Model Documentation

NAST [1] is a highly reduced coarse-grained model in which the entire nucleotide is represented as a single bead located on the C3' carbon atom of the sugar-phosphate backbone. Such significant geometric simplification allows for computationally efficient sampling of the conformational space, even for large RNA molecules [1]. This model utilizes an energy function based on statistical potentials, defined for, among others, bond lengths, bond angles, and torsion angles. Due to the lack of representation of nitrogenous bases, the model does not allow for de novo folding based on the RNA sequence. It is used for RNA tertiary structure prediction using molecular dynamics simulations, although the model requires input regarding secondary structure and tertiary constraints [2].

YUP [1] reduces the nucleotide representation to a single bead located at the phosphorus atom P. This model relies on an energy function based on statistical potentials. YUP is utilized in Monte Carlo simulations for RNA folding, and - using experimental data regarding the molecule's secondary structure and tertiary constraints - it is employed in tertiary structure prediction [2].

NARES-2P [1] is a model that reduces the geometry of nucleic acids (both DNA and RNA) to two beads per nucleotide: a bead corresponding to the phosphate group - placed halfway between consecutive sugar rings, and a bead representing the nitrogenous base - located at the geometric center of the base. To faithfully reproduce the backbone geometry, the model defines an additional, third bead (also called virtual), positioned at the geometric center of the ribose. It does not participate in physical interactions; therefore, the authors present NARES-2P as a two-point model (2P in the model name stands for 2-point model). This approach is based on a bottom-up strategy and aims to reproduce the actual forces acting within the molecule, rather than relying solely on the statistics of known structures [1]. This model combines elements based on knowledge and physical theory. The energy function is divided into local interactions, which enforce faithful bond and angle geometry within the nucleotide (KBP), and non-local interactions, including - among others - dipole interactions between bases (TBP) that are crucial for helix stability [2][3]. To search the conformational space, the model utilizes a global optimization algorithm (Conformational Space Annealing - CSA). This model is particularly effective in reproducing the thermodynamics of folding and double helix formation from unpaired strands [2].

Vfold [1] is a model that combines the reduction of degrees of freedom via a coarse-grained approach with a fragment assembly method. The physical basis of the model is the virtual bond model concept. Vectors connecting selected atoms play a key role in describing the backbone geometry, defining the molecule's conformation [1]. Each nucleotide is represented by bonds connecting the phosphorus atom P and the sugar backbone carbon atom C4'. An extended version of this model accounts for an additional bond connecting the C4' atom with the nitrogen atom N1 for pyrimidines or N9 for purines [2], which allows for the definition of the nitrogenous base orientation.The energy function utilizes virtual bond conformation parameters to effectively estimate the conformational entropy of RNA loops and the folding of structural motifs. In this model, the RNA conformational space is sampled using a discrete space (so-called lattice models) [1], which drastically reduces computational complexity by limiting possible molecular conformations to a finite set of states. Vfold3D is an implementation of this approach for 3D RNA structure prediction. It utilizes the RNA secondary structure and relies on assembling the structure from tertiary fragments (also called templates) retrieved from a database that match specific secondary motifs [3].

FebRNA [1] is a coarse-grained model that utilizes secondary structure-based fragment assembly for tertiary structure prediction. The coarse-grained representation describes a nucleotide as three beads corresponding to the positions of heavy atoms - the phosphate atom P, the ribose atom C4', and the nitrogen atom N1 for pyrimidines or N9 for purines [1]. This model does not employ an energy function to fold the molecule; instead, it generates a pool of complete structures via fragment assembly and subsequently selects the best one based on the cgRNASP-Feb scoring function. This function consists of a statistical potential (evaluation of non-bonded interactions derived from known RNA structures from the PDB database) and a bonded potential (evaluation of the backbone geometry correctness) [1]. FebRNA is utilized in predicting 3D RNA structures containing diverse motifs [1].

iFoldRNA [1][2] is a coarse-grained model that reduces the complexity of the all-atom RNA structure to a three-bead representation. In this model, each nucleotide is represented by three beads placed at the centers of mass of the phosphate group, the sugar ring, and the nitrogenous base [3]. Such geometry allows for the preservation of essential spatial features of the backbone and base orientation while significantly reducing the system's degrees of freedom. The model utilizes an energy function based on statistical potentials and thermodynamics. The energy function accounts for bonded interactions, which define the molecule's geometric constraints and are derived from experimental structures (bond lengths, bond angles, and torsion angles), as well as non-bonded interactions describing spatial interactions between beads (base pairing, base stacking, hydrophobic effect, and electrostatic repulsion of phosphate groups) [4]. iFoldRNA is a model used for investigating RNA thermodynamic properties, simulating de novo RNA folding via discrete molecular dynamics (DMD), and predicting tertiary structures [4]. iFoldRNAv2 is an improved version of this algorithm and is characterized by a reduction of the conformational space through the utilization of molecular geometric constraints provided by experimental data [2].

