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A nucleotide-level coarse-grained model of RNA
Petr Šulc, Flavio Romano, Thomas E. Ouldridge, Jonathan P. K. Doye, Ard A. Louis
TL;DR
Existing RNA models face a trade-off between computational efficiency, structural detail, and thermodynamic or mechanical fidelity. This paper introduces oxRNA, a nucleotide-level off-lattice coarse-grained model with pairwise interactions fitted to RNA properties and tests it across structural, thermodynamic, and mechanical applications. The model reproduces a broad range of RNA behavior semi-quantitatively while enabling efficient simulations of large structures and multi-strand systems.
Problem
RNA modeling needs a computationally efficient representation that retains relevant structural, thermodynamic, and mechanical behavior for complex and multi-strand systems.
Method
The paper develops oxRNA, an off-lattice model representing each nucleotide as a rigid body with multiple pairwise interaction sites and parameters fitted to RNA thermodynamics.
Results
OxRNA semi-quantitatively reproduces thermodynamic data, models structures including a 264-nucleotide RNA nanoring, and matches hairpin-unzipping experiments within 1 pN.
Takeaways & Limitations
OxRNA supports efficient simulations of large RNA structures and reactions involving multiple strands, including nanotechnology-relevant systems.
Takeaways & Limitations
The model is parametrized at high salt and omits several tertiary interactions, while detailed dynamics were not investigated in this study.
Abstract
from arXiv · showhide
We present a new, nucleotide-level model for RNA, oxRNA, based on the coarse-graining methodology recently developed for the oxDNA model of DNA. The model is designed to reproduce structural, mechanical and thermodynamic properties of RNA, and the coarse-graining level aims to retain the relevant physics for RNA hybridization and the structure of single- and double-stranded RNA. In order to explore its strengths and weaknesses, we test the model in a range of nanotechnological and biological settings. Applications explored include the folding thermodynamics of a pseudoknot, the formation of a kissing loop complex, the structure of a hexagonal RNA nanoring, and the unzipping of a hairpin motif. We argue that the model can be used for efficient simulations of the structure of systems with thousands of base pairs, and for the assembly of systems of up to hundreds of base pairs. The source code implementing the model is released for public use.
I. INTRODUCTION
RNA modeling requires a balance between structural detail, thermodynamic accuracy, and computational efficiency. oxRNA addresses this need with an off-lattice nucleotide-level model intended to capture RNA structure, mechanics, thermodynamics, and multi-strand processes.
- Applications: The model targets RNA nanotechnology and biological applications where RNA sequences form functional structures and interact with proteins or other RNA molecules.RNA nanotechnology examples include self-assembling nanocubes, tiles, and proposed strand-displacement cascades.
- Existing approaches: Nearest-neighbor methods describe secondary-structure thermodynamics efficiently, but their discrete representation lacks structural and mechanical detail.These methods calculate motif free energies and can be extended with simple folding kinetics, yet remain limited in what they can treat.
- Motivation: Coarse-grained descriptions reduce computational cost for rare events and large RNA structures, but require a compromise between accuracy, efficiency, and detail.Atomistic simulations are limited in timescale, while coarse-graining integrates out atoms and often solvent molecules.
- Limitations of prior models: Most existing RNA coarse-grained models prioritize folded-structure prediction, leaving thermodynamic and mechanical properties less comprehensively characterized.Structure-focused models are difficult to compare with thermodynamic experiments, and mechanical properties had not been reported for these models.
- oxRNA contribution: oxRNA represents each RNA nucleotide as a single rigid body with multiple interaction sites and uses pairwise interactions to model A-helices and RNA thermodynamics.The model is designed to capture topological, mechanical, spatial, and kinetic properties beyond nearest-neighbor thermodynamics.
II. THE RNA MODEL AND ITS PARAMETRIZATION
oxRNA uses a nucleotide-level rigid-body representation with anisotropic interactions and parameters fitted to nearest-neighbor RNA thermodynamics. Its potentials encode backbone connectivity, stacking, hydrogen bonding, cross-stacking, coaxial stacking, and excluded volume, with explicit scope limits for salt and tertiary interactions.
- D. Parametrization of the model: OxRNA is parametrized against averaged nearest-neighbor melting temperatures that depend on sequence length and secondary-structure motif rather than particular base identity.The fitting averages Watson-Crick base-pair steps and motif-specific enthalpy and entropy contributions over possible bases.
