Search

Deep learning developers typically rely on deep learning software frameworks (DLSFs)—simply described as pre-packaged libraries of programming components that provide high-level access to deep learning functionality. New DLSFs progressively encapsulate mathematical, statistical and computational complexity. Such higher levels of abstraction subsequently make it easier for deep learning methodology to spread through mimesis (i.e., imitation of models perceived as successful). In this study, we quantify this increase in abstraction and discuss its implications. Analyzing publicly available code from Github, we found that the introduction of DLSFs correlates both with significant increases in the number of deep learning projects and substantial reductions in the number of lines of code used. We subsequently discuss and argue the importance of abstraction in deep learning with respect to ephemeralization, technological advancement, democratization, adopting timely levels of abstraction, the emergence of mimetic deadlocks, issues related to the use of black box methods including privacy and fairness, and the concentration of technological power. Finally, we also discuss abstraction as a symptom of an ongoing technological metatransition.

Optimal superposition of protein structures is crucial for understanding their structure, function, dynamics and evolution. We investigate the use of probabilistic programming to superimpose protein structures guided by a Bayesian model. Our model THESEUS-PP is based on the THESEUS model, a probabilistic model of protein superposition based on rotation, translation and perturbation of an underlying, latent mean structure. The model was implemented in the deep probabilistic programming language Pyro. Unlike conventional methods that minimize the sum of the squared distances, THESEUS takes into account correlated atom positions and heteroscedasticity (i.e., atom positions can feature different variances). THESEUS performs maximum likelihood estimation using iterative expectation-maximization. In contrast, THESEUS-PP allows automated maximum a-posteriori (MAP) estimation using suitable priors over rotation, translation, variances and latent mean structure. The results indicate that probabilistic programming is a powerful new paradigm for the formulation of Bayesian probabilistic models concerning biomolecular structure. Specifically, we envision the use of the THESEUS-PP model as a suitable error model or likelihood in Bayesian protein structure prediction using deep probabilistic programming.

Optimally superimposing protein structures is essential to study their structure, function, dynamics and evolution. We present THESEUS NUTS (No U-Turn Sampler), a Bayesian version of the THESEUS model [1] –[3] which relies on maximum likelihood estimation. The probabilistic model interprets each protein as a rotated and translated noisy observation of a latent mean structure. Unlike conventional methods [4], THESEUS takes into account the differences in correlations between the atoms in the structure. This paper extends the previous THESEUS MAP (Maximum A Posteriori) model, [5] to full Bayesian inference by making use of the iterative NUTS [6], a Hamiltonian Monte Carlo method. The model delivers consistent results and is computationally efficient thanks to its implementation in the probabilistic programming language NumpPyro [7], [8] which in turn relies upon JAX [9], a system for high-performance machine learning.

The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few methods are sensitive to topologic-geometric features, the examples being knots, slipknots, lassos, links, and pokes, and with each method aimed only for a specific set of such configurations.We here propose a general method which transforms a structure into a “fingerprint of topological-geometric values” consisting in a series of real-valued descriptors from mathematical Knot Theory. The extent to which a structure contains unusual configurations can then be judged from this fingerprint. The method is therefore not confined to a particular pre-defined topology or geometry (like a knot or a poke), and so, unlike existing methods, it is general. To achieve this our new algorithm, GISA, as a key novelty produces the descriptors, so called Gauss integrals, not only for the full chains of a protein but for all its sub-chains, thereby allowing fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds.Applying GISA to a set of about 8000 high resolution structures (top8000), we first show how it enables swift identification of predefined geometries such as pokes and links. We then apply GISA with no restrictions on geometry, to show how it allows identifying rare conformations by finding rare invariant values only. In this unrestricted search, pokes and links are still found, but also knotted conformations, as well as more highly entangled configurations not previously described. Thus, applying the basic scan method in GISA’s tool-box to the top8000 set, 10 known cases of knots are ranked as the top positive Gauss number cases, while placing at the top of the negative Gauss numbers 14 cases in cis-trans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed.Potential applications of the GISA tools include finding errors in protein models and identifying unusual conformations that might be important for protein folding and function. By its broad potential, we believe that GISA will be of general benefit to the structural bioinformatics community.GISA is coded in C and comes as a command line tool. Source and compiled code for GISA plus read-me and examples are publicly available at GitHub (https://github.com).

Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a generative, evolutionary model of protein structure and sequence that is valid on a local length scale. The model concerns the local dependencies between sequence and structure evolution in a pair of homologous proteins. The evolutionary trajectory between the two structures in the protein pair is treated as a random walk in dihedral angle space, which is modelled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modelling both "smooth" conformational changes and "catastrophic" conformational jumps, conditioned on the amino acid changes. The model has interpretable parameters and is comparatively more realistic than previous stochastic models, providing new insights into the relationship between sequence and structure evolution. For example, using the trained model we were able to identify an apparent sequence-structure evolutionary motif present in a large number of homologous protein pairs. The generative nature of our model enables us to evaluate its validity and its ability to simulate aspects of protein evolution conditioned on an amino acid sequence, a related amino acid sequence, a related structure or any combination thereof., Comment: 23 pages, 10 figures. Supplementary material: 5 pages, 4 figures

We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues of the Ornstein-Uhlenbeck process. Their likelihood function is a product of transition densities with no analytical expression, but that can be calculated by solving the Fokker-Planck equation numerically through adequate schemes. We propose three approximate likelihoods that are computationally tractable: (i) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji-Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate transition densities to the exact ones, and investigates the empirical performance of the approximate likelihoods. Finally, two diffusions are used to model the evolution of the backbone angles of the protein G (PDB identifier 1GB1) during a molecular dynamics simulation. The software package sdetorus implements the estimation methods and applications presented in the paper., 29 pages, 8 figures, 5 tables

Introduction Christophe Ley and Thomas Verdebout 1. Directional Statistics in Protein Bioinformatics Kanti V. Mardia, Jesper Illemann Foldager, and Jes Frellsen 2. Statistics of Orientations of Symmetrical Objects Richard Arnold and Peter Jupp 3. Correlated Cylindrical Data Francesco Lagona 4. Toroidal Diffusions and Protein Structure Evolution Eduardo Garcia-Portugues, Michael Golden, Michael Soerensen, Kanti V. Mardia, Thomas Hamelryck, Jotun Hein 5. Noisy Directional Data Thanh Mai Pham Ngoc 6. On Modelling of SE(3) Objects Louis-Paul Rivest and Karim Oualkacha 7. Spatial and Spatio-temporal Circular Processes with Application to Wave Direction Giovanna Jona-Lasinio, Alan E. Gelfand, and Gianluca Mastrantonio 8. Cylindrical Distributions and their Applications to Biological Data Toshihiro Abe & Ichiro Ken Shimatani 9. Directional Statistics for Wildfires Jose Ameijeiras-Alonso, Rosa M. Crujeiras, Alberto Rodriguez Casal 10. Bayesian Analysis of Circular Data in Social and Behavioural Sciences Irene Klugkist, Jolien Cremers, and Kees Mulder 11. Nonparametric Classification for Circular Data Marco Di Marzio, Stefania Fensore, and Charles C. Taylor 12. Directional Statistics in Machine Learning: A Brief Review Suvrit Sra 13. Applied Directional Statistics with R: an Overview Arthur Pewsey

Evaluating the model quality of protein structures that evolve in environments with particular physicochemical properties requires scoring functions that are adapted to their specific residue compositions and/or structural characteristics. Thus, computational methods developed for structures from the cytosol cannot work properly on membrane or secreted proteins. Here, we present MyPMFs, an easy-to-use tool that allows users to train statistical potentials of mean force (PMFs) on the protein structures of their choice, with all parameters being adjustable. We demonstrate its use by creating an accurate statistical potential for transmembrane protein domains. We also show its usefulness to study the influence of the physical environment on residue interactions within protein structures. Our open-source software is freely available for download at https://github.com/bibip-impmc/mypmfs .

