Abstract: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 equilib… Show more
“…The graph representation (Fig. 1B), which is used to direct the construction of the 3D model, is almost identical to the skeleton graph described by Lamiable et al (2013), and will be referred to as such in the rest of this article. The following definitions assume the lack of pseudoknots in the secondary structure.…”
Section: Secondary Structure Elements and Graph Definitionmentioning
confidence: 99%
“…It is derived from RNA secondary structures and defines the structural relations of individual helices. Similar graph representations and their use in structure prediction have been mentioned by Zhao et al (2012), Lamiable et al (2013), and Kim et al (2014) but we aim to formalize their definition and illustrate its use as a guide for building a coarse-grain 3D structure. II.…”
A 3D model of RNA structure can provide information about its function and regulation that is not possible with just the sequence or secondary structure. Current models suffer from low accuracy and long running times and either neglect or presume knowledge of the long-range interactions which stabilize the tertiary structure. Our coarse-grained, helix-based, tertiary structure model operates with only a few degrees of freedom compared with all-atom models while preserving the ability to sample tertiary structures given a secondary structure. It strikes a balance between the precision of an all-atom tertiary structure model and the simplicity and effectiveness of a secondary structure representation. It provides a simplified tool for exploring global arrangements of helices and loops within RNA structures. We provide an example of a novel energy function relying only on the positions of stems and loops. We show that coupling our model to this energy function produces predictions as good as or better than the current state of the art tools. We propose that given the wide range of conformational space that needs to be explored, a coarse-grain approach can explore more conformations in less iterations than an all-atom model coupled to a finegrain energy function. Finally, we emphasize the overarching theme of providing an ensemble of predicted structures, something which our tool excels at, rather than providing a handful of the lowest energy structures.
“…The graph representation (Fig. 1B), which is used to direct the construction of the 3D model, is almost identical to the skeleton graph described by Lamiable et al (2013), and will be referred to as such in the rest of this article. The following definitions assume the lack of pseudoknots in the secondary structure.…”
Section: Secondary Structure Elements and Graph Definitionmentioning
confidence: 99%
“…It is derived from RNA secondary structures and defines the structural relations of individual helices. Similar graph representations and their use in structure prediction have been mentioned by Zhao et al (2012), Lamiable et al (2013), and Kim et al (2014) but we aim to formalize their definition and illustrate its use as a guide for building a coarse-grain 3D structure. II.…”
A 3D model of RNA structure can provide information about its function and regulation that is not possible with just the sequence or secondary structure. Current models suffer from low accuracy and long running times and either neglect or presume knowledge of the long-range interactions which stabilize the tertiary structure. Our coarse-grained, helix-based, tertiary structure model operates with only a few degrees of freedom compared with all-atom models while preserving the ability to sample tertiary structures given a secondary structure. It strikes a balance between the precision of an all-atom tertiary structure model and the simplicity and effectiveness of a secondary structure representation. It provides a simplified tool for exploring global arrangements of helices and loops within RNA structures. We provide an example of a novel energy function relying only on the positions of stems and loops. We show that coupling our model to this energy function produces predictions as good as or better than the current state of the art tools. We propose that given the wide range of conformational space that needs to be explored, a coarse-grain approach can explore more conformations in less iterations than an all-atom model coupled to a finegrain energy function. Finally, we emphasize the overarching theme of providing an ensemble of predicted structures, something which our tool excels at, rather than providing a handful of the lowest energy structures.
“…In graph theory techniques, RNA is depicted topologically to build RNA structures; this improves sampling and even allows for creation of novel RNA motifs. Graph theory techniques63 are utilized by RAG/RAGTOP64656667 and others68697071. In physics based methods, the RNA is built from sequence into a 3D structure, and these 3D RNA structures are sampled using Monte Carlo or Molecular Dynamics (MD) protocols.…”
We introduce a coarse-grained RNA model for molecular dynamics simulations, RACER (RnA CoarsE-gRained). RACER achieves accurate native structure prediction for a number of RNAs (average RMSD of 2.93 Å) and the sequence-specific variation of free energy is in excellent agreement with experimentally measured stabilities (R2 = 0.93). Using RACER, we identified hydrogen-bonding (or base pairing), base stacking, and electrostatic interactions as essential driving forces for RNA folding. Also, we found that separating pairing vs. stacking interactions allowed RACER to distinguish folded vs. unfolded states. In RACER, base pairing and stacking interactions each provide an approximate stability of 3–4 kcal/mol for an A-form helix. RACER was developed based on PDB structural statistics and experimental thermodynamic data. In contrast with previous work, RACER implements a novel effective vdW potential energy function, which led us to re-parameterize hydrogen bond and electrostatic potential energy functions. Further, RACER is validated and optimized using a simulated annealing protocol to generate potential energy vs. RMSD landscapes. Finally, RACER is tested using extensive equilibrium pulling simulations (0.86 ms total) on eleven RNA sequences (hairpins and duplexes).
“…These are based on the observation that macromolecules often do not attain the global minimum of free energy. Therefore, Lamiable et al 17 replaced the global optimization by a local optimization, where each component of the RNA molecule ''selfishly'' maximizes its own payoff function. The theoretical justification of such a decomposition of the energy function is not yet, however, fully clear.…”
In this and an accompanying paper we review the use of game theoretical concepts in cell biology and molecular biology. This review focuses on the subcellular level by considering viruses, genes, and molecules as players. We discuss in which way catalytic RNA can be treated by game theory. Moreover, genes can compete for success in replication and can have different strategies in interactions with other genetic elements. Also transposable elements, or "jumping genes", can act as players because they usually bear different traits or strategies. Viruses compete in the case of co-infecting a host cell. Proteins interact in a game theoretical sense when forming heterodimers. Finally, we describe how the Shapley value can be applied to enzymes in metabolic pathways. We show that game theory can be successfully applied to describe and analyse scenarios at the molecular level resulting in counterintuitive conclusions.
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