Ever since the seminal work of Zuker and Stiegler, the field of RNA bioinformatics has been characterized by a strong emphasis on the secondary structure. This discrete abstraction of the 3D conformation of RNA has paved the way for a development of quantitative approaches in RNA computational biology, revealing unexpected connections between combinatorics and molecular biology. Using our strong background in enumerative combinatorics, we propose generic and efficient algorithms, both for sampling and counting structures using dynamic programming. These general techniques have been applied to study the sequence-structure relationship  , the correction of pyrosequencing errors  , and the efficient detection of multi-stable RNAs (riboswitches)  , .

It is a natural pursue to build on our understanding of the secondary structure to construct artificial RNAs performing predetermined functions, ultimately targeting therapeutic and synthetic biology applications. Towards this goal, a key element is the design of RNA sequences that fold into a predetermined secondary structure, according to established energy models (inverse-folding problem). Quite surprisingly, and despite two decades of studies of the problem, the computational complexity of the inverse-folding problem is currently unknown.

Within our group, we offer a new methodology, based on weighted random generation  and multidimensional Boltzmann sampling, for this problem. Initially lifting the constraint of folding back into the target structure, we explored the random generation of sequences that are compatible with the target, using a probability distribution which favors exponentially sequences of high affinity towards the target. A simple posterior rejection step selects sequences that effectively fold back into the latter, resulting in a global sampling pipeline that showed comparable performances to its competitors based on local search  .

The modeling of large RNA 3D structures, that is predicting the three-dimensional structure of a given RNA sequence, relies on two complementary approaches. The approach by homology is used when the structure of a sequence homologous to the sequence of interest has already been resolved experimentally. The main problem then is to calculate an alignment between the known structure and the sequence. The ab initio approach is required when no homologous structure is known for the sequence of interest (or for some parts of it). We work in both directions.

Despite being able to correctly model small globular proteins, the computational structural biology community still craves for efficient force fields and scoring functions for prediction but also good sampling and dynamics strategies.

Our current and future efforts towards knowledge-based scoring function and ion location prediction have been described in .

Over the last two decades a strong connection between robotics and computational structural biology has emerged, in which internal coordinates of proteins are interpreted as a kinematic linkage with rotatable bonds as joints and corresponding groups of atoms as links , , , . Initially, fragments in proteins limited to tens of residues were modeled as a kinematic linkage, but this approach has been extended to encompass (multi-domain) proteins . For RNA, progress in this direction has been realized as well. A kinematics-based conformational sampling algorithm, KGS, for loops was recently developed , but it does not fully utilize the potential of a kinematic model. It breaks and recloses loops using six torsional degrees of freedom, which results in a finite number of solutions. The discrete nature of the solution set in the conformational space makes difficult an optimization of a target function with a gradient descent method. Our methods overcome this limitation by performing a conformational sampling and optimization in a co-dimension 6 subspace. Fragments remain closed, but these methods are limited to proteins. Our objective is to extend the approach proposed in , to nucleic acids and protein/nucleic acid complexes with a view towards improving structure determination of nucleic acids and their complexes and in silico docking experiments of protein/RNA complexes. For that purpose, we have developed a generic strategy for differentiable statistical potentials , that can be directly integrated in the procedure.

Results from in silico docking experiments will also directly benefit structure determination of complexes which, in turn, will provide structural insights in nucleic acid and protein/nucleic acid complexes. From the small proof-of-concept single chain protein implementation of the KGS strategy, we have developed a robust preliminary implementation that can handle RNA and will be further developed to account for multi-chain molecules. Rasmus Fonseca, post-doctoral scholar in the project is currently performing an extensive computational and biological validation.

Besides applications of analytic combinatorics to computational biology problems, the team addressed general combinatorial problems on words and fundamental issues on languages and data structures.

Molecular interactions often involve specific motifs. One may cite protein-DNA (cis-regulation), protein-protein (docking), RNA-RNA (miRNA, frameshift, circularisation). Motif detection combines an algorithmic search of potential sites and a significance assessment. Assessment significance requires a quantitative criterium. It is generally accepted that the p-value is a reliable tool that outperforms older criteria such as the z-score. Amib develops a long term research on word combinatorics. In the recent years, a general scheme of derivation of analytic formula for the pvalue under different constraints ($k$-occurrence, first occurrence, overrepresentation in large sequences,...) has been provided. It relies on a representation of word overlaps in a graph . Recursive equations to compute pvalues may be reduced to a traversal of that graph, leading to a linear algorithm. It allows for a derivation of pvalues, decreasing the space and time complexity of the generating function approach or previous probabilistic weighted automata.

In the mean time, continuous sequences of overlapping words, currently named clumps or clusters turn out to be crucial in random words counting. Notably, they play a fundamental role in the Chen-Stein method of compound Poisson approximation. A first characterization was proposed by Nicodème and al. and this work is currently extended.

