Computing Partition Functions and Pair Probabilities
RNA Secondary Structure Prediction

This section provides information about all functions and variables related to the calculation of the partition function and base pair probabilities. More...

Collaboration diagram for Computing Partition Functions and Pair Probabilities:

## Modules

| Compute the structure with maximum expected accuracy (MEA)
| Compute the centroid structure
| Partition Function for two hybridized Sequences
| Partition Function Cofolding.
| Partition Function for two hybridized Sequences as a stepwise Process
| Partition Function Cofolding as a stepwise process.
| Partition Function and Base Pair Probabilities for Sequence Alignment(s)
| Partition functions for locally stable secondary structures
| Calculate Partition Functions of a Distance Based Partitioning
| Compute the partition function and stochastically sample secondary structures for a partitioning of the secondary structure space according to the base pair distance to two fixed reference structures.

## Files

file | boltzmann_sampling.h
| Boltzmann Sampling of secondary structures from the ensemble.
file | equilibrium_probs.h
| Equilibrium Probability implementations.
file | part_func.h
| Partition function of single RNA sequences.

## Functions

double | vrna_mean_bp_distance_pr (int length, FLT_OR_DBL *pr)
| Get the mean base pair distance in the thermodynamic ensemble from a probability matrix. More...
double | vrna_mean_bp_distance (vrna_fold_compound_t *vc)
| Get the mean base pair distance in the thermodynamic ensemble. More...
vrna_plist_t * | vrna_stack_prob (vrna_fold_compound_t *vc, double cutoff)
| Compute stacking probabilities. More...
float | vrna_pf (vrna_fold_compound_t *vc, char *structure)
| Compute the partition function for a given RNA sequence, or sequence alignment. More...
float | vrna_pf_fold (const char *sequence, char *structure, vrna_plist_t **pl)
| Compute Partition function (and base pair probabilities) for an RNA sequence using a comparative method. More...
float | vrna_pf_circfold (const char *sequence, char *structure, vrna_plist_t **pl)
| Compute Partition function (and base pair probabilities) for a circular RNA sequences using a comparative method. More...
float | pf_fold_par (const char *sequence, char *structure, vrna_exp_param_t *parameters, int calculate_bppm, int is_constrained, int is_circular)
| Compute the partition function for a given RNA sequence. More...
float | pf_fold (const char *sequence, char *structure)
| Compute the partition function of an RNA sequence. More...
float | pf_circ_fold (const char *sequence, char *structure)
| Compute the partition function of a circular RNA sequence. More...
void | free_pf_arrays (void)
| Free arrays for the partition function recursions. More...
void | update_pf_params (int length)
| Recalculate energy parameters. More...
void | update_pf_params_par (int length, vrna_exp_param_t *parameters)
| Recalculate energy parameters. More...
FLT_OR_DBL * | export_bppm (void)
| Get a pointer to the base pair probability arrayAccessing the base pair probabilities for a pair (i,j) is achieved by. More...
int | get_pf_arrays (short **S_p, short **S1_p, char **ptype_p, FLT_OR_DBL **qb_p, FLT_OR_DBL **qm_p, FLT_OR_DBL **q1k_p, FLT_OR_DBL **qln_p)
| Get the pointers to (almost) all relavant computation arrays used in partition function computation. More...
double | mean_bp_distance (int length)
| Get the mean base pair distance of the last partition function computation. More...
double | mean_bp_distance_pr (int length, FLT_OR_DBL *pr)
| Get the mean base pair distance in the thermodynamic ensemble. More...
vrna_plist_t * | vrna_plist_from_probs (vrna_fold_compound_t *vc, double cut_off)
| Create a vrna_plist_t from base pair probability matrix. More...
void | assign_plist_from_pr (vrna_plist_t **pl, FLT_OR_DBL *probs, int length, double cutoff)
| Create a vrna_plist_t from a probability matrix. More...

## Detailed Description

This section provides information about all functions and variables related to the calculation of the partition function and base pair probabilities.

Instead of the minimum free energy structure the partition function of all possible structures and from that the pairing probability for every possible pair can be calculated, using a dynamic programming algorithm as described in [13].

