# The equilibrium partition function and base pair binding probabilities for RNA secondary structure

@article{McCaskill1990TheEP, title={The equilibrium partition function and base pair binding probabilities for RNA secondary structure}, author={John S. McCaskill}, journal={Biopolymers}, year={1990}, volume={29} }

A novel application of dynamic programming to the folding problem for RNA enables one to calculate the full equilibrium partition function for secondary structure and the probabilities of various substructures. In particular, both the partition function and the probabilities of all base pairs are computed by a recursive scheme of polynomial order N3 in the sequence length N. The temperature dependence of the partition function gives information about melting behavior for the secondary structure…

## 1,295 Citations

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This work presents an O(N(6) time and O(4) time dynamics programming algorithm for computing the full partition function for RIP which is based on the combinatorial notion of 'tight structures', equivalent to recent work by H. Chitsaz and collaborators.

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A helix-based strategy for RNA folding landscape partition and alternative secondary structure determination and the predicted structures and equilibrium populations of metastable conformations for the 2′dG-sensing riboswitch reveal the allosteric conformational switch on transcript length, which is consistent with the experimental study.

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A new subset approximation model for the full RNA folding model is presented, methods to analyze its accuracy and the relative merits of the model as compared with a pre-existing subset approximation are discussed.

Partition function and base pairing probabilities of RNA heterodimers

- BiologyAlgorithms for Molecular Biology
- 2006

A program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules, and provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures.

A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: I.

- BiologyJournal of theoretical biology
- 2001

A global strategy for estimating the entropy of long sequences of RNA is proposed to help improve the predictive capacity of RNA secondary structure dynamic programming algorithm (DPA) free energy…

A partition function algorithm for nucleic acid secondary structure including pseudoknots

- Computer ScienceJ. Comput. Chem.
- 2003

An O(N5) dynamic programming algorithm is described, where N is the length of the strand, for computing the partition function and minimum energy structure over this class of secondary structures, to determine the probability of sampling the lowest energy structure, or any other structure of particular interest.

Energy-directed RNA structure prediction.

- BiologyMethods in molecular biology
- 2014

In this chapter we present the classic dynamic programming algorithms for RNA structure prediction by energy minimization, as well as variations of this approach that allow to compute suboptimal…

Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure.

- EngineeringJournal of molecular biology
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An improved dynamic programming algorithm is reported for RNA secondary structure prediction by free energy minimization and experimental constraints, derived from enzymatic and flavin mononucleotide cleavage, improve the accuracy of structure predictions.

Efficient Computation of Base-pairing Probabilities in Multi-strand RNA Folding

- Computer ScienceBIOINFORMATICS
- 2020

It is shown here how cubic running time asymptotically equal to McCaskill’s partition function algorithm can be achieved by introducing linear-size auxiliary arrays.

## References

SHOWING 1-10 OF 39 REFERENCES

Improved free-energy parameters for predictions of RNA duplex stability.

- Biology, ChemistryProceedings of the National Academy of Sciences of the United States of America
- 1986

These parameters predict melting temperatures of most oligonucleotide duplexes within 5 degrees C, about as good as can be expected from the nearest-neighbor model.

Computer-aided prediction of RNA secondary structures

- BiologyNucleic Acids Res.
- 1982

An argument is made for integrating the two approaches presented in this paper, enabling the user to generate proposed structures using thermodynamic criteria, allowing interactive refinement of these structures through the application of experimentally derived data.

Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information

- BiologyNucleic Acids Res.
- 1981

A new computer method for folding an RNA molecule that finds a conformation of minimum free energy using published values of stacking and destabilizing energies and is much more efficient, faster, and can fold larger molecules than procedures which have appeared up to now in the biological literature.

Improved parameters for prediction of RNA structure.

- BiologyCold Spring Harbor symposia on quantitative biology
- 1987

Thermodynamic studies of oligoribonucleotides are providing parameters and insights for the fundamental interactions that determine RNA structure, and parameters for stacking and hydrogen bonding will likely be important for predicting the three-dimensional structures of RNAs and for interpreting RNA-RNA associations.

Theory of oligonucleotide stabilization. I. The effect of single‐strand stacking

- ChemistryBiopolymers
- 1973

The theory leads to length dependent heats and entropies for short single strands in a natural way, and permits a more accurate assessment of the contribution of partially bonded states in thermal transitions than has previously been possible.

Small changes in free energy assignments for unpaired bases do not affect predicted secondary structures in single stranded RNA

- ChemistryNucleic Acids Res.
- 1982

Tuncating the free energies of hairpin loops, bulges, internal loops and multibranched junctions to two significant digits yields structures nearly identical to those generated using three digit values, showing that one can safely use truncated values in RNA folding calculations.

Stability of ribonucleic acid double-stranded helices.

- Biology, ChemistryJournal of molecular biology
- 1974

Structural analysis of self-replicating RNA synthesized by Qbeta replicase.

- Chemistry, BiologyJournal of molecular biology
- 1982

Solution conformations of B. subtilis ribosomal 5S RNA: A calorimetric study

- BiologyBiopolymers
- 1986

The conformational changes demonstrated here may facilitate the movement of the protein synthesis machinery during RNA translation and be interpreted according to hypothetical secondary and tertiary base‐pairing schemes.