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The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using 'morphing' techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http://lorentz.dynstr.pasteur.fr/joel/index.php.

Coarse‐grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff‐based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay‐based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B‐factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non‐linear optimization problem whose parameters describe both rigid‐body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes. [ABSTRACT FROM AUTHOR]

Knowledge-based potentials are energy functions derived from the analysis of databases of protein structures and sequences. They can be divided into two classes. Potentials from the first class are based on a direct conversion of the distributions of some geometric properties observed in native protein structures into energy values, while potentials from the second class are trained to mimic quantitatively the geometric differences between incorrectly folded models and native structures. In this paper, we focus on the relationship between energy and geometry when training the second class of knowledge-based potentials. We assume that the difference in energy between a decoy structure and the corresponding native structure is linearly related to the distance between the two structures. We trained two distance-based knowledge-based potentials accordingly, one based on all inter-residue distances (PPD), while the other had the set of all distances filtered to reflect consistency in an ensemble of decoys (PPE). We tested four types of metric to characterize the distance between the decoy and the native structure, two based on extrinsic geometry (RMSD and GTD-TS*), and two based on intrinsic geometry (Q* and MT). The corresponding eight potentials were tested on a large collection of decoy sets. We found that it is usually better to train a potential using an intrinsic distance measure. We also found that PPE outperforms PPD, emphasizing the benefits of capturing consistent information in an ensemble. The relevance of these results for the design of knowledge-based potentials is discussed. [ABSTRACT FROM AUTHOR]

Elastic network models (ENM) are based on the idea that the geometry of a protein structure provides enough information for computing its fluctuations around its equilibrium conformation. This geometry is represented as an elastic network (EN) that is, a network of links between residues. A spring is associated with each of these links. The normal modes of the protein are then identified with the normal modes of the corresponding network of springs. Standard approaches for generating ENs rely on a cutoff distance. There is no consensus on how to choose this cutoff. In this work, we propose instead to filter the set of all residue pairs in a protein using the concept of alpha shapes. The main alpha shape we considered is based on the Delaunay triangulation of the Cα positions; we referred to the corresponding EN as EN( ∞). We have shown that heterogeneous anisotropic network models, called αHANMs, that are based on EN( ∞) reproduce experimental B-factors very well, with correlation coefficients above 0.99 and root-mean-square deviations below 0.1 Å2 for a large set of high resolution protein structures. The construction of EN( ∞) is simple to implement and may be used automatically for generating ENs for all types of ENMs. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We propose a new analytical method for detecting and computing contacts between atoms in biomolecules. It is based on the alpha shape theory and proceeds in three steps. First, we compute the weighted Delaunay triangulation of the union of spheres representing the molecule. In the second step, the Delaunay complex is filtered to derive the dual complex. Finally, contacts between spheres are collected. In this approach, two atoms i and j are defined to be in contact if their centers are connected by an edge in the dual complex. The contact areas between atom i and its neighbors are computed based on the caps formed by these neighbors on the surface of i; the total area of all these caps is partitioned according to their spherical Laguerre Voronoi diagram on the surface of i. This method is analytical and its implementation in a new program BallContact is fast and robust. We have used BallContact to study contacts in a database of 1551 high resolution protein structures. We show that with this new definition of atomic contacts, we generate realistic representations of the environments of atoms and residues within a protein. In particular, we establish the importance of nonpolar contact areas that complement the information represented by the accessible surface areas. This new method bears similarity to the tessellation methods used to quantify atomic volumes and contacts, with the advantage that it does not require the presence of explicit solvent molecules if the surface of the protein is to be considered. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Insoluble proteins dissolved in unsalted water appear to have no well-folded tertiary structures. This raises a fundamental question as to whether being unstructured is due to the absence of salt ions. To address this issue, we solubilized the insoluble ephrin-B2 cytoplasmic domain in unsalted water and first confirmed using NMR spectroscopy that it is only partially folded. Using NMR HSQC titrations with 14 different salts, we further demonstrate that the addition of salt triggers no significant folding of the protein within physiologically relevant ion concentrations. We reveal however that their 8 anions bind to the ephrin-B2 protein with high affinity and specificity at biologically-relevant concentrations. Interestingly, the binding is found to be both salt- and residue-specific. [Copyright &y& Elsevier]

Assembling fragments from known protein structures is a widely used approach to construct structural models for new proteins. We describe an application of this idea to an important inverse kinematics problem in structural biology: the loop closure problem. We have developed an algorithm for generating the conformations of candidate loops that fit in a gap of given length in a protein structure framework. Our method proceeds by concatenating small fragments of protein chosen from small libraries of representative fragments. Our approach has the advantages of ab initio methods since we are able to enumerate all candidate loops in the discrete approximation of the conformational space accessible to the loop, as well as the advantages of database search approach since the use of fragments of known protein structures guarantees that the backbone conformations are physically reasonable. We test our approach on a set of 427 loops, varying in length from four residues to 14 residues. The quality of the candidate loops is evaluated in terms of global coordinate root mean square (cRMS). The top predictions vary between 0.3 and 4.2 Å for four-residue loops and between 1.5 and 3.1 Å far 14-residue loops, respectively. [ABSTRACT FROM AUTHOR]