## Function Documentation

double vrna_mean_bp_distance_pr | ( | int | length,
|  | FLT_OR_DBL * | pr
| ) |  |

`#include <ViennaRNA/equilibrium_probs.h>`

Get the mean base pair distance in the thermodynamic ensemble from a probability matrix.

this can be computed from the pair probs as

Parameters

  length | The length of the sequence
  pr | The matrix containing the base pair probabilities

Returns
  The mean pair distance of the structure ensemble

double vrna_mean_bp_distance | ( | vrna_fold_compound_t * | vc | ) |

`#include <ViennaRNA/equilibrium_probs.h>`

Get the mean base pair distance in the thermodynamic ensemble.

this can be computed from the pair probs as

Parameters

  vc | The fold compound data structure

Returns
  The mean pair distance of the structure ensemble

vrna_plist_t* vrna_stack_prob | ( | vrna_fold_compound_t * | vc,
|  | double | cutoff
| ) |  |

`#include <ViennaRNA/equilibrium_probs.h>`

Compute stacking probabilities.

For each possible base pair , compute the probability of a stack , .

Parameters

  vc | The fold compound data structure with precomputed base pair probabilities
  cutoff | A cutoff value that limits the output to stacks with .

Returns
  A list of stacks with enclosing base pair and probabiltiy

float vrna_pf | ( | vrna_fold_compound_t * | vc,
|  | char * | structure
| ) |  |

`#include <ViennaRNA/part_func.h>`

Compute the partition function for a given RNA sequence, or sequence alignment.

If structure is not a NULL pointer on input, it contains on return a string consisting of the letters " . , | { } ( ) " denoting bases that are essentially unpaired, weakly paired, strongly paired without preference, weakly upstream (downstream) paired, or strongly up- (down-)stream paired bases, respectively. If the parameter calculate_bppm is set to 0 base pairing probabilities will not be computed (saving CPU time), otherwise after calculations took place pr will contain the probability that bases i and j pair.

Note
  This function is polymorphic. It accepts vrna_fold_compound_t of type VRNA_VC_TYPE_SINGLE, and VRNA_VC_TYPE_ALIGNMENT.

See also
  vrna_fold_compound_t, vrna_fold_compound(), vrna_pf_fold(), vrna_pf_circfold(), vrna_fold_compound_comparative(), vrna_pf_alifold(), vrna_pf_circalifold(), vrna_db_from_probs(), vrna_exp_params(), vrna_aln_pinfo()

Parameters

  [in,out] | vc | The fold compound data structure
  [in,out] | structure | A pointer to the character array where position-wise pairing propensity will be stored. (Maybe NULL)

Returns
  The Gibbs free energy of the ensemble ( ) in kcal/mol

float vrna_pf_fold | ( | const char * | sequence,
|  | char * | structure,
|  | vrna_plist_t ** | pl
| ) |  |

`#include <ViennaRNA/part_func.h>`

Compute Partition function (and base pair probabilities) for an RNA sequence using a comparative method.

This simplified interface to vrna_pf() computes the partition function and, if required, base pair probabilities for an RNA sequence using default options. Memory required for dynamic programming (DP) matrices will be allocated and free'd on-the-fly. Hence, after return of this function, the recursively filled matrices are not available any more for any post-processing.

Note
  In case you want to use the filled DP matrices for any subsequent post-processing step, or you require other conditions than specified by the default model details, use vrna_pf(), and the data structure vrna_fold_compound_t instead.

See also
  vrna_pf_circfold(), vrna_pf(), vrna_fold_compound(), vrna_fold_compound_t

Parameters

  sequence | RNA sequence
  structure | A pointer to the character array where position-wise pairing propensity will be stored. (Maybe NULL)
  pl | A pointer to a list of vrna_plist_t to store pairing probabilities (Maybe NULL)

Returns
  The Gibbs free energy of the ensemble ( ) in kcal/mol

float vrna_pf_circfold | ( | const char * | sequence,
|  | char * | structure,
|  | vrna_plist_t ** | pl
| ) |  |

`#include <ViennaRNA/part_func.h>`

Compute Partition function (and base pair probabilities) for a circular RNA sequences using a comparative method.