TOPRNA [1] is a three-bead coarse-grained model. Each nucleotide is represented by three interaction centers: a phosphate bead - placed on the phosphorus atom P, and a nucleobase bead - defined as the geometric center of the nitrogen N and carbon C atoms located within the base ring. The sugar bead is placed at the geometric center of the ribose, calculated as the arithmetic mean of the positions of the carbon atoms C1', C2', C3', C4', C5' and the oxygen atom O4' [1]. The knowledge-based energy function utilizes bond lengths, bond angles, and torsion angles, as well as Van der Waals interactions, with its parameters fitted to statistical potentials from databases of similar structures. The model employs molecular dynamics methods to search the conformational space [2].

In the isRNA1 [1] model, each nucleotide is represented by 4 (for pyrimidines) or 5 beads (for purines). The sugar-phosphate backbone is defined by the P bead, located at the phosphorus atom P, and the S bead at the C4' carbon atom of the ribose. The representation of nitrogenous bases is based on beads placed at the centers of mass of specific heavy atom groups. The knowledge-based energy function of the model accounts for bonded and non-bonded interactions. Molecular dynamics simulations are utilized to search the conformational space. The final structure prediction is the result of clustering analysis performed on the set of lowest-energy conformations obtained during the simulation [2]. The model finds application in the de novo folding of small RNA molecules. Furthermore, it is applied in the prediction of larger structures using data on the molecule's secondary structure [2].

isRNA2 [1] is an extension of the isRNA1 model. A change compared to the previous version is the standardization of the bead count to five. This measure aimed to improve the model regarding the modeling of non-canonical bonds and the more accurate simulation of molecules containing such bonds. The representation of nitrogenous bases was expanded by altering the bead representation in guanine and splitting the pyrimidine beads into two smaller ones. The bead representation for the sugar-phosphate backbone remains unchanged relative to isRNA1. The general parameters of the energy function and the conformational space search method remained largely unchanged compared to the previous version of the model; however, a significant modification was the optimization of the model in terms of computational complexity. The training set used for the parameterization of interactions was enriched with RNA molecules containing non-canonical base pairs. These changes make this model more effective in predicting tertiary structures of RNA containing non-canonical bonds and enable the efficient study of larger molecular systems [1].

RNAJP [1] coarse-grains RNA molecules at both the nucleotide and helix levels. Each residue is represented by five beads, two of which are placed at the phosphorus atom P and the ribose carbon atom C4'. Nucleobases are described by three beads, which for pyrimidines correspond to atoms N1, C2, and C4, and for purines - to atoms N9, C2, and C6. Such geometry is characterized by high efficiency, as information regarding backbone conformation, base pairing, and stacking is preserved [1]. A characteristic feature of this model is the treatment of an RNA molecule segment consisting of at least two base pairs (G-C, A-U, or G-U) as a rigid A-form helix. The entire spatial structure of the helix is determined solely by four terminal nucleotides. This approach allows for a reduction in the helix's degrees of freedom and a decrease in computational complexity, as the model does not need to independently simulate the position of every nucleotide within the helix [1]. The energy function relies on bonded and non-bonded interactions, and its parameters were determined using statistical potentials. Additionally, the model accounts for interactions between intertwined helices, strands within junctions, and long-range interactions between loops. RNAJP cannot fold RNA molecules de novo; however, it can effectively predict the tertiary structure of three- and four-way junctions based on the sequence and secondary structure [2]. The model utilizes Monte Carlo and molecular dynamics algorithms for more efficient conformational space sampling [1].

The SimRNA [1] model features a five-bead representation of the nucleotide. The sugar-phosphate backbone is defined by two beads, located at the phosphorus atom P and the C4' carbon atom, while nitrogenous bases are described by three beads - for pyrimidines, on atoms N1, C2, and C4, or N9, C2, and C6 for purines [1]. The components of the model's energy function include bonded interactions, which describe the backbone geometry, and non-bonded interactions between nucleotide residues, based on statistical potentials [2]. SimRNA utilizes a Monte Carlo sampling method to search the conformational space. The model is used for the prediction and simulation of structures of short RNA sequences (below 50 nucleotides), and - given provided information regarding secondary and tertiary constraints - it is also effective for larger molecules [3].

HiRE-RNA [1] is a high-resolution model in which a nucleotide is represented by 6 or 7 beads. These include a bead on the phosphorus atom P, four beads for the ribose on atoms O5', C5', C4', and C1', and one bead for pyrimidines or two beads for purines located at the centers of mass of the heavy atoms of the nucleobase rings. The model preserves three of the seven torsion angles. Such a detailed description of the molecule translates into better simulation result quality and more effective investigation of RNA-protein complexes [1]. Bonded interactions (bond lengths, bond angles, and torsion angles), non-bonded interactions (electrostatic interactions between phosphate groups, canonical and non-canonical base pairing, stacking), and hydrogen bonds constitute the energy function of this model. It is physical in nature (TBP) [2]. HiRE-RNA enables the prediction of small RNA structures de novo without utilizing information regarding the secondary structure; however, providing these constraints and information regarding tertiary geometry allows for the simulation of larger molecules. The model is also used for the evaluation of RNA motifs [2].