This chapter shows how toroidal diffusions are convenient methodological tools for modelling protein evolution in a probabilistic framework. The chapter addresses the construction of ergodic diffusions with stationary distributions equal to well-known directional distributions, which can be regarded as toroidal analogues of the Ornstein-Uhlenbeck process. The important challenges that arise in the estimation of the diffusion parameters require the consideration of tractable approximate likelihoods and, among the several approaches introduced, the one yielding a specific approximation to the transition density of the wrapped normal process is shown to give the best empirical performance on average. This provides the methodological building block for Evolutionary Torus Dynamic Bayesian Network (ETDBN), a hidden Markov model for protein evolution that emits a wrapped normal process and two continuous-time Markov chains per hidden state. The chapter describes the main features of ETDBN, which allows for both "smooth" conformational changes and "catastrophic" conformational jumps, and several empirical benchmarks. The insights into the relationship between sequence and structure evolution that ETDBN provides are illustrated in a case study.

Methods of protein structure determination based on NMR chemical shifts are becoming increasingly common. The most widely used approaches adopt the molecular fragment replacement strategy, in which structural fragments are repeatedly reassembled into different complete conformations in molecular simulations. Although these approaches are effective in generating individual structures consistent with the chemical shift data, they do not enable the sampling of the conformational space of proteins with correct statistical weights. Here, we present a method of molecular fragment replacement that makes it possible to perform equilibrium simulations of proteins, and hence to determine their free energy landscapes. This strategy is based on the encoding of the chemical shift information in a probabilistic model in Markov chain Monte Carlo simulations. First, we demonstrate that with this approach it is possible to fold proteins to their native states starting from extended structures. Second, we show that the method satisfies the detailed balance condition and hence it can be used to carry out an equilibrium sampling from the Boltzmann distribution corresponding to the force field used in the simulations. Third, by comparing the results of simulations carried out with and without chemical shift restraints we describe quantitatively the effects that these restraints have on the free energy landscapes of proteins. Taken together, these results demonstrate that the molecular fragment replacement strategy can be used in combination with chemical shift information to characterize not only the native structures of proteins but also their conformational fluctuations.

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.

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. © 2013 Wiley Periodicals, Inc.

Protein structure prediction methods typically use statistical potentials, which rely on statistics derived from a database of know protein structures. In the vast majority of cases, these potentials involve pairwise distances or contacts between amino acids or atoms. Although some potentials beyond pairwise interactions have been described, the formulation of a general multibody potential is seen as intractable due to the perceived limited amount of data. In this article, we show that it is possible to formulate a probabilistic model of higher order interactions in proteins, without arbitrarily limiting the number of contacts. The success of this approach is based on replacing a naive table-based approach with a simple hierarchical model involving suitable probability distributions and conditional independence assumptions. The model captures the joint probability distribution of an amino acid and its neighbors, local structure and solvent exposure. We show that this model can be used to approximate the conditional probability distribution of an amino acid sequence given a structure using a pseudo-likelihood approach. We verify the model by decoy recognition and site-specific amino acid predictions. Our coarse-grained model is compared to state-of-art methods that use full atomic detail. This article illustrates how the use of simple probabilistic models can lead to new opportunities in the treatment of nonlocal interactions in knowledge-based protein structure prediction and design. Proteins 2013; 81:1340–1350. © 2013 Wiley Periodicals, Inc.