- A. RNA thermodynamics and the nearest-neighbor model: The nearest-neighbor thermodynamic reference uses standard Gibbs free energy, enthalpy, entropy, and strand concentrations to define duplex and hairpin yields.Duplex melting temperature is the point where half the duplexes dissociate, whereas hairpin melting temperature corresponds to a 50% open probability.
- B. The Representation: oxRNA models each nucleotide as one rigid body with backbone, stacking, cross-stacking, hydrogen-bonding, and excluded-volume interaction sites.The representation uses effective interactions whose functional forms are chosen to reproduce experimentally measured RNA properties.
- B. The Representation: The model’s pairwise potential combines nearest-neighbor backbone and stacking terms with non-nearest-neighbor hydrogen-bonding, cross-stacking, excluded-volume, and coaxial-stacking terms.The backbone uses an isotropic FENE potential, while the other interactions impose distance- and orientation-dependent constraints.
- B. The Representation: Hydrogen bonding represents Watson-Crick and wobble pairs, stacking acts between adjacent nucleotides with temperature-dependent strength, and cross-stacking and coaxial stacking represent additional duplex and tertiary stabilization.The model includes AU, GC, and GU hydrogen bonding and cross-stacking associated with A-helix geometry and 3′ overhang stabilization.
- B. The Representation: The model is fitted at 1 M sodium, omits explicit phosphate electrostatics, and excludes Hoogsteen, sugar-edge, and ribose-zipper interactions.These omitted tertiary interactions lack systematic thermodynamic data for parameterization in this version.
1. Algorithms
oxRNA uses VMMC, umbrella sampling, and histogram reweighting to calculate thermodynamics, while fitting interaction parameters to averaged and sequence-dependent nearest-neighbor melting temperatures.
- Algorithms: VMMC simulations, often combined with umbrella sampling, generate thermodynamic ensembles across order-parameter regions such as base-pair counts.Umbrella sampling helps systems overcome free-energy barriers by weighting configuration-space regions.
- Algorithms: The force field is also implemented in molecular dynamics with Langevin or Andersen-like thermostats, extending simulations beyond Monte Carlo workflows.The reported molecular-dynamics simulations use the Andersen-like thermostat.
- Algorithms: Histogram reweighting recalculates bonded-state ratios and melting temperatures for alternative temperatures and interaction strengths from sampled states.The method assumes the original sampled ensemble represents the states relevant to the recalculated conditions.
- Parametrization: The model includes temperature-dependent stacking, hydrogen-bonding, cross-stacking, coaxial-stacking, and sequence-dependent interaction parameters.Interaction strengths distinguish nucleotide types where supported by the fitting ensemble, while the average-base model removes sequence dependence.
- Parametrization: Model fitting minimizes absolute melting-temperature differences from nearest-neighbor predictions using simulated annealing and reweighted VMMC ensembles.The procedure first targets averaged nearest-neighbor thermodynamics, then fits sequence-dependent interactions for Watson-Crick and wobble pairs.
A. Structure of the model
oxRNA is designed to reproduce A-form RNA duplex structure and thermodynamic behavior across duplexes, hairpins, and secondary-structure motifs. Its strongest agreement is for ordinary duplexes and hairpins, while GU/UG steps and internal mismatches expose specific limitations.
- A. Structure of the model: The oxRNA duplex reproduces key A-RNA geometry, with 0.28 nm rise, 33.0° twist, and a 10.9-base-pair helical pitch.The model’s measured helix width is 2.5 nm, with major and minor grooves of 0.48 nm and 1.07 nm.
- 1. Duplex and hairpin melting: Average-base oxRNA melting-temperature differences are roughly within the nearest-neighbor model’s own accuracy for Watson-Crick structures.The comparison uses the average-base parametrization against averaged nearest-neighbor thermodynamics.
- 1. Duplex and hairpin melting: 2.1 °C average duplex deviation and 3.4 °C average absolute deviation occur without GU/UG or UG/GU steps, versus 9.4 °C and 9.7 °C with those steps.The larger wobble-step discrepancy arises because oxRNA’s pairwise interactions cannot represent their destabilizing nearest-neighbor contribution.
- 1. Duplex and hairpin melting: −2.8 °C average hairpin melting-temperature difference and 4.1 °C average absolute deviation are obtained for randomly generated hairpins.The model was parametrized jointly to duplex and hairpin ensembles because hairpins are a prominent RNA secondary-structure motif.
1. Persistence length
The model’s persistence length is estimated from local helix-axis correlations and compared with experimental dsRNA values. Its force-extension behavior is also fitted with an extensible worm-like chain model, but the extracted parameters are sensitive to the fitting interval.