This research area is widened by new problems arising from de novo genome assembly or re-assembly. For example, unique mappability of short reads strongly depends of the repetition of words. Although the average values for the length have been studied for long under different constraints, their distribution or profile remained unknown until the seminal paper which provides formulae for binary tries. A collaboration has been started with Lob at Ecole Polytechnique to check these formulae on real data, namely Archae genomes (internship of D. Busatto-Gaston). This collaboration has been extended since Lob bought a sequencing machineand a co-advisd thesis (Alice Héliou) on circular RNA characterization hasjust started.

As a third example, one objective is to develop a model of errors, including a statistical model, that takes into account the quality of data for the different sequencing technologies, and their volume. This is the subject of an international collaboration with V. Makeev's lab (IoGene, Moscow) and Magnome project-team. Finally, Next Generation Sequencing open the way to the study of structural variants in the genome, as recently described in . Defining a probabilistic model that takes into account main dependencies -such as the GC content- is a task of D. Iakovishina's thesis, to be defended in 2015, in a collaboration with V. Boeva (Curie Institute).

Analytical methods may fail when both sequential and structural constraints of sequences are to be modelled or, more generally, when molecular structures such as RNA structures have to be handled. The random generation of combinatorial objects is a natural, alternative, framework to assess the significance of observed phenomena. General and efficient techniques have been developed over the last decades to draw objects uniformly at random from an abstract specification. However, in the context of biological sequences and structures, the uniformity assumption becomes unrealistic, and one has to consider non-uniform distributions in order to derive relevant estimates. Typically, context-free grammars can handle certain kinds of long-range interactions such as base pairings in secondary RNA structures.

In 2005, a new paradigm appeared in the ab initio secondary structure prediction : instead of formulating the problem as a classic optimization, this new approach uses statistical sampling within the space of solutions. Besides giving better, more robust, results, it allows for a fruitful adaptation of tools and algorithms derived in a purely combinatorial setting. Indeed, we have done significant and original progress in this area recently  , , including combinatorial models for structures with pseudoknots. Our aim is to combine this paradigm with a fragment based approach for decomposing structures, such as the cycle decomposition used within F. Major's group  .

Besides, our work on random generation is also applied in a different fields, namely software testing and model-checking, in a continuing collaboration with the Fortesse group at Lri  , .

Protein structure prediction has been and still is extensively studied. Computational approaches have shown interesting results for globular proteins but transmembrane proteins remain a difficult case.

Transmembrane beta-barrel proteins (TMB) account for 20 to 30% of identified proteins in a genome but, due to difficulties with standard experimental techniques, they are only 2% of the RCSB Protein Data Bank. As TMB perform many vital functions, the prediction of their structure is a challenge for life sciences, while the small number of known structures prohibits knowledge-based methods for structure prediction.

As barrel proteins are strongly structured objects, model based methodologies are an interesting alternative to these conventional methods. Jérome Waldisphül's thesis at Lix had opened this track for the common case where a protein folds respecting the order of the sequence, leaving a structure where each strand is bound to the preceding and succeeding ones. The matching constraints were expressed by a grammatical model, for which relatively simple dynamic programming schemes exist.

However, more sophisticated schemes are required when the arrangements of the strands along the barrel do not follow their order in the sequence, as it is the case for Greek key or Jelly roll motifs. The prediction algorithm may then be driven by a permutation on the order of the bonded strands. In his thesis , Van Du Tran developed a methodology for compiling a given permutation into a dynamic programming scheme that may predict the folding of sequences into the corresponding TMB secondary structure. Polynomial complexity upper bounds follow from the calculated DP scheme. Through tree decompositions of the graph that expresses constraints between strands in the barrel, better schemes were investigated in .

The efficiently obtained 3D structures provide a good model for further 3D and interaction analyses.

To better model complexes, various aspects of the scoring problem for protein-protein docking need being addressed . It is also of great interest to introduce a hierarchical analysis of the original complex three-dimensional structures used for learning, obtained by clustering.

A protein-protein docking procedure traditionally consists in two successive tasks: a search algorithm generates a large number of candidate solutions, and then a scoring function is used to rank them in order to extract a native-like conformation. We demonstrated that, using Voronoi constructions and a defined set of parameters, we could optimize an accurate scoring function and interaction detection . We also focused on developing other geometric constructions for that purpose: being related to the Voronoi construction, the Laguerre tessellation was expected to better represent the physico-chemical properties of the partners. It also allows a fast computation without losing the intrinsic properties of the biological objects. In , we compare both constructions. We also worked on introducing a hierarchical analysis of the original complex three-dimensional structures used for learning, obtained by clustering. Using this clustering model, in combination with a strong emphasis on the design of efficient complex filters collaborative filtering, we can optimize the scoring functions and get more accurate solutions .