Despite the development of powerful computational tools, the full-sequence design of proteins still remains a challenging task. To investigate the limits and capabilities of computational tools, we conducted a study of the ability of the program Rosetta to predict sequences that recreate the authentic fold of thioredoxin. Focusing on the influence of conformational details in the template structures, we based our study on 8 experimentally determined template structures and generated 120 designs from each. For experimental evaluation, we chose six sequences from each of the eight templates by objective criteria. The 48 selected sequences were evaluated based on their progressive ability to (1) produce soluble protein in Escherichia coli and (2) yield stable monomeric protein, and (3) on the ability of the stable, soluble proteins to adopt the target fold. Of the 48 designs, we were able to synthesize 32, 20 of which resulted in soluble protein. Of these, only two were sufficiently stable to be purified. An X-ray crystal structure was solved for one of the designs, revealing a close resemblance to the target structure. We found a significant difference among the eight template structures to realize the above three criteria despite their high structural similarity. Thus, in order to improve the success rate of computational full-sequence design methods, we recommend that multiple template structures are used. Furthermore, this study shows that special care should be taken when optimizing the geometry of a structure prior to computational design when using a method that is based on rigid conformations.

Motivated by examples in protein bioinformatics, we study a mixture model of multivariate angular distributions. The distribution treated here (multivariate sine distribution) is a multivariate extension of the well-known von Mises distribution on the circle. The density of the sine distribution has an intractable normalizing constant and here we propose to replace it in the concentrated case by a simple approximation. We study the EM algorithm for this distribution and apply it to a practical example from protein bioinformatics.

Although Markov chain Monte Carlo (MC) simulation is a potentially powerful approach for exploring conformational space, it has been unable to compete with molecular dynamics (MD) in the analysis of high density structural states, such as the native state of globular proteins. Here, we introduce a kinetic algorithm, CRISP, that greatly enhances the sampling efficiency in all-atom MC simulations of dense systems. The algorithm is based on an exact analytical solution to the classic chain-closure problem, making it possible to express the interdependencies among degrees of freedom in the molecule as correlations in a multivariate Gaussian distribution. We demonstrate that our method reproduces structural variation in proteins with greater efficiency than current state-of-the-art Monte Carlo methods and has real-time simulation performance on par with molecular dynamics simulations. The presented results suggest our method as a valuable tool in the study of molecules in atomic detail, offering a potential alternative to molecular dynamics for probing long time-scale conformational transitions.

The motions of biological macromolecules are tightly coupled to their functions. However, while the study of fast motions has become increasingly feasible in recent years, the study of slower, biologically important motions remains difficult. Here, we present a method to construct native state ensembles of proteins by the combination of physical force fields and experimental data through modern statistical methodology. As an example, we use NMR residual dipolar couplings to determine a native state ensemble of the extensively studied third immunoglobulin binding domain of protein G (GB3). The ensemble accurately describes both local and nonlocal backbone fluctuations as judged by its reproduction of complementary experimental data. While it is difficult to assess precise time-scales of the observed motions, our results suggest that it is possible to construct realistic conformational ensembles of biomolecules very efficiently. The approach may allow for a dramatic reduction in the computational as well as experimental resources needed to obtain accurate conformational ensembles of biological macromolecules in a statistically sound manner.

The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble., Physical Chemistry Chemical Physics, 18 (8), ISSN:1463-9084, ISSN:1463-9076

Protein chemical shifts are routinely used to augment molecular mechanics force fields in protein structure simulations, with weights of the chemical shift restraints determined empirically. These weights, however, might not be an optimal descriptor of a given protein structure and predictive model, and a bias is introduced which might result in incorrect structures. In the inferential structure determination framework, both the unknown structure and the disagreement between experimental and back-calculated data are formulated as a joint probability distribution, thus utilizing the full information content of the data. Here, we present the formulation of such a probability distribution where the error in chemical shift prediction is described by either a Gaussian or Cauchy distribution. The methodology is demonstrated and compared to a set of empirically weighted potentials through Markov chain Monte Carlo simulations of three small proteins (ENHD, Protein G and the SMN Tudor Domain) using the PROFASI force field and the chemical shift predictor CamShift. Using a clustering-criterion for identifying the best structure, together with the addition of a solvent exposure scoring term, the simulations suggests that sampling both the structure and the uncertainties in chemical shift prediction leads more accurate structures compared to conventional methods using empirical determined weights. The Cauchy distribution, using either sampled uncertainties or predetermined weights, did, however, result in overall better convergence to the native fold, suggesting that both types of distribution might be useful in different aspects of the protein structure prediction.

