The amounts of thermal vibrations and static disorder in protein X-ray crystallographic B-factors.

Crystallographic B-factors provide direct dynamical information on the internal mobility of proteins that is closely linked to function, and are also widely used as a benchmark in assessing elastic network models. A significant question in the field is: what is the exact amount of thermal vibrations in protein crystallographic B-factors? This work sets out to answer this question. First, we carry out a thorough, statistically sound analysis of crystallographic B-factors of over 10 000 structures. Second, by employing a highly accurate all-atom model based on the well-known CHARMM force field, we obtain computationally the magnitudes of thermal vibrations of nearly 1000 structures. Our key findings are: (i) the magnitude of thermal vibrations, surprisingly, is nearly protein-independent, as a corollary to the universality for the vibrational spectra of globular proteins established earlier; (ii) the magnitude of thermal vibrations is small, less than 0.1 Å2 at 100 K; (iii) the percentage of thermal vibrations in B-factors is the lowest at low resolution and low temperature (<10%) but increases to as high as 60% for structures determined at high resolution and at room temperature. The significance of this work is that it provides for the first time, using an extremely large dataset, a thorough analysis of B-factors and their thermal and static disorder components. The results clearly demonstrate that structures determined at high resolution and at room temperature have the richest dynamics information. Since such structures are relatively rare in the PDB database, the work naturally calls for more such structures to be determined experimentally.

Memory effects in a random walk description of protein structure ensembles.

In this paper, we show that ensembles of well-structured and unstructured proteins can be distinguished by borrowing concepts from non-equilibrium statistical mechanics. For this purpose, we represent proteins by two different polymer models and interpret the resulting polymer configurations as random walks of a diffusing particle in space. The first model is the trace of the Cα-atoms along the protein main chain, and the second is their projections onto the protein axis. The resulting trajectories are subsequently analyzed using the theory of the generalized Langevin equation. Velocities are replaced by displacements relating consecutive points on the discrete protein axes and equilibrium ensemble averages by averages over appropriate protein structure ensembles. The resulting displacement autocorrelation functions resemble those of the velocity autocorrelation functions of simple liquids and display a minimum, which can be related to the lengths of secondary structure elements. This minimum is clearly more pronounced for well-structured proteins than for unstructured ones, and the corresponding memory function displays a slower decay, indicating a stronger "folding memory."

Verifiability in computer-aided research: the role of digital scientific notations at the human-computer interface.

Most of today's scientific research relies on computers and software for processing scientific information. Examples of such computer-aided research are the analysis of experimental data or the simulation of phenomena based on theoretical models. With the rapid increase of computational power, scientific software has integrated more and more complex scientific knowledge in a black-box fashion. As a consequence, its users do not know, and do not even have a chance of finding out, which assumptions and approximations their computations are based on. This black-box nature of scientific software has made the verification of much computer-aided research close to impossible. The present work starts with an analysis of this situation from the point of view of human-computer interaction in scientific research. It identifies the key role of digital scientific notations at the human-computer interface, reviews the most popular ones in use today, and describes a proof-of-concept implementation of Leibniz, a language designed as a verifiable digital scientific notation for models formulated as mathematical equations.

Sustainable computational science: the ReScience initiative.

Computer science offers a large set of tools for prototyping, writing, running, testing, validating, sharing and reproducing results; however, computational science lags behind. In the best case, authors may provide their source code as a compressed archive and they may feel confident their research is reproducible. But this is not exactly true. James Buckheit and David Donoho proposed more than two decades ago that an article about computational results is advertising, not scholarship. The actual scholarship is the full software environment, code, and data that produced the result. This implies new workflows, in particular in peer-reviews. Existing journals have been slow to adapt: source codes are rarely requested and are hardly ever actually executed to check that they produce the results advertised in the article. ReScience is a peer-reviewed journal that targets computational research and encourages the explicit replication of already published research, promoting new and open-source implementations in order to ensure that the original research can be replicated from its description. To achieve this goal, the whole publishing chain is radically different from other traditional scientific journals. ReScience resides on GitHub where each new implementation of a computational study is made available together with comments, explanations, and software tests.

Communication: A multiscale Bayesian inference approach to analyzing subdiffusion in particle trajectories.

Anomalous diffusion is characterized by its asymptotic behavior for t → ∞. This makes it difficult to detect and describe in particle trajectories from experiments or computer simulations, which are necessarily of finite length. We propose a new approach using Bayesian inference applied directly to the observed trajectories sampled at different time scales. We illustrate the performance of this approach using random trajectories with known statistical properties and then use it for analyzing the motion of lipid molecules in the plane of a lipid bilayer.

Protein secondary-structure description with a coarse-grained model.

A coarse-grained geometrical model for protein secondary-structure description and analysis is presented which uses only the positions of the C(α) atoms. A space curve connecting these positions by piecewise polynomial interpolation is constructed and the folding of the protein backbone is described by a succession of screw motions linking the Frenet frames at consecutive C(α) positions. Using the ASTRAL subset of the SCOPe database of protein structures, thresholds are derived for the screw parameters of secondary-structure elements and demonstrate that the latter can be reliably assigned on the basis of a C(α) model. For this purpose, a comparative study with the widely used DSSP (Define Secondary Structure of Proteins) algorithm was performed and it was shown that the parameter distribution corresponding to the ensemble of all pure C(α) structures in the RCSB Protein Data Bank matches that of the ASTRAL database. It is expected that this approach will be useful in the development of structure-refinement techniques for low-resolution data.