- Persistence-length estimate: The persistence length is obtained by fitting an exponential decay to correlations in the orientation of local helical axes along a simulated 142-bp duplex.Ten base pairs at each duplex end were excluded to reduce edge effects.
- Persistence-length estimate: 101 bp is the estimated persistence length, versus an expected 171 bp at the studied salt concentration, placing the model within a factor of 2 of experiment.The authors conclude that oxRNA captures the correct order of magnitude, although its persistence length is smaller than measured values.
- Limitations: The model’s persistence length is difficult to reproduce accurately, and the authors expect this challenge to affect other coarse-grained models as well.They note that persistence length had not yet been measured for other coarse-grained models.
- Force-extension behavior: L0 = 23.4 nm, K = 296 pN and Lp = 26.0 nm are obtained from the force-extension fit over forces between 2.4 pN and 69 pN.The fit used an extensible worm-like chain model with L0, K and Lp as free parameters.
- Force-extension behavior: Changing the force-fitting interval can alter the extracted parameters substantially, including changing the fitted persistence length by more than a factor of two.The residual error remains small despite this sensitivity, so the reported parameter uncertainties should be considered large.
3. Overstretching
oxRNA simulations characterize MMTV pseudoknot thermodynamics and folding pathways, reproducing its overall secondary structure while revealing a mismatch-stabilization geometry that differs from experiment.
- A. Pseudoknots: Equal yields occur at 67.7 °C for pseudoknot versus hairpin 2 and at 84.8 °C for hairpin 2 versus the unstructured strand.The higher-temperature transition coincides with a heat-capacity peak, while the lower-temperature transition produces a shoulder.
- A. Pseudoknots: At 48 °C, folding most likely proceeds by forming one stem first—preferentially the more stable stem 2—then closing the second stem.Simultaneous formation of both stems is less favored along the minimum free-energy pathway.
- A. Pseudoknots: A seventh GU base pair sometimes forms, but its 5 kBT penalty changes equal-yield temperatures by less than 0.3 °C.Including this pair changes folding-pathway free energies by at most 0.5 kBT, so it is excluded from the stem-1 definition.
- A. Pseudoknots: The simulated MMTV pseudoknot typically stacks its AA mismatch and produces an inter-stem angle near 160°, versus about 112° from NMR.The authors attribute this geometry to overestimated mismatch stability in simpler motifs.
- A. Pseudoknots: The model reproduces pseudoknot thermodynamics and stem stabilities, supporting the assignment of the higher-temperature heat-capacity peak to the pseudoknot-to-hairpin transition.The overall secondary structure is correct, although the simulated angle between stems is larger than experimentally reported.
B. Kissing hairpin complex
oxRNA captures kissing-hairpin thermodynamics and geometry, constructs a 264-nucleotide hexagonal nanoring, and reproduces CD4 hairpin unzipping forces with temperature dependence.
- B. Kissing hairpin complex: The sequence-dependent model predicts a kissing-complex melting temperature of 44.8 °C, close to 45.2 °C for the matching 7-bp duplex.The average-base model gives approximately 53.6 °C for the duplex comparison, and free-energy profiles are shown at 45 °C.
- B. Kissing hairpin complex: For most sequences, kissing hairpin loops are more stable than separate duplexes because constrained loops lose less configurational entropy and gain coaxial-stacking stabilization.At low temperature, a perfectly formed duplex can instead be more stable because it receives stronger enthalpic contributions.
- B. Kissing hairpin complex: The simulated kissing-complex transition is quasi-two-state, unlike the experimentally inferred thermodynamic behavior, and predicts yields of 36% at 35 °C and 5% at 45 °C after concentration extrapolation.The authors suggest the experimental analysis may be affected by assuming the ITC transition was fully saturated.
- B. Kissing hairpin complex: The oxRNA-built hexagonal nanoring contains six strands and 264 nucleotides; its kissing-complex angle fluctuates around 124.9° with a 14.4° standard deviation.Structural relaxation times are about a minute of CPU time or less on a standard 2.2 GHz processor.
- C. Hairpin unzipping: OxRNA reproduces CD4 hairpin unzipping forces with 5% (1 pN) accuracy and fully captures their temperature trend.The fitted temperature coefficient matches experiment, while the fitted intercept differs by less than 2%.
V. SUMMARY AND CONCLUSIONS
oxRNA is an off-lattice, nucleotide-level coarse-grained RNA model designed to reproduce structural, thermodynamic, and mechanical properties while enabling efficient simulations of large and multistrand systems. Tests cover secondary and tertiary motifs, nanostructures, and mechanical behavior, while identifying limitations in quantitative accuracy and scope.