The legume lectins are widely used as a model system for studying protein-carbohydrate and protein-protein interactions. They exhibit a fascinating quaternary structure variation, which becomes important when they interact with multivalent glycoconjugates, for instance those on cell surfaces. Recently, it has become clear that certain lectins form weakly associated oligomers. This phenomenon may play a role in the regulation of receptor crosslinking and subsequent signal transduction. The crystal structure of DB58, a dimeric lectin from the legume Dolichos biflorus reveals a separate dimer of a previously unobserved type, in addition to a tetramer consisting of two such dimers. This tetramer resembles that formed by DBL, the seed lectin from the same plant. A single amino acid substitution in DB58 affects the conformation and flexibility of a loop in the canonical dimer interface. This disrupts the formation of a stable DBL-like tetramer in solution, but does not prohibit its formation in suitable conditions, which greatly increases the possibilities for the crosslinking of multivalent ligands. The non-canonical DB58 dimer has a buried symmetrical α helix, which can be present in the crystal in either of two antiparallel orientations. Two existing structures and datasets for lectins with similar quaternary structures were reconsidered. A central α helix could be observed in the soybean lectin, but not in the leucoagglutinating lectin from Phaseolus vulgaris. The relative position and orientation of the carbohydrate-binding sites in the DB58 dimer may affect its ability to crosslink mulitivalent ligands, compared to the other legume lectin dimers.

Binding of multivalent glycoconjugates by lectins often leads to the formation of cross-linked complexes. Type I cross-links, which are one-dimensional, are formed by a divalent lectin and a divalent glycoconjugate. Type II cross-links, which are two or three-dimensional, occur when a lectin or glycoconjugate has a valence greater than two. Type II complexes are a source of additional specificity, since homogeneous type II complexes are formed in the presence of mixtures of lectins and glycoconjugates. This additional specificity is thought to become important when a lectin interacts with clusters of glycoconjugates, e.g. as is present on the cell surface. The cryst1al structure of the Glc/Man binding legume lectin FRIL in complex with a trisaccharide provides a molecular snapshot of how weak protein-protein interactions, which are not observed in solution, can become important when a cross-linked complex is formed. In solution, FRIL is a divalent dimer, but in the crystal FRIL forms a tetramer, which allows for the formation of an intricate type II cross-linked complex with the divalent trisaccharide. The dependence on weak protein-protein interactions can ensure that a specific type II cross-linked complex and its associated specificity can occur only under stringent conditions, which explains why lectins are often found forming higher-order oligomers.

Several novel structures of legume lectins have led to a thorough understanding of monosaccharide and oligosaccharide specificity, to the determination of novel and surprising quaternary structures and, most importantly, to the structural identification of the binding site for adenine and plant hormones. This deepening of our understanding of the structure/function relationships among the legume lectins is paralleled by advances in two other plant lectin families - the monocot lectins and the jacalin family. As the number of available crystal structures increases, more parallels between plant and animal lectins become apparent.

