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Journal ArticleDOI

Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis.

26 Aug 1996-Physical Review Letters (American Physical Society)-Vol. 77, Iss: 9, pp 1905-1908
TL;DR: It is shown that a single-parameter potential is sufficient to reproduce the slow dynamics of proteins obtained with vastly more complex empirical potentials, which inevitably leads to unstable modes which must be eliminated through elaborate methods, and which cast doubts on the validity of the analysis.
Abstract: Normal mode analysis (NMA) is a leading method for studying long-time dynamics and elasticity of biomolecules. The method proceeds from complex semiempirical potentials characterizing the covalent and noncovalent interactions between atoms. It is widely accepted that such detailed potentials are essential to the success of NMA’s. We show that a single-parameter potential is sufficient to reproduce the slow dynamics in good detail. Costly and inaccurate energy minimizations are eliminated, permitting direct analysis of crystal coordinates. The technique can be used for new applications, such as mapping of one crystal form to another by means of slow modes, and studying anomalous dynamics of large proteins and complexes. [S0031-9007(96)01063-0] PACS numbers: 87.15.By, 87.15.He Thermal equilibrium fluctuations of the x-ray crystal coordinates of proteins provide a basis for understanding the complex dynamics and elasticity of biological macromolecules [1]. Analysis of the normal modes of globular proteins shows an interesting anomaly. The density of the slow vibrational modes is proportional to their frequency, gsv d, v, rather than gsv d, v 2 as predicted by Debye’s theory [2]. Yet, the atoms in globular proteins are packed as tightly as in solids. We show that a single-parameter potential reproduces the slow elastic modes of proteins obtained with vastly more complex empirical potentials. The simplicity of the potential permits greater insight and understanding of the mechanisms that underlie the slow, anomalous motions in biological macromolecules such as proteins. To date, normal modes of globular proteins have been used to reproduce crystallographic temperature factors [3] and diffuse scatter [4]. Normal mode analyses (NMA’s) shed light on shear and hinge motions necessary for catalytic reactions, and have been used with some success to map one crystal form of a protein into another [5]. Finally, NMA’s yield macroscopic elastic moduli of large protein assemblies, based on their microscopic structure [6]. NMA studies of macromolecules are handicapped, however, by the complex phenomenological potentials used to model the covalent and nonbonded interactions between atom pairs. The necessary initial energy minimization requires a great deal of computer time and memory, and is virtually impossible for even moderately large proteins (with typically thousands of degrees of freedom) with a reasonable degree of accuracy. This inevitably leads to unstable modes which must be eliminated through elaborate methods, and which cast doubts on the validity of the analysis. Moreover, partly because the minimization is carried out in vacuo, the final configuration disagrees with the known crystallographic structure, complicating the interpretation of the results of NMA. A typical example of a semiempirical potential used in molecular dynamics studies and NMA’s has the form [7] Ep › 1 X bonds Kbsb 2 b0d 2 1 1 X angles Kus u2u 0 d 2

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Journal ArticleDOI
TL;DR: An overview of the CHARMM program as it exists today is provided with an emphasis on developments since the publication of the original CHARMM article in 1983.
Abstract: CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

7,035 citations

Journal ArticleDOI
TL;DR: A new tool is presented and applied to the retinol-binding protein, which indicates enhanced flexibility in the region of entry to the ligand binding site and for the portion of the protein binding to its carrier protein.

1,573 citations


Cites methods from "Large Amplitude Elastic Motions in ..."

  • ...For example, Tirion showed that the residue fluctuations predicted for G-actin with a single-parameter model are almost indistinguishable from those obtained with a classical NMA using an elaborate force field (Tirion, 1996)....

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Journal ArticleDOI
TL;DR: The simple model and method proposed here provide a satisfactory description of the correlations between atomic fluctuations and are achieved within computation times at least one order of magnitude shorter than commonly used molecular approaches.

1,349 citations


Cites methods from "Large Amplitude Elastic Motions in ..."

  • ...Note that in comparison with the CPU times reported by Tirion [5] for NMA with energy minimization, the present computation times are at least one order of magnitude shorter....

    [...]

  • ...Following the model network of randomly fluctuating junctions postulated above, the fluctuations DRij in the separation Rij =Rj – Ri between the ith and jth Ca atoms in the folded protein are assumed to obey a Gaussian distribution: W(DRij) = (g*/p)3/2 exp(– g* DRij2) (1) Here, the normalization constant g* is the counterpart of the single parameter in the Hookean potential adopted by Tirion [5]....

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  • ...The latter replaces the single parameter C used by Tirion....

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  • ...We note that the recent NMA study by Tirion [5] demonstrates that contributions to fluctuations from nonlinearities in the potentials are negligibly small....

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  • ...Recently, a single-parameter Hookean potential was adopted for the pairwise interaction of all atoms in X-ray crystallographic structures in a normal mode analysis (NMA) of large-amplitude elastic motions [5]....

    [...]

Journal ArticleDOI
TL;DR: In this article, a review of the use of small angle X-ray scattering (SAXS) for modeling macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, is presented.
Abstract: Crystallography supplies unparalleled detail on structural information critical for mechanistic analyses; however, it is restricted to describing low energy conformations of macromolecules within crystal lattices. Small angle X-ray scattering (SAXS) offers complementary information about macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, but without the size limitations inherent in NMR and electron microscopy studies. Together these techniques can allow multi-scale modeling to create complete and accurate images of macromolecules for modeling allosteric mechanisms, supramolecular complexes, and dynamic molecular machines acting in diverse processes ranging from eukaryotic DNA replication, recombination and repair to microbial membrane secretion and assembly systems. This review addresses both theoretical and practical concepts, concerns and considerations for using these techniques in conjunction with computational methods to productively combine solution scattering data with high-resolution structures. Detailed aspects of SAXS experimental results are considered with a focus on data interpretation tools suitable to model protein and nucleic acid macromolecular structures, including membrane protein, RNA, DNA, and protein-nucleic acid complexes. The methods discussed provide the basis to examine molecular interactions in solution and to study macromolecular flexibility and conformational changes that have become increasingly relevant for accurate understanding, simulation, and prediction of mechanisms in structural cell biology and nanotechnology.

1,065 citations

Journal ArticleDOI
TL;DR: This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool, and covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role.
Abstract: The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations. Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time. Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function. This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized. 1.1. Historical Background MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics. As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today. The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly. The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1. Open in a separate window Figure 1 Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.

999 citations