Algorithmic Graph Theory, Reinforcement Learning and Game Theory in MD Simulations: From 3D Structures to Topological 2D-Molecular Graphs (2D-MolGraphs) and Vice Versa.

This paper reviews graph-theory-based methods that were recently developed in our group for post-processing molecular dynamics trajectories. We show that the use of algorithmic graph theory not only provides a direct and fast methodology to identify conformers sampled over time but also allows to follow the interconversions between the conformers through graphs of transitions in time. Examples of gas phase molecules and inhomogeneous aqueous solid interfaces are presented to demonstrate the power of topological 2D graphs and their versatility for post-processing molecular dynamics trajectories. An even more complex challenge is to predict 3D structures from topological 2D graphs. Our first attempts to tackle such a challenge are presented with the development of game theory and reinforcement learning methods for predicting the 3D structure of a gas-phase peptide.

On the predictibility of A-minor motifs from their local contexts.

This study investigates the importance of the structural context in the formation of a type I/II A-minor motif. This very frequent structural motif has been shown to be important in the spatial folding of RNA molecules. We developed an automated method to classify A-minor motif occurrences according to their 3D context similarities, and we used a graph approach to represent both the structural A-minor motif occurrences and their classes at different scales. This approach leads us to uncover new subclasses of A-minor motif occurrences according to their local 3D similarities. The majority of classes are composed of homologous occurrences, but some of them are composed of non-homologous occurrences. The different classifications we obtain allow us to better understand the importance of the context in the formation of A-minor motifs. In a second step, we investigate how much knowledge of the context around an A-minor motif can help to infer its presence (and position). More specifically, we want to determine what kind of information, contained in the structural context, can be useful to characterize and predict A-minor motifs. We show that, for some A-minor motifs, the topology combined with a sequence signal is sufficient to predict the presence and the position of an A-minor motif occurrence. In most other cases, these signals are not sufficient for predicting the A-minor motif, however we show that they are good signals for this purpose. All the classification and prediction pipelines rely on automated processes, for which we describe the underlying algorithms and parameters.

GARN2: coarse-grained prediction of 3D structure of large RNA molecules by regret minimization.

MOTIVATION: Predicting the 3D structure of RNA molecules is a key feature towards predicting their functions. Methods which work at atomic or nucleotide level are not suitable for large molecules. In these cases, coarse-grained prediction methods aim to predict a shape which could be refined later by using more precise methods on smaller parts of the molecule. RESULTS: We developed a complete method for sampling 3D RNA structure at a coarse-grained model, taking a secondary structure as input. One of the novelties of our method is that a second step extracts two best possible structures close to the native, from a set of possible structures. Although our method benefits from the first version of GARN, some of the main features on GARN2 are very different. GARN2 is much faster than the previous version and than the well-known methods of the state-of-art. Our experiments show that GARN2 can also provide better structures than the other state-of-the-art methods. AVAILABILITY AND IMPLEMENTATION: GARN2 is written in Java. It is freely distributed and available at http://garn.lri.fr/. CONTACT: melanie.boudard@lri.fr or johanne.cohen@lri.fr. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Can one and two-dimensional solid-state NMR fingerprint zeolite framework topology?

In this contribution, we have explored the potential and strength of one-dimensional (1D) (29)Si and two-dimensional (2D) (29)S-(29)Si and (29)Si-(17)O NMR as invariants of non-oriented graph for fingerprinting zeolite frameworks. 1D and 2D (29)Si NMR can indeed provide indications on the graph vertices, edges and allow the construction of the adjacency matrix, i.e. the set of connections between the graph vertices. From the structural data, hypothetical 1D (29)Si and 2D (29)Si-(29)Si NMR signatures for 193 of the zeolite frameworks reported in the Atlas of Zeolite Structures have been generated. Comparison between all signatures shows that thanks to the 1D (29)Si NMR data only, almost 20% of the known zeolite frameworks could be distinguished. Further NMR signatures were generated by taking into account 2D (29)Si-(29)Si and (29)Si-(17)O correlations. By sorting and comparison of all the NMR data, up to 80% of the listed zeolites could be unambiguously discriminated. This work indicates that (i) solid-state NMR data indeed represent a rather strong graph invariant for zeolite framework, (ii) despite their difficulties and costs (isotopic labeling is often required, the NMR measurements can be long), (29)Si and (17)O NMR measurements are worth being investigated in the frame of zeolites structure resolution. This approach could also be generalized to other zeolite-related materials containing NMR-measurable nuclides.