This simplified interface to vrna_pf() computes the partition function and, if required, base pair probabilities for a circular RNA sequence using default options. Memory required for dynamic programming (DP) matrices will be allocated and free'd on-the-fly. Hence, after return of this function, the recursively filled matrices are not available any more for any post-processing.

Note
  In case you want to use the filled DP matrices for any subsequent post-processing step, or you require other conditions than specified by the default model details, use vrna_pf(), and the data structure vrna_fold_compound_t instead.

Folding of circular RNA sequences is handled as a post-processing step of the forward recursions. See [7] for further details.

See also
  vrna_pf_fold(), vrna_pf(), vrna_fold_compound(), vrna_fold_compound_t

Parameters

  sequence | A circular RNA sequence
  structure | A pointer to the character array where position-wise pairing propensity will be stored. (Maybe NULL)
  pl | A pointer to a list of vrna_plist_t to store pairing probabilities (Maybe NULL)

Returns
  The Gibbs free energy of the ensemble ( ) in kcal/mol

float pf_fold_par | ( | const char * | sequence,
|  | char * | structure,
|  | vrna_exp_param_t * | parameters,
|  | int | calculate_bppm,
|  | int | is_constrained,
|  | int | is_circular
| ) |  |

`#include <ViennaRNA/part_func.h>`

Compute the partition function for a given RNA sequence.

If structure is not a NULL pointer on input, it contains on return a string consisting of the letters " . , | { } ( ) " denoting bases that are essentially unpaired, weakly paired, strongly paired without preference, weakly upstream (downstream) paired, or strongly up- (down-)stream paired bases, respectively. If fold_constrained is not 0, the structure string is interpreted on input as a list of constraints for the folding. The character "x" marks bases that must be unpaired, matching brackets " ( ) " denote base pairs, all other characters are ignored. Any pairs conflicting with the constraint will be forbidden. This is usually sufficient to ensure the constraints are honored. If the parameter calculate_bppm is set to 0 base pairing probabilities will not be computed (saving CPU time), otherwise after calculations took place pr will contain the probability that bases i and j pair.

Deprecated:
  Use vrna_pf() instead

Note
  The global array pr is deprecated and the user who wants the calculated base pair probabilities for further computations is advised to use the function export_bppm()

Postcondition
  After successful run the hidden folding matrices are filled with the appropriate Boltzmann factors. Depending on whether the global variable do_backtrack was set the base pair probabilities are already computed and may be accessed for further usage via the export_bppm() function. A call of free_pf_arrays() will free all memory allocated by this function. Successive calls will first free previously allocated memory before starting the computation.

See also
  vrna_pf(), bppm_to_structure(), export_bppm(), vrna_exp_params(), free_pf_arrays()

Parameters

  [in] | sequence | The RNA sequence input
  [in,out] | structure | A pointer to a char array where a base pair probability information can be stored in a pseudo-dot-bracket notation (may be NULL, too)
  [in] | parameters | Data structure containing the precalculated Boltzmann factors
  [in] | calculate_bppm | Switch to Base pair probability calculations on/off (0==off)
  [in] | is_constrained | Switch to indicate that a structure contraint is passed via the structure argument (0==off)
  [in] | is_circular | Switch to (de-)activate postprocessing steps in case RNA sequence is circular (0==off)

Returns
  The Gibbs free energy of the ensemble ( ) in kcal/mol

float pf_fold | ( | const char * | sequence,
|  | char * | structure
| ) |  |

`#include <ViennaRNA/part_func.h>`

Compute the partition function of an RNA sequence.

If structure is not a NULL pointer on input, it contains on return a string consisting of the letters " . , | { } ( ) " denoting bases that are essentially unpaired, weakly paired, strongly paired without preference, weakly upstream (downstream) paired, or strongly up- (down-)stream paired bases, respectively. If fold_constrained is not 0, the structure string is interpreted on input as a list of constraints for the folding. The character "x" marks bases that must be unpaired, matching brackets " ( ) " denote base pairs, all other characters are ignored. Any pairs conflicting with the constraint will be forbidden. This is usually sufficient to ensure the constraints are honored. If do_backtrack has been set to 0 base pairing probabilities will not be computed (saving CPU time), otherwise pr will contain the probability that bases i and j pair.

