NMR order parameters and free energy: an analytical approach and its application to cooperative calcium(2+) binding by calbindin D9k

Akke, Mikael; Brueschweiler, Rafael; Palmer, Arthur G.

doi:10.1021/ja00074a073

Cited by 342 publications

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“…Because of rotational tumbling, the S 2 values obtained from standard relaxation experiments are not affected by long-time-scale internal motion, increasing the difficulty of extracting thermodynamic information directly from the experiments. 29 In contrast, thermodynamic information obtained from MD simulations is limited only by the time scale of sampling and the accuracy of the force fields employed. To the extent that the results of MD simulations and NMR relaxation experiments can be reconciled within an analytical framework like that described in this paper, we expect that MD simulations will prove to be a valuable tool in the extraction of thermodynamic quantities from NMR experiments.…”

Section: Discussionmentioning

confidence: 99%

Microsecond Molecular Dynamics Simulation Shows Effect of Slow Loop Dynamics on Backbone Amide Order Parameters of Proteins

et al. 2008

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A molecular-level understanding of the function of a protein requires knowledge of both its structural and dynamic properties. NMR spectroscopy allows the measurement of generalized order parameters that provide an atomistic description of picosecond and nanosecond fluctuations in protein structure. Molecular dynamics (MD) simulation provides a complementary approach to the study of protein dynamics on similar time scales. Comparisons between NMR spectroscopy and MD simulations can be used to interpret experimental results and to improve the quality of simulation-related force fields and integration methods. However, apparent systematic discrepancies between order parameters extracted from simulations and experiments are common, particularly for elements of noncanonical secondary structure. In this paper, results from a 1.2 µs explicit solvent MD simulation of the protein ubiquitin are compared with previously determined backbone order parameters derived from NMR relaxation experiments [Tjandra, N.; Feller, S. E.; Pastor, R. W.; Bax, A. J. Am. Chem. Soc. 1995, 117, 12562-12566]. The simulation reveals fluctuations in three loop regions that occur on time scales comparable to or longer than that of the overall rotational diffusion of ubiquitin and whose effects would not be apparent in experimentally derived order parameters. A coupled analysis of internal and overall motion yields simulated order parameters substantially closer to the experimentally determined values than is the case for a conventional analysis of internal motion alone. Improved agreement between simulation and experiment also is encouraging from the viewpoint of assessing the accuracy of long MD simulations.

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Section: Discussionmentioning

confidence: 99%

Microsecond Molecular Dynamics Simulation Shows Effect of Slow Loop Dynamics on Backbone Amide Order Parameters of Proteins

et al. 2008

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“…Because these fast-timescale dynamics are, ultimately, connected to entropy, NMR spectroscopy has been used extensively to investigate the entropic contribution of the protein to biomolecular binding (in protein-protein, protein-DNA, protein-RNA and protein-other-ligand interactions) [65][66][67][68][69] . Here, we use calmodulin to illustrate the advantages and limitations of this method for quantifying entropic contributions to affinity, because the natural function of calmodulin is to bind to a variety of target proteins.…”

Section: Fast Timescalesmentioning

confidence: 99%

Dynamic personalities of proteins

Henzler-Wildman

Kern

2007

Nature

2,150

2,222

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Life is marked by change over time, and biologists explore this phenomenon by watching, for example, Caenorhabditis elegans developing from embryos into adults, mice running in a cage, and nerve cells firing. In search of how and why, biology arrived at the molecular level. Understanding protein function on an atomic level has been revolutionized by high-resolution X-ray crystallography, resulting in a surge in studies of structure-function relationships. The detail in these colourful structures flooding the covers of modern journals can be deceptive, suggesting that one unique structure, the 'folded state' , is the final answer. Ironically, the dynamic nature of biology seems to have been forgotten at this microscopic level.Physicists, however, will object to a static picture: they see proteins as soft materials that sample a large ensemble of conformations around the average structure as a result of thermal energy. A complete description of proteins requires a multidimensional energy landscape that defines the relative probabilities of the conformational states (thermodynamics) and the energy barriers between them (kinetics). In biology, this concept has recently gained traction, leading to an extension of the structure-function paradigm to include dynamics. To understand proteins in action, the fourth dimension, time, must be added to the snapshots of proteins frozen in crystal structures. A major obstacle is that it is not possible to watch experimentally individual atoms moving within a protein. Instead, sophisticated biophysical methods are needed to measure the physical properties from which the dynamics can be inferred.In this review, we discuss how protein function is rooted in the energy landscape. The basic concepts and the biophysical methods are illustrated by several examples. To avoid past semantic confusion about the term protein dynamics, we define it as any time-dependent change in atomic coordinates. Protein dynamics thus includes both equilibrium fluctuations and non-equilibrium effects. The fluctuations observed at equilibrium seem to govern biological function in processes both near and far from equilibrium; therefore, we focus on these motions. Non-equilibrium effects are also called dynamical effects 1 (the source of confusion 2 ), and they have a minimal effect on the overall rates of biological processes 3,4 . Biological motors that convert chemical energy to mechanical energy 5,6 are not discussed here. The energy landscapeAlthough the idea of an energy landscape might be most familiar in the context of protein folding (for example, the folding funnel hypothesis) [7][8][9] , this concept had already been applied to folded proteins more than 30 years ago by Frauenfelder and co-workers . Subsequent studies on myoglobin led to the idea that substates are in thermal equilibrium and that both solvent 13-15 and ligands influence the landscape (Fig. 1a). At the glass transition temperature 10,12 , an increase in anharmonic dynamics occurs in proteins, and this is interpreted as the protein no...

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“…30,[52][53][54] This requires the equilibrium probability distribution function, P eq (Ω C'M ), of the M frame relative to the local director, C'. P eq (Ω C'M ) is calculated automatically in SRLS using a potential form as general as justified by the quality of the experimental data.…”

Section: Residual Configurational Entropymentioning

confidence: 99%

An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of ²H Spin Relaxation

et al. 2007

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Protein dynamics is intimately related to biological function. Core dynamics is usually studied with 2 H spin relaxation of the 13 CDH 2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering has axial symmetry. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (J. Phys. Chem. 1995, 99, 1099), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15 − 45 °C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries, and dynamically by tenfold slower rates of local motion. On average potential rhombicity decreases, mode-coupling increases and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 ± 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 o C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences. Keywords slowly relaxing local structure; methyl dynamics in proteins; NMR spin relaxation in proteins

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NMR order parameters and free energy: an analytical approach and its application to cooperative calcium(2+) binding by calbindin D9k

Cited by 342 publications

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Microsecond Molecular Dynamics Simulation Shows Effect of Slow Loop Dynamics on Backbone Amide Order Parameters of Proteins

Microsecond Molecular Dynamics Simulation Shows Effect of Slow Loop Dynamics on Backbone Amide Order Parameters of Proteins

Dynamic personalities of proteins

An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of ²H Spin Relaxation

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NMR order parameters and free energy: an analytical approach and its application to cooperative calcium(2+) binding by calbindin D9k

Cited by 342 publications

References 0 publications

Microsecond Molecular Dynamics Simulation Shows Effect of Slow Loop Dynamics on Backbone Amide Order Parameters of Proteins

Microsecond Molecular Dynamics Simulation Shows Effect of Slow Loop Dynamics on Backbone Amide Order Parameters of Proteins

Dynamic personalities of proteins

An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of 2H Spin Relaxation

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An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of ²H Spin Relaxation