Residues in proteins that are in close spatial proximity are more prone to covariate as their interactions are likely to be preserved due to structural and evolutionary constraints. If we can detect and quantify such covariation, physical contacts may then be predicted in the structure of a protein solely from the sequences that decorate it. To carry out such predictions, and following the work of others, we have implemented a multivariate Gaussian model to analyze correlation in multiple sequence alignments. We have explored and tested several numerical encodings of amino acids within this model. We have shown that 1D encodings based on amino acid biochemical and biophysical properties, as well as higher dimensional encodings computed from the principal components of experimentally derived mutation/substitution matrices, do not perform as well as a simple twenty dimensional encoding with each amino acid represented with a vector of one along its own dimension and zero elsewhere. The optimum obtained from representations based on substitution matrices is reached by using 10 to 12 principal components; the corresponding performance is less than the performance obtained with the 20-dimensional binary encoding. We highlight also the importance of the prior when constructing the multivariate Gaussian model of a multiple sequence alignment. [ABSTRACT FROM AUTHOR]

Abstract: Finding structural similarities between proteins often helps reveal shared functionality, which otherwise might not be detected by native sequence information alone. Such similarity is usually detected and quantified by protein structure alignment. Determining the optimal alignment between two protein structures, however, remains a hard problem. An alternative approach is to approximate each three-dimensional protein structure using a sequence of motifs derived from a structural alphabet. Using this approach, structure comparison is performed by comparing the corresponding motif sequences or structural sequences. In this article, we measure the performance of such alphabets in the context of the protein structure classification problem. We consider both local and global structural sequences. Each letter of a local structural sequence corresponds to the best matching fragment to the corresponding local segment of the protein structure. The global structural sequence is designed to generate the best possible complete chain that matches the full protein structure. We use an alphabet of 20 letters, corresponding to a library of 20 motifs or protein fragments having four residues. We show that the global structural sequences approximate well the native structures of proteins, with an average coordinate root mean square of 0.69 Å over 2225 test proteins. The approximation is best for all α-proteins, while relatively poorer for all β-proteins. We then test the performance of four different sequence representations of proteins (their native sequence, the sequence of their secondary-structure elements, and the local and global structural sequences based on our fragment library) with different classifiers in their ability to classify proteins that belong to five distinct folds of CATH. Without surprise, the primary sequence alone performs poorly as a structure classifier. We show that addition of either secondary-structure information or local information from the structural sequence considerably improves the classification accuracy. The two fragment-based sequences perform better than the secondary-structure sequence but not well enough at this stage to be a viable alternative to more computationally intensive methods based on protein structure alignment. [Copyright &y& Elsevier]

Abstract: Distance-dependent, pairwise, statistical potentials are based on the concept that the packing observed in known protein structures can be used as a reference for comparing different 3D models for a protein. Here, packing refers to the set of all pairs of atoms in the molecule. Among all methods developed to assess three-dimensional models, statistical potentials are subject both to praise for their power of discrimination, and to criticism for the weaknesses of their theoretical foundations. Classical derivations of pairwise potentials assume statistical independence of all pairs of atoms. This assumption, however, is not valid in general. We show that we can filter the list of all interactions in a protein to generate a much smaller subset of pairs that retains most of the structural information contained in proteins. The filter is based on a geometric method called alpha shapes that captures the packing in a conformation. Statistical scoring functions derived from such subsets perform as well as scoring functions derived from the set of all pairwise interactions. [Copyright &y& Elsevier]

Abstract: Phycocyanobilin:ferredoxin oxidoreductase (PcyA) catalyzes the proton-coupled four-electron reduction of biliverdin IXα’s two vinyl groups to produce phycocyanobilin, an essential chromophore for phytochromes, cyanobacteriochromes and phycobiliproteins. Previous site directed mutagenesis studies indicated that the fully conserved residue His74 plays a critical role in the H-bonding network that permits proton transfer. Here, we exploit X-ray crystallography, enzymology and molecular dynamics simulations to understand the functional role of this invariant histidine. The structures of the H74A, H74E and H74Q variants of PcyA reveal that a “conserved” buried water molecule that bridges His74 and catalytically essential His88 is not required for activity. Despite distinct conformations of Glu74 and Gln74 in the H74E and H74Q variants, both retain reasonable activity while the H74A variant is inactive, suggesting smaller residues may generate cavities that increase flexibility, thereby reducing enzymatic activity. Molecular dynamic simulations further reveal that the crucial active site residue Asp105 is more dynamic in H74A compared to wild-type PcyA and the two other His74 variants, supporting the conclusion that the Ala74 mutation has increased the flexibility of the active site. [Copyright &y& Elsevier]