of dimensionality reduction algorithms for estimating intrinsic dimensionality and the relationship to the Whitney embedding theorem. Additionally, we investigate the influence of the choice of high-dimensional encoding on the reduction. We show for the case studied that, in terms of reconstruction error root mean square deviation, Cartesian coordinate representations and encodings based on interatom distances provide better performance than encodings based on a dihedral angle representation.

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“…Note that Equation (8) is valid only for τ 0 . Then, by integrating expression given by Equation (8), we can simply find a general expression for the double diffusion model, which has also been used elsewhere [54] …”

Section: Methods For Determining Dynamic Frictionmentioning

confidence: 86%

“…Here, we have employed the same theoretical frame work as in Ref. [54], which corresponds to a double diffusion model, i.e. a short time diffusion D 0 within a configurational space region which can be approximated by a single harmonic well, followed by a diffusion between harmonic well regions that can be approximated by a long time diffusion constant D ∞ .…”

Section: Methods For Determining Dynamic Frictionmentioning

confidence: 99%

A theoretical model for the collective motion of proteins by means of principal component analysis

Kamberaj

2010

Open Physics

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Abstract:A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the C α atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0 2 − 0 4 ps and slow relaxation time of long diffusion about 1 − 2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from −0 746 to −0 938 for the real part and from −0 528 to −0 665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.

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A kinetic model for the internal motions of proteins: Diffusion between multiple harmonic wells

Cited by 39 publications

References 4 publications

Native-state dynamics of the ubiquitin family: implications for function and evolution

Native-state dynamics of the ubiquitin family: implications for function and evolution

Algorithmic dimensionality reduction for molecular structure analysis

A theoretical model for the collective motion of proteins by means of principal component analysis

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