Time-Resolved Graphs of Polymorphic Cycles for H-Bonded Network Identification in Flexible Biomolecules.

A novel approach based on a coarse-grained representation of topological graphs is proposed for the automatic analysis of molecular dynamics (MD) trajectories of hydrogen-bonded (H-Bonded) flexible biomolecules. Herein, our approach models an H-Bonded biomolecule by its H-Bonded cycles and its graph of cycles in which the vertices and links represent the intersections between these cycles. We propose a methodology in which each identified conformer/isomer from the MD is represented by a well-chosen set of H-Bonded cycles called a minimum cycle basis. The key component is the "polycycles" that distinguish the cycles that play the same polymorphic role in the molecule from the ones that lead to an actual conformational change of the molecule. The relevance of our proposed method is evaluated on MD trajectories of gas-phase biomolecules, for which the covalent bonds are unchanged over time and only the hydrogen bonds change over time. The polygraphs and their time evolution are shown to reveal the dynamicity of the metastructure(s) of the H-Bonded biomolecules while providing polymorphic information on the cycles. Such information on the dynamics and changes in the H-bond network, as some cycles change identity while retaining the same role in the overall structure, is not easily captured at the atomic level of representation. Such information can instead be captured by polymorphic cycles.

Improving graphs of cycles approach to structural similarity of molecules.

This paper focuses on determining the structural similarity of two molecules, i.e., the similarity of the interconnection of all the elementary cycles in the corresponding molecular graphs. In this paper, we propose and analyze an algorithmic approach based on the resolution of the Maximum Common Edge Subgraph (MCES) problem with graphs representing the interaction of cycles molecules. Using the ChEBI database, we compare the effectiveness of this approach in terms of structural similarity and computation time with two calculations of similarity of molecular graphs, one based on the MCES, the other on the use of different fingerprints (Daylight, ECFP4, ECFP6, FCFP4, FCFP6) to measure Tanimoto coefficient. We also analyze the obtained structural similarity results for a selected subset of molecules.

GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies.

Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.

An algorithmic game-theory approach for coarse-grain prediction of RNA 3D structure.

We present a new approach for the prediction of the coarse-grain 3D structure of RNA molecules. We model a molecule as being made of helices and junctions. Those junctions are classified into topological families that determine their preferred 3D shapes. All the parts of the molecule are then allowed to establish long-distance contacts that induce a 3D folding of the molecule. An algorithm relying on game theory is proposed to discover such long-distance contacts that allow the molecule to reach a Nash equilibrium. As reported by our experiments, this approach allows one to predict the global shape of large molecules of several hundreds of nucleotides that are out of reach of the state-of-the-art methods.

Automated prediction of three-way junction topological families in RNA secondary structures.

We present an algorithm for automatically predicting the topological family of any RNA three-way junction, given only the information from the secondary structure: the sequence and the Watson-Crick pairings. The parameters of the algorithm have been determined on a data set of 33 three-way junctions whose 3D conformation is known. We applied the algorithm on 53 other junctions and compared the predictions to the real shape of those junctions. We show that the correct answer is selected out of nine possible configurations 64% of the time. Additionally, these results are noticeably improved if homology information is used. The resulting software, Cartaj, is available online and downloadable (with source) at: http://cartaj.lri.fr.