Note
  The global array pr is deprecated and the user who wants the calculated base pair probabilities for further computations is advised to use the function export_bppm().
  OpenMP: This function is not entirely threadsafe. While the recursions are working on their own copies of data the model details for the recursions are determined from the global settings just before entering the recursions. Consider using pf_fold_par() for a really threadsafe implementation.

Precondition
  This function takes its model details from the global variables provided in RNAlib

Postcondition
  After successful run the hidden folding matrices are filled with the appropriate Boltzmann factors. Depending on whether the global variable do_backtrack was set the base pair probabilities are already computed and may be accessed for further usage via the export_bppm() function. A call of free_pf_arrays() will free all memory allocated by this function. Successive calls will first free previously allocated memory before starting the computation.

See also
  pf_fold_par(), pf_circ_fold(), bppm_to_structure(), export_bppm()

Parameters

  sequence | The RNA sequence input
  structure | A pointer to a char array where a base pair probability information can be stored in a pseudo-dot-bracket notation (may be NULL, too)

Returns
  The Gibbs free energy of the ensemble ( ) in kcal/mol

float pf_circ_fold | ( | const char * | sequence,
|  | char * | structure
| ) |  |

`#include <ViennaRNA/part_func.h>`

Compute the partition function of a circular RNA sequence.

Note
  The global array pr is deprecated and the user who wants the calculated base pair probabilities for further computations is advised to use the function export_bppm().
  OpenMP: This function is not entirely threadsafe. While the recursions are working on their own copies of data the model details for the recursions are determined from the global settings just before entering the recursions. Consider using pf_fold_par() for a really threadsafe implementation.

Precondition
  This function takes its model details from the global variables provided in RNAlib

Postcondition
  After successful run the hidden folding matrices are filled with the appropriate Boltzmann factors. Depending on whether the global variable do_backtrack was set the base pair probabilities are already computed and may be accessed for further usage via the export_bppm() function. A call of free_pf_arrays() will free all memory allocated by this function. Successive calls will first free previously allocated memory before starting the computation.

See also
  vrna_pf()

Deprecated:
  Use vrna_pf() instead!

Parameters

  [in] | sequence | The RNA sequence input
  [in,out] | structure | A pointer to a char array where a base pair probability information can be stored in a pseudo-dot-bracket notation (may be NULL, too)

Returns
  The Gibbs free energy of the ensemble ( ) in kcal/mol

void free_pf_arrays | ( | void |  | ) |

`#include <ViennaRNA/part_func.h>`

Free arrays for the partition function recursions.

Call this function if you want to free all allocated memory associated with the partition function forward recursion.

Note
  Successive calls of pf_fold(), pf_circ_fold() already check if they should free any memory from a previous run.
  OpenMP notice:
  This function should be called before leaving a thread in order to avoid leaking memory

Deprecated:
  See vrna_fold_compound_t and its related functions for how to free memory occupied by the dynamic programming matrices

Postcondition
  All memory allocated by pf_fold_par(), pf_fold() or pf_circ_fold() will be free'd

See also
  pf_fold_par(), pf_fold(), pf_circ_fold()

void update_pf_params | ( | int | length | ) |

`#include <ViennaRNA/part_func.h>`

Recalculate energy parameters.

Call this function to recalculate the pair matrix and energy parameters after a change in folding parameters like temperature

Deprecated:
  Use vrna_exp_params_subst() instead

void update_pf_params_par | ( | int | length,
|  | vrna_exp_param_t * | parameters
| ) |  |

`#include <ViennaRNA/part_func.h>`

Recalculate energy parameters.

Deprecated:
  Use vrna_exp_params_subst() instead

FLT_OR_DBL* export_bppm | ( | void |  | ) |

`#include <ViennaRNA/part_func.h>`

Get a pointer to the base pair probability arrayAccessing the base pair probabilities for a pair (i,j) is achieved by.