These techniques have been extended to the analysis of protein-nucleic acid complexes : developments and tests are performed by A. Guilhot (See figure ) in his PhD thesis.

Scientific workflows management systems are increasingly used to specify and manage bioinformatics experiments. Their programming model appeals to bioinformaticians, who use them to easily specify complex data processing pipelines. Such a model is underpinned by a graph structure, where nodes represent bioinformatics tasks and links represent the dataflow. As underlined both in a study and a review of existing approaches, the complexity of such graph structures is increasing over time, making them more difficult to share and reuse.

One of the major current challenges is thus to provide means to reduce the structural complexity of workflows while ensuring that any structural transformation will not have any impact on the executions of the transformed workflows, that is, preserving provenance.

We are addressing the increase of the number of resources available. The BioGuide project aim at helping user navigation in the maze of available biological sources. More recently, a second problem was tackled: the number of answers returned by even one single queried biological resource may be too large for the user to deal with. We have provided solutions for ranking biological data. The main difficulty lies in considering various ranking criteria (recent data first, popular data first, curated data first...). Many approaches combine ranking criteria to design a ranking function, possibly leading to arbitrary choices made in the way of combining the ranking criteria. Instead, in collaboration with the University of Montreal, we have proposed to follow a median ranking approach named BioConsert (for generating Biological Consensus ranking with ties): considering as many rankings as they are ranking criteria for the same data set, and providing a consensus ranking that minimizes the disagreements between the input rankings. We have shown the benefit of using median ranking in several biological settings.

Additionally, in a close collaboration with the Institut Curie, we have also developed the GeneValorization tool that ranks a list of genes of interest given as input with respect to a set of keywords representing the context of study. Here the single ranking criterion considered for each gene is the number of publications in PubMed co-citing the gene name and the keywords. The tool is able to make use of the MeSH taxonomy when considering the keywords and the dictionary of gene names and aliases for the gene names.

Elementary flux mode analysis is a powerful tool for the theoretical study of simple metabolic networks. However, when the networks are complex, the determination of elementary flux modes leads to a combinatorial explosion of their number which prevents from drawing simple conclusions from their analysis. Since the concept of elementary flux mode analysis was introduced in 1994, there has been an important and ongoing effort to develop more efficient algorithms. However, these methods share a common bottleneck: they enumerate all the elementary flux modes which make the computation impossible when the metabolic network is large and only few works try to search only elementary flux mode with specific properties. We have shown that enumerating all the elementary flux modes is not necessary in many cases and it is possible to directly query the network instead with an appropriate tool. For ensuring a good query time, we have relied on a state of the art SAT solver, working on a propositional encoding of elementary flux mode, and enriched with a simple SMT-like solver ensuring elementary flux mode consistency with stoichiometric constraints. We have illustrated our new framework by providing experimental evidences of almost immediate answer times on a non trivial metabolic network  , .

Signaling pathways involving G protein-coupled receptors (GPCR) are excellent targets in pharmacogenomics research. Large amounts of experiments are available in this context while globally interpreting all the experimental data remains a very challenging task for biologists. Our goal is to help the understanding of signaling pathways involving (GPCR) and to provide means to semi-automatically construct the signaling networks.

We have introduced a logic-based method to infer molecular networks and show how it allows inferring signaling networks from the design of a knowledge base. Provenance of inferred data has been carefully collected, allowing quality evaluation. Our method (i) takes into account various kinds of biological experiments and their origin; (ii) mimics the scientist’s reasoning within a first-order logic setting; (iii) specifies precisely the kind of interaction between the molecules; (iv) provides the user with the provenance of each interaction; (v) automatically builds and draws the inferred network .

Observe that a logic-based formalisation is used as in some works carried out in Inria team Dyliss. Amib aim is different, as the design of the network lies on a knowledge-based system describing experimental facts and ontological relationships on backgound knowledge, together with a set of generic and expressive rules, that mimick the expert's reasoning.

This is a collaboration with A. Poupon (Inra-Bios, Tours) that was supported by an Inra-Inria starting grant in 2011-2012.

A great number of methods have been proposed for the study of the behavior of large biological systems. The first one is based on a discrete and direct simulation of the various interactions between the reactants using an entity-centered approach; the second one implements a very efficient variant of the Gillespie stochastic algorithm that can be mixed with the entity-centered method to get the best of both worlds; the third one uses differential equations automatically generated from the set of reactions defining the network.

These three methods have been implemented in an integrated tool, the Hsim system  . It mimics the interactions of biomolecules in an environment modelling the membranes and compartments found in real cells. It has been applied to the modelling of the circadian clock of the cyanobacterium, and we have shown pertinent results regarding the spontaneous appearance of oscillations and the factors governing their period  .