Turner Energy Model

The foundational energy unit of the Turner model. Rather than treating base pairs independently, the model assigns a unique free energy change to each adjacent stacking interaction (e.g., 5'-AU-3' stacked on 5'-UA-3'). These parameters, derived from optical melting experiments on short duplexes, capture the sequence-dependent enthalpic and entropic contributions of base stacking, hydrogen bonding, and solvation effects. The total helical stability is the sum of all nearest-neighbor increments.

Unpaired regions impose a thermodynamic cost that opposes folding. The Turner model categorizes and parameterizes these motifs distinctly:

• Hairpin loops: Destabilizing penalty that scales with loop size, with a minimum for tetraloops (e.g., GNRA, UNCG) which are exceptionally stable.
• Internal loops & bulges: Penalized based on size, asymmetry, and sequence-dependent closure energetics.
• Multi-branch loops: Modeled using a linear approximation with an intercept penalty plus a per-helix branching term.

Unpaired nucleotides at the termini of helices can stack coaxially on the adjacent base pair, providing additional stabilization. The Turner model includes parameters for 5' and 3' dangling ends, where the identity of the dangling nucleotide and the closing base pair determine the magnitude of the favorable free energy increment. This effect is critical for accurately predicting the stability of short helices and multi-loop junctions where coaxial stacking mimics continuous helices.

Non-canonical base pairs within a helix are not simply destabilizing errors; they have specific thermodynamic signatures. The Turner model includes parameters for single mismatches (e.g., G·U wobble pairs) and tandem mismatches (two consecutive non-canonical pairs). Tandem mismatches can be surprisingly stabilizing due to cross-strand stacking and specific hydrogen bonding networks, making their accurate parameterization essential for predicting biologically relevant structures like internal loops.

The standard Turner parameters are defined at 1 M NaCl and 37°C. To predict folding under physiological or non-standard conditions, correction terms are applied:

• Salt correction: A term derived from polyelectrolyte theory adjusts the entropic penalty of folding based on monovalent and divalent cation concentration, reflecting the reduced charge repulsion as counterions condense on the backbone.
• Temperature extrapolation: Standard enthalpy and entropy values allow free energy calculation at any temperature using the Gibbs-Helmholtz equation, enabling prediction of melting temperatures (Tm).

When two helices meet within a multi-branch loop, their terminal base pairs can stack coaxially to form a pseudo-continuous helix. This interaction is not explicitly parameterized in the original linear multi-loop model but is a critical determinant of 3D architecture. Modern implementations incorporate coaxial stacking free energy increments—often approximated by the nearest-neighbor parameter for the stacked interface—to favor junction topologies observed in phylogenetic structures and crystallography.

The thermodynamic principle that predicts the single most stable RNA secondary structure by minimizing the sum of empirically derived loop and stacking energy parameters. The Turner model provides the nearest-neighbor parameters that make MFE calculations possible.

• Uses dynamic programming (Zuker algorithm) to efficiently search the space of possible structures
• The structure with the lowest ΔG° is considered the biologically relevant fold
• MFE prediction accuracy depends directly on the quality of Turner parameters

A statistical mechanics calculation that sums the Boltzmann-weighted free energies of all possible RNA secondary structures to derive base pairing probabilities and ensemble properties. The Turner energy parameters serve as the Hamiltonian for this calculation.

• Computes the equilibrium ensemble rather than a single structure
• Yields per-base pairing probabilities used in centroid structure prediction
• Enables calculation of ensemble diversity and Shannon entropy of the structural landscape

The fundamental assumption that the stability of an RNA base pair depends on the identity and orientation of adjacent base pairs, not just the pair itself. The Turner model quantifies this with experimentally measured parameters.

• Each stacking interaction between adjacent base pairs has a distinct ΔG° value
• Parameters are derived from optical melting experiments on short model duplexes
• Accounts for sequence-dependent effects like the 5'-GC-3' vs 5'-CG-3' asymmetry

A standard string representation of RNA secondary structure where matching parentheses denote canonical base pairs and dots represent unpaired nucleotides. This format is the direct output of Turner-model-based folding algorithms.

• Example: (((...))) represents a simple stem-loop
• Serves as the training target for deep learning models predicting secondary structure
• Extended notation uses brackets [] and braces {} to annotate pseudoknots

The Turner model assigns distinct thermodynamic penalties to different loop types based on size, sequence, and closure geometry. These parameters are critical for accurately predicting multi-branch junctions.

• Hairpin loops: Sequence-dependent penalties for tetraloops like GNRA and UNCG
• Internal loops: Asymmetric and symmetric loops with size-dependent initiation costs
• Multi-branch loops: Linear approximation using junction initiation penalty and per-helix bonus
• Bulge loops: Single-nucleotide bulges have specific stacking context parameters

An extension of Turner-model folding that incorporates experimental reactivity data as a pseudo-free energy term to constrain structure prediction. SHAPE (Selective 2'-Hydroxyl Acylation analyzed by Primer Extension) measures nucleotide flexibility.

• Reactivity values are converted to ΔG° penalties for base-paired nucleotides that appear flexible
• Dramatically improves prediction accuracy, especially for long RNAs
• Bridges the gap between purely thermodynamic prediction and experimental observation