FLT_OR_DBL *pr = export_bppm();
pr_ij = pr[iindx[i]-j];

Precondition
  Call pf_fold_par(), pf_fold() or pf_circ_fold() first to fill the base pair probability array

See also
  pf_fold(), pf_circ_fold(), vrna_idx_row_wise()

Returns
  A pointer to the base pair probability array

int get_pf_arrays | ( | short ** | S_p,
|  | short ** | S1_p,
|  | char ** | ptype_p,
|  | FLT_OR_DBL ** | qb_p,
|  | FLT_OR_DBL ** | qm_p,
|  | FLT_OR_DBL ** | q1k_p,
|  | FLT_OR_DBL ** | qln_p
| ) |  |

`#include <ViennaRNA/part_func.h>`

Get the pointers to (almost) all relavant computation arrays used in partition function computation.

Precondition
  In order to assign meaningful pointers, you have to call pf_fold_par() or pf_fold() first!

See also
  pf_fold_par(), pf_fold(), pf_circ_fold()

Parameters

  [out] | S_p | A pointer to the 'S' array (integer representation of nucleotides)
  [out] | S1_p | A pointer to the 'S1' array (2nd integer representation of nucleotides)
  [out] | ptype_p | A pointer to the pair type matrix
  [out] | qb_p | A pointer to the QB matrix
  [out] | qm_p | A pointer to the QM matrix
  [out] | q1k_p | A pointer to the 5' slice of the Q matrix ( )
  [out] | qln_p | A pointer to the 3' slice of the Q matrix ( )

Returns
  Non Zero if everything went fine, 0 otherwise

double mean_bp_distance | ( | int | length | ) |

`#include <ViennaRNA/part_func.h>`

Get the mean base pair distance of the last partition function computation.

Deprecated:
  Use vrna_mean_bp_distance() or vrna_mean_bp_distance_pr() instead!

See also
  vrna_mean_bp_distance(), vrna_mean_bp_distance_pr()

Parameters

  length |

Returns
  mean base pair distance in thermodynamic ensemble

double mean_bp_distance_pr | ( | int | length,
|  | FLT_OR_DBL * | pr
| ) |  |

`#include <ViennaRNA/part_func.h>`

Get the mean base pair distance in the thermodynamic ensemble.

This is a threadsafe implementation of mean_bp_dist() !

this can be computed from the pair probs as

Deprecated:
  Use vrna_mean_bp_distance() or vrna_mean_bp_distance_pr() instead!

Parameters

  length | The length of the sequence
  pr | The matrix containing the base pair probabilities

Returns
  The mean pair distance of the structure ensemble

vrna_plist_t* vrna_plist_from_probs | ( | vrna_fold_compound_t * | vc,
|  | double | cut_off
| ) |  |

`#include <ViennaRNA/structure_utils.h>`

Create a vrna_plist_t from base pair probability matrix.

The probability matrix provided via the vrna_fold_compound_t is parsed and all pair probabilities above the given threshold are used to create an entry in the plist

The end of the plist is marked by sequence positions i as well as j equal to 0. This condition should be used to stop looping over its entries

Parameters

  [in] | vc | The fold compound
  [in] | cut_off | The cutoff value

Returns
  A pointer to the plist that is to be created

void assign_plist_from_pr | ( | vrna_plist_t ** | pl,
|  | FLT_OR_DBL * | probs,
|  | int | length,
|  | double | cutoff
| ) |  |

`#include <ViennaRNA/structure_utils.h>`

Create a vrna_plist_t from a probability matrix.

The probability matrix given is parsed and all pair probabilities above the given threshold are used to create an entry in the plist

The end of the plist is marked by sequence positions i as well as j equal to 0. This condition should be used to stop looping over its entries

Note
  This function is threadsafe

Deprecated:
  Use vrna_plist_from_probs() instead!

Parameters

  [out] | pl | A pointer to the vrna_plist_t that is to be created
  [in] | probs | The probability matrix used for creating the plist
  [in] | length | The length of the RNA sequence
  [in] | cutoff | The cutoff value