- Model and scope: oxRNA uses a minimal single-rigid-body nucleotide representation with pairwise potentials and systematically targets structural, thermodynamic, and mechanical properties rather than structure alone.The model is top-down parametrized using experimental free-energy differences and is closely linked to the oxDNA coarse-graining strategy.
- Applications and validation: OxRNA reproduces coaxial stacking, kissing-loop interactions, pseudoknots, and experimental mechanical behavior across diverse RNA systems.Applications include pseudoknot thermodynamics, kissing-hairpin structure and thermodynamics, nanoring structure, and hairpin unzipping.
- Limitations: OxRNA is currently parametrized at 1 M salt without explicit electrostatics, and improved accuracy may require electrostatics or additional tertiary-contact interactions.The authors also note that detailed dynamics were beyond this study’s scope, although similar simulations are considered feasible.
- Limitations: RNA thermodynamics is harder to parametrize than DNA because sequence effects are stronger and neighboring wobble pairs can contribute positively to duplex free energy.The current representation cannot capture this wobble-pair effect, although structural improvements may help.
- Mechanical properties: The model’s duplex persistence length is about half the reported high-salt RNA value but remains the correct order of magnitude for applications with shorter helical sections.Such sections are likely to be much shorter than the persistence length, reducing the practical impact of this discrepancy.
- Applications and scalability: 264 nucleotides were modeled in an RNA nanoring on a single CPU, demonstrating oxRNA’s utility for relatively large RNA nanostructures.The reported computational cost is similar to oxDNA, which has simulated a DNA origami motif with 12,391 nucleotides.
a. Representation
OxRNA represents each nucleotide as a rigid body with multiple sites and orientation vectors that encode backbone, base-pairing, stacking, and cross-stacking geometry. These sites and vectors define the distances and angles used by the interaction potentials.
- Nucleotide geometry: Each nucleotide is a single rigid body with backbone, hydrogen-bonding, cross-stacking, coaxial-stacking, and 3′- and 5′-stacking sites.Its position and orientation are specified by the center of mass and perpendicular unit vectors a3 and a1, with a2 = a3 × a1.
- Nucleotide geometry: The a1 vector points from the center of mass to the hydrogen-bonding site, while a3 points toward the 5′ neighbor in a duplex configuration.These orientation vectors, together with a2, define the nucleotide’s local frame.
- Interaction coordinates: Interaction geometry is encoded through distances between backbone, hydrogen-bonding, coaxial-stacking, and stacking sites.The defined vectors include δr_backbone, δr_HB, δr_coaxial st., δr_stack, and backbone–base or base–backbone vectors.
- Interaction coordinates: Angles between intersite vectors and orientation vectors a3, a1, p3′, and p5′ modulate the anisotropic interactions.The notation distinguishes the orientation vectors of the two nucleotides participating in an interaction.
b. Potentials
OxRNA combines radial, angular, smoothing, excluded-volume, backbone, and handedness terms to represent nucleotide interactions. The potential functions are truncated smoothly and parameterized in the model’s internal units.
- Potential construction: The total oxRNA potential sums functions representing stacking, hydrogen bonding, cross-stacking, coaxial stacking, backbone connectivity, excluded volume, and angular modulation.Some interaction potentials are products of multiple functions, whereas excluded volume is a sum of terms.
- Cutoffs and continuity: Smooth cutoff functions make the interaction potentials differentiable and zero beyond specified cutoff distances.The smoothing parameters are determined by differentiability conditions at the boundaries rather than independently listed.
- Radial interactions: Morse terms model radial stacking and hydrogen bonding, while harmonic terms model cross-stacking and coaxial-stacking distances.Lennard-Jones terms provide excluded-volume interactions, and FENE springs maintain bonded-neighbor backbone connectivity.
- Angular interactions: Angular modulation functions impose preferred geometries for stacking, hydrogen bonding, cross-stacking, and coaxial stacking.A separate modulation term imposes right-handedness in the relevant interactions.
- Excluded volume: Bonded-neighbor excluded volume omits the backbone term because the FENE backbone interaction already prevents the backbone sites from approaching too closely.This avoids duplicating the same short-range backbone constraint in V′_exc.
- Parameterization: Model parameters are specified in tables using internal simulation units for energy and distance.The interaction parameter tables list values for backbone, hydrogen-bonding, stacking, excluded-volume, and related terms.
Interaction Parameters
Further model parameters are provided in Table A-II.
- Interaction Parameters: Table A-II lists further parameters used by the oxRNA interaction model.