# 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…

## 1,303 Citations

### Partition function and base pairing probabilities for RNA-RNA interaction prediction

- Computer ScienceBioinform.
- 2009

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.

### Base Pairing Probabilities in a Complete HIV-1 RNA

- Computer ScienceJ. Comput. Biol.
- 1996

This work calculates the base pair probability distribution for the secondary structure of a full length HIV-1 genome using the partition function approach introduced by McCaskill (1990), and introduces methods that condense the information in the probability distribution to one value per nucleotide in the sequence.

### Unified approach to partition functions of RNA secondary structures

- BiologyJournal of mathematical biology
- 2014

This work proves a generic theorem for the calculation of RNA folding partition functions and shows that this approach can be applied to the study of the molten-native transition, denaturation of RNA molecules, as well as to studies of the glass phase of random RNA sequences.

### Helix-Based RNA Landscape Partition and Alternative Secondary Structure Determination

- BiologyACS omega
- 2019

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.

### Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization.

- BiologyRNA
- 2004

A partition function calculation for RNA secondary structure is presented that uses a current set of nearest neighbor parameters for conformational free energy at 37 degrees C, including coaxial stacking to demonstrate pairs with high probability that are therefore well determined as compared to base pairs with lower probability of pairing.

### Equilibrium Distribution of Secondary Structures for Large RNA

- Biology
- 1993

This computation may be extended to sequences of lengths 5000 to 10000, providing the only feasible means of gaining structural information on viral size RNA, and requires a further reduction in the computational order of the algorithm.

### A new model for approximating RNA folding trajectories and population kinetics

- Biology
- 2013

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.

### Statistical thermodynamics for RNA structures with simple tertiary contacts and pseudoknots

- Biology
- 2006

Though the model is based on a two-dimensional lattice chain representation, the general principles developed in the model are directly applicable to the conformations at the atomic level.

### RNA multi-structure landscapes

- PhysicsEuropean Biophysics Journal
- 2004

Just as with landscapes based on most stable secondary structure prediction, the landscapes defined on the full biophysical GCAU alphabet are much smoother than the landscapes restricted to pure GC sequences and the correlation lengths are almost constant fractions of the chain lengths.

### 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.

## References

SHOWING 1-10 OF 39 REFERENCES

### Method for predicting RNA secondary structure.

- ChemistryProceedings of the National Academy of Sciences of the United States of America
- 1975

In nearly all cases the cloverleaf is predicted to be the structure with the lowest free energy of formation.

### An energy model that predicts the correct folding of both the tRNA and the 5S RNA molecules

- ChemistryNucleic Acids Res.
- 1984

A new set of energy values to predict the secondary structures in RNA molecules has been derived through a multiple-step refinement procedure and achieves more than 80% success in predicting the cloverleaf pattern in tRNA and the consensus folding of 5S RNA.

### 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.

### Simultaneous Solution of the RNA Folding, Alignment and Protosequence Problems

- Biology
- 1985

This work combines the objective functions for alignment (parsimony, or minimal mutations) and folding (free energy), and presents an algorithm which solves all three problems simultaneously for a set of N sequences of length n in time proportional to storage and alignment.

### 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.

### Prediction of the native conformation of a polypeptide by a statistical‐mechanical procedure. I. Backbone structure of enkephalin

- ChemistryBiopolymers
- 1985

Initial results on the backbone structure of Met‐enkephalin indicate that an equilibrium statistical‐mechanical procedure, coupled with an adaptive Monte Carlo algorithm, can overcome many of the problems associated with the standard methods of direct energy minimization.

### 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.