PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure.

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Fast large-scale clustering of protein structures using Gauss integrals.

MOTIVATION: Clustering protein structures is an important task in structural bioinformatics. De novo structure prediction, for example, often involves a clustering step for finding the best prediction. Other applications include assigning proteins to fold families and analyzing molecular dynamics trajectories. RESULTS: We present Pleiades, a novel approach to clustering protein structures with a rigorous mathematical underpinning. The method approximates clustering based on the root mean square deviation by first mapping structures to Gauss integral vectors--which were introduced by Røgen and co-workers--and subsequently performing K-means clustering. CONCLUSIONS: Compared to current methods, Pleiades dramatically improves on the time needed to perform clustering, and can cluster a significantly larger number of structures, while providing state-of-the-art results. The number of low energy structures generated in a typical folding study, which is in the order of 50,000 structures, can be clustered within seconds to minutes.

Four simple recommendations to encourage best practices in research software.

Scientific research relies on computer software, yet software is not always developed following practices that ensure its quality and sustainability. This manuscript does not aim to propose new software development best practices, but rather to provide simple recommendations that encourage the adoption of existing best practices. Software development best practices promote better quality software, and better quality software improves the reproducibility and reusability of research. These recommendations are designed around Open Source values, and provide practical suggestions that contribute to making research software and its source code more discoverable, reusable and transparent. This manuscript is aimed at developers, but also at organisations, projects, journals and funders that can increase the quality and sustainability of research software by encouraging the adoption of these recommendations.

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics.

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts--sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond ((h3)J(NC')) spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to obtain this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.

An efficient null model for conformational fluctuations in proteins.

Protein dynamics play a crucial role in function, catalytic activity, and pathogenesis. Consequently, there is great interest in computational methods that probe the conformational fluctuations of a protein. However, molecular dynamics simulations are computationally costly and therefore are often limited to comparatively short timescales. TYPHON is a probabilistic method to explore the conformational space of proteins under the guidance of a sophisticated probabilistic model of local structure and a given set of restraints that represent nonlocal interactions, such as hydrogen bonds or disulfide bridges. The choice of the restraints themselves is heuristic, but the resulting probabilistic model is well-defined and rigorous. Conceptually, TYPHON constitutes a null model of conformational fluctuations under a given set of restraints. We demonstrate that TYPHON can provide information on conformational fluctuations that is in correspondence with experimental measurements. TYPHON provides a flexible, yet computationally efficient, method to explore possible conformational fluctuations in proteins.

Potentials of mean force for protein structure prediction vindicated, formalized and generalized.

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances--so-called "potentials of mean force" (PMFs)--have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state--a necessary component of these potentials--is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities "reference ratio distributions" deriving from the application of the "reference ratio method." This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

Structural and theoretical studies indicate that the cylindrical protease ClpP samples extended and compact conformations.

The highly conserved ClpP protease consists of two heptameric rings that interact by the interdigitation of an alpha-helix beta strand handle domain motif to form a tetradecameric cylinder. We previously proposed that protease dynamics results in the temporary unstructuring of interacting pairs of handle domains, opening transient equatorial side pores that allow for peptide egress. Here, we report the structure of an Escherichia coli ClpP mutant in which each opposing pair of protomers is linked by a disulfide bond. This structure resembles the compact structures of Streptococcus pneumoniae, Mycobacterium tuberculosis, and Plasmodium falciparum ClpPs, rather than the active, extended structures that have previously been determined for E. coli ClpPs. The structural data, along with normal mode analysis, support a model whereby the ClpP cylinder switches dynamically between an active extended state required for substrate degradation and an inactive compact state allowing peptide product release.

Structural studies of FF domains of the transcription factor CA150 provide insights into the organization of FF domain tandem arrays.

FF domains are poorly understood protein interaction modules that are present within eukaryotic transcription factors, such as CA150 (TCERG-1). The CA150 FF domains have been shown to mediate interactions with the phosphorylated C-terminal domain of RNA polymerase II (phosphoCTD) and a multitude of transcription factors and RNA processing proteins, and may therefore have a central role in organizing transcription. FF domains occur in tandem arrays of up to six domains, although it is not known whether they adopt higher-order structures. We have used the CA150 FF1+FF2 domains as a model system to examine whether tandem FF domains form higher-order structures in solution using NMR spectroscopy. In the solution structure of FF1 fused to the linker that joins FF1 to FF2, we observed that the highly conserved linker peptide is ordered and forms a helical extension of helix alpha3, suggesting that the interdomain linker might have a role in orientating FF1 relative to FF2. However, examination of the FF1+FF2 domains using relaxation NMR experiments revealed that although these domains are not rigidly orientated relative to one another, they do not tumble independently. Thus, the FF1+FF2 structure conforms to a dumbbell-shape in solution, where the helical interdomain linker maintains distance between the two dynamic FF domains without cementing their relative orientations. This model for FF domain organization within tandem arrays suggests a general mechanism by which individual FF domains can manoeuvre to achieve optimal recognition of flexible binding partners, such as the intrinsically-disordered phosphoCTD.

Polyelectrostatic interactions of disordered ligands suggest a physical basis for ultrasensitivity.

Regulation of biological processes often involves phosphorylation of intrinsically disordered protein regions, thereby modulating protein interactions. Initiation of DNA replication in yeast requires elimination of the cyclin-dependent kinase inhibitor Sic1 via the SCF(Cdc4) ubiquitin ligase. Intriguingly, the substrate adapter subunit Cdc4 binds to Sic1 only after phosphorylation of a minimum of any six of the nine cyclin-dependent kinase sites on Sic1. To investigate the physical basis of this ultrasensitive interaction, we consider a mean-field statistical mechanical model for the electrostatic interactions between a single receptor site and a conformationally disordered polyvalent ligand. The formulation treats phosphorylation sites as negative contributions to the total charge of the ligand and addresses its interplay with the strength of the favorable ligand-receptor contact. Our model predicts a threshold number of phosphorylation sites for receptor-ligand binding, suggesting that ultrasensitivity in the Sic1-Cdc4 system may be driven at least in part by cumulative electrostatic interactions. This hypothesis is supported by experimental affinities of Cdc4 for Sic1 fragments with different total charges. Thus, polyelectrostatic interactions may provide a simple yet powerful framework for understanding the modulation of protein interactions by multiple phosphorylation sites in disordered protein regions.

Density of configurational states from first-principles calculations: the phase diagram of Al-Na surface alloys.

The structural phases of Al(x)Na(1-x) surface alloys have been investigated theoretically and experimentally. We describe the system using a lattice-gas Hamiltonian, determined from density functional theory, together with Monte Carlo (MC) calculations. The obtained phase diagram reproduces the experiment on a quantitative level. From calculation of the (configurational) density of states by the recently introduced Wang-Landau MC algorithm, we derive thermodynamic quantities, such as the free energy and entropy, which are not directly accessible from conventional MC simulations. We accurately reproduce the stoichiometry, as well as the temperature at which an order-disorder phase transition occurs, and demonstrate the crucial role, and magnitude, of the configurational entropy.