The crystal structures of concanavalin A in complex with Man(α1–6)Man(α1-O)Me and Man(α1–3)Man(α1-O)Me were determined at resolutions of 2.0 and 2.8 A, respectively. In both structures, the O-1-linked mannose binds in the conserved monosaccharide-binding site. The O-3-linked mannose of Man(α1–3)Man(α1-O)Me binds in the hydrophobic subsite formed by Tyr-12, Tyr-100, and Leu-99. The shielding of a hydrophobic surface is consistent with the associated large heat capacity change. The O-6-linked mannose of Man(α1–6)Man(α1-O)Me binds in the same subsite formed by Tyr-12 and Asp-16 as the reducing mannose of the highly specific trimannose Man(α1–3)[Man(α1–6)]Man(α1-O)Me. However, it is much less tightly bound. Its O-2 hydroxyl makes no hydrogen bond with the conserved water 1. Water 1 is present in all the sugar-containing concanavalin A structures and increases the complementarity between the protein-binding surface and the sugar, but is not necessarily a hydrogen-bonding partner. A water analysis of the carbohydrate-binding site revealed a conserved water molecule replacing O-4 on the α1–3-linked arm of the trimannose. No such water is found for the reducing or O-6-linked mannose. Our data indicate that the central mannose of Man(α1–3)[Man(α1–6)]Man(α1-O)Me primarily functions as a hinge between the two outer subsites.

The seed lectin (DBL) from the leguminous plant Dolichos biflorus has a unique specificity among the members of the legume lectin family because of its high preference for GalNAc over Gal. In addition, precipitation of blood group A+H substance by DBL is slightly better inhibited by a blood group A trisaccharide (GalNAc(α1-3)[Fuc(α1-2)]Gal) containing pentasaccharide, and about 40 times better by the Forssman disaccharide (GalNAc(α1-3)GalNAc) than by GalNAc. We report the crystal structures of the DBL-blood group A trisaccharide complex and the DBL-Forssman disaccharide complex. A comparison with the binding sites of Gal-binding legume lectins indicates that the low affinity of DBL for Gal is due to the substitution of a conserved aromatic residue by an aliphatic residue (Leu127). Binding studies with a Leu127Phe mutant corroborate these conclusions. DBL has a higher affinity for GalNAc because the N-acetyl group compensates for the loss of aromatic stacking in DBL by making a hydrogen bond with the backbone amide group of Gly103 and a hydrophobic contact with the side-chains of Trp132 and Tyr104. Some legume lectins possess a hydrophobic binding site that binds adenine and adenine-derived plant hormones, i.e. cytokinins. The exact function of this binding site is unknown, but adenine/cytokinin-binding legume lectins might be involved in storage of plant hormones or plant growth regulation. The structures of DBL in complex with adenine and of the dimeric stem and leaf lectin (DB58) from the same plant provide the first structural data on these binding sites. Both oligomers possess an unusual architecture, featuring an α-helix sandwiched between two monomers. In both oligomers, this α-helix is directly involved in the formation of the hydrophobic binding site. DB58 adopts a novel quaternary structure, related to the quaternary structure of the DBL heterotetramer, and brings the number of know legume lectin dimer types to four.

The legume lectins are a family of carbohydrate binding proteins found in the Leguminosae plants and are used as a model system for studying protein-carbohydrate interactions. The different legume lectins show a remarkable range of sugar specificities, despite the high sequential and structural similarity of their subunits. Moreover, their subunits can associate into a number of different multimers. The unique variability of quaternary structure has implications for the formation of cross-linked lattices and binding of hydrophobic ligands.

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 (h3JNC') 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 refine protein structures to 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., Comment: PLOS ONE accepted, Nov 2013

Inference of protein structure from experimental data is of crucial interest in science, medicine and biotechnology. Low-resolution methods, such as small angle X-ray scattering (SAXS), play a major role in investigating important biological questions regarding the structure of proteins in solution.To infer protein structure from SAXS data, it is necessary to calculate the expected experimental observations given a protein structure, by making use of a so-called forward model. This calculation needs to be performed many times during a conformational search. Therefore, computational efficiency directly determines the complexity of the systems that can be explored.We present an efficient implementation of the forward model for SAXS with full hardware utilization of Graphics Processor Units (GPUs). The proposed algorithm is orders of magnitude faster than an efficient CPU implementation, and implements a caching procedure employed in the partial forward model evaluations within a Markov chain Monte Carlo framework.