Construction and validation of an atomic model for bacterial TSPO from electron microscopy density, evolutionary constraints, and biochemical and biophysical data.

The 18 kDa protein TSPO is a highly conserved transmembrane protein found in bacteria, yeast, animals and plants. TSPO is involved in a wide range of physiological functions, among which the transport of several molecules. The atomic structure of monomeric ligand-bound mouse TSPO in detergent has been published recently. A previously published low-resolution structure of Rhodobacter sphaeroides TSPO, obtained from tubular crystals with lipids and observed in cryo-electron microscopy, revealed an oligomeric structure without any ligand. We analyze this electron microscopy density in view of available biochemical and biophysical data, building a matching atomic model for the monomer and then the entire crystal. We compare its intra- and inter-molecular contacts with those predicted by amino acid covariation in TSPO proteins from evolutionary sequence analysis. The arrangement of the five transmembrane helices in a monomer of our model is different from that observed for the mouse TSPO. We analyze possible ligand binding sites for protoporphyrin, for the high-affinity ligand PK 11195, and for cholesterol in TSPO monomers and/or oligomers, and we discuss possible functional implications.

Computational science: shifting the focus from tools to models.

Computational techniques have revolutionized many aspects of scientific research over the last few decades. Experimentalists use computation for data analysis, processing ever bigger data sets. Theoreticians compute predictions from ever more complex models. However, traditional articles do not permit the publication of big data sets or complex models. As a consequence, these crucial pieces of information have disappeared from the scientific record. Moreover, they have become prisoners of scientific software: many models exist only as software implementations, and the data are often stored in proprietary formats defined by the software. In this article, I argue that this emphasis on software tools over models and data is detrimental to science in the long term, and I propose a means by which this can be reversed.

ActivePapers: a platform for publishing and archiving computer-aided research.

The lack of replicability and reproducibility of scientific studies based on computational methods has lead to serious mistakes in published scientific findings, some of which have been discovered and publicized recently. Many strategies are currently pursued to improve the situation. This article reports the first conclusions from the ActivePapers project, whose goal is the development and application of a computational platform that allows the publication of computational research in a form that enables installation-free deployment, encourages reuse, and permits the full integration of datasets and software into the scientific record. The main finding is that these goals can be achieved with existing technology, but that there is no straightforward way to adapt legacy software to such a framework.

MOSAIC: a data model and file formats for molecular simulations.

The MOlecular SimulAtion Interchange Conventions (MOSAIC) consist of a data model for molecular simulations and of concrete implementations of this data model in the form of file formats. MOSAIC is designed as a modular set of specifications, of which the initial version covers molecular structure and configurations. A reference implementation in the Python language facilitates the development of simulation software based on MOSAIC.

A comparison of reduced coordinate sets for describing protein structure.

In all-atom molecular simulation studies of proteins, each atom in the protein is represented by a point mass and interactions are defined in terms of the atomic positions. In recent years, various simplified approaches have been proposed. These approaches aim to improve computational efficiency and to provide a better physical insight. The simplified models can differ widely in their description of the geometry and the interactions inside the protein. This study explores the most fundamental choice in the simplified protein models: the choice of a coordinate set defining the protein structure. A simplified model can use fewer point masses than the all-atom model and/or eliminate some of the internal coordinates of the molecule by setting them to an average or ideal value. We look at the implications of such choices for the overall protein structure. We find that care must be taken for angular coordinates, where even very small variations can lead to significant changes in the positions of far away atoms. In particular, we show that the φ/ψ torsion angles are not a sufficient coordinate set, whereas another coordinate set with two degrees of freedom per residue, virtual Cα backbone bond, and torsion angles performs satisfactorily.

Model-free simulation approach to molecular diffusion tensors.

In the present work, we propose a simple model-free approach for the computation of molecular diffusion tensors from molecular dynamics trajectories. The method uses a rigid body trajectory of the molecule under consideration, which is constructed a posteriori by an accumulation of quaternion-based superposition fits of consecutive conformations. From the rigid body trajectory, we compute the translational and angular velocities of the molecule and by integration of the latter also the corresponding angular trajectory. All quantities can be referred to the laboratory frame and a molecule-fixed frame. The 6 × 6 diffusion tensor is computed from the asymptotic slope of the tensorial mean square displacement and, for comparison, also from the Kubo integral of the velocity correlation tensor. The method is illustrated for two simple model systems - a water molecule and a lysozyme molecule in bulk water. We give estimations of the statistical accuracy of the calculations.

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions.

Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

nMoldyn 3: using task farming for a parallel spectroscopy-oriented analysis of molecular dynamics simulations.

We present a new version of the program package nMoldyn, which has been originally developed for a neutron-scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys. Commun. 1995, 91, 191) and was later rewritten to include in-depth time series analyses and a graphical user interface (Rog et al., J. Comput. Chem. 2003, 24, 657). The main improvement in this new version and the focus of this article are the parallelization of all the analysis algorithms for use on multicore desktop computers as well as distributed-memory computing clusters. The parallelization is based on a task farming approach which maintains a simple program structure permitting easy modification and extension of the code to integrate new analysis methods.

A path-integral Langevin equation treatment of low-temperature doped helium clusters.

We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package.

Communication: a minimal model for the diffusion-relaxation backbone dynamics of proteins.

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.