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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.

RNA SHAPE experiments have become important and successful sources of information for RNA structure prediction. In such experiments, chemical reagents are used to probe RNA backbone flexibility at the nucleotide level, which in turn provides information on base pairing and therefore secondary structure. Little is known, however, about the statistics of such SHAPE data. In this work, we explore different representations of noise in SHAPE data and propose a statistically sound framework for extracting reliable reactivity information from multiple SHAPE replicates. Our analyses of RNA SHAPE experiments underscore that a normal noise model is not adequate to represent their data. We propose instead a log-normal representation of noise and discuss its relevance. Under this assumption, we observe that processing simulated SHAPE data by directly averaging different replicates leads to bias. Such bias can be reduced by analyzing the data following a log transformation, either by log-averaging or Kalman filtering. Application of Kalman filtering has the additional advantage that a prior on the nucleotide reactivities can be introduced. We show that the performance of Kalman filtering is then directly dependent on the quality of that prior. We conclude the paper with guidelines on signal processing of RNA SHAPE data.

Background Alignment-free methods for comparing protein sequences have proved to be viable alternatives to approaches that first rely on an alignment of the sequences to be compared. Much work however need to be done before those methods provide reliable fold recognition for proteins whose sequences share little similarity. We have recently proposed an alignment-free method based on the concept of string kernels, SeqKernel (Nojoomi and Koehl, BMC Bioinformatics, 2017, 18:137). In this previous study, we have shown that while Seqkernel performs better than standard alignment-based methods, its applications are potentially limited, because of biases due mostly to sequence length effects. Methods In this study, we propose improvements to SeqKernel that follows two directions. First, we developed a weighted version of the kernel, WSeqKernel. Second, we expand the concept of string kernels into a novel framework for deriving information on amino acids from protein sequences. Results Using a dataset that only contains remote homologs, we have shown that WSeqKernel performs remarkably well in fold recognition experiments. We have shown that with the appropriate weighting scheme, we can remove the length effects on the kernel values. WSeqKernel, just like any alignment-based sequence comparison method, depends on a substitution matrix. We have shown that this matrix can be optimized so that sequence similarity scores correlate well with structure similarity scores. Starting from no information on amino acid similarity, we have shown that we can derive a scoring matrix that echoes the physico-chemical properties of amino acids. Conclusion We have made progress in characterizing and parametrizing string kernels as alignment-based methods for comparing protein sequences, and we have shown that they provide a framework for extracting sequence information from structure. Electronic supplementary material The online version of this article (doi:10.1186/s12859-017-1795-5) contains supplementary material, which is available to authorized users.

We propose a new method inspired from statistical mechanics for extracting geometric information from undirected binary networks and generating random networks that conform to this geometry. In this method an undirected binary network is perceived as a thermodynamic system with a collection of permuted adjacency matrices as its states. The task of extracting information from the network is then reformulated as a discrete combinatorial optimization problem of searching for its ground state. To solve this problem, we apply multiple ensembles of temperature regulated Markov chains to establish an ultrametric geometry on the network. This geometry is equipped with a tree hierarchy that captures the multiscale community structure of the network. We translate this geometry into a Parisi adjacency matrix, which has a relative low energy level and is in the vicinity of the ground state. The Parisi adjacency matrix is then further optimized by making block permutations subject to the ultrametric geometry. The optimal matrix corresponds to the macrostate of the original network. An ensemble of random networks is then generated such that each of these networks conforms to this macrostate; the corresponding algorithm also provides an estimate of the size of this ensemble. By repeating this procedure at different scales of the ultrametric geometry of the network, it is possible to compute its evolution entropy, i.e. to estimate the evolution of its complexity as we move from a coarse to a fine description of its geometric structure. We demonstrate the performance of this method on simulated as well as real data networks.

Background: The problem of determining the physical conformation of a protein dimer, given the structures of the two interacting proteins in their unbound state, is a difficult one. The location of the docking interface is determined largely by geometric complementarity, but finding complementary geometry is complicated by the flexibility of the backbone and side-chains of both proteins. We seek to generate candidates for docking that approximate the bound state well, even in cases where there is backbone and/or side-chain difference from unbound to bound states. Results: We divide the surfaces of each protein into local patches and describe the effect of side-chain flexibility on each patch by sampling the space of conformations of its side-chains. Likely positions of individual side-chains are given by a rotamer library; this library is used to derive a sample of possible mutual conformations within the patch. We enforce broad coverage of torsion space. We control the size of the sample by using energy criteria to eliminate unlikely configurations, and by clustering similar configurations, resulting in 50 candidates for a patch, a manageable number for docking. Conclusions: Using a database of protein dimers for which the bound and unbound structures of the monomers are known, we show that from the unbound patch we are able to generate candidates for docking that approximate the bound structure. In patches where backbone change is small (within 1 A RMSD of bound), we are able to account for flexibility and generate candidates that are good approximations of the bound state (82% are within 1 A and 98% are within 1.4 A RMSD of the bound conformation). We also find that even in cases of moderate backbone flexibility our candidates are able to capture some of the overall shape change. Overall, in 650 of 700 test patches we produce a candidate that is either within 1 A RMSD of the bound conformation or is closer to the bound state than the unbound is. Background This paper concerns one aspect of the problem of predicting the interface region of two docking proteins, namely the flexibility of side-chains. We consider sampling the possible side-chain conformations to improve the match of local shape complementarity. The main challenge we face is reducing the exponential complexity of the conformation space to a reasonably sized sample. Proteins are at the heart of all biological processes, and their functions are largely determined by their geometric structures. The number of biomolecular protein complexes is expected to be far more than the number of individual proteins in a given proteome; in addition, their structures are more difficult to obtain through NMR and X-ray crystallographic studies. So the difficult problem of docking, that is, the computational prediction of a protein complex from the structures of its constituent proteins, is an important focus of current research. The constituent structures may be determined experimentally or may be computed by a protein structure prediction algorithm. Docking is a difficult problem and it has received much attention [1-6]. In the docked configuration, two proteins demonstrate excellent shape complementarity, with the molecular surfaces matching each other closely over an interface region which is several square A in area. This excellent fit is difficult to find, however, since

International audience; 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.