# Global Partition Function and Equilibrium Probabilities

Variations of the global partition function algorithm.

We provide implementations of the global partition function algorithm for

- Single sequences,

- Multiple sequence alignments (MSA), and

- RNA-RNA hybrids

  Basic global partition function interface

  FLT_OR_DBL vrna_pf(vrna_fold_compound_t *fc, char *structure)
    #include <ViennaRNA/part_func.h>

    Compute the partition function \(Q\) 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 model’s compute_bpp 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.

    SWIG Wrapper Notes:

      This function is attached as method `pf()` to objects of type `fold_compound`. See, e.g. `RNA.fold_compound.pf()` in the Python API.

    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()

    Note

    This function is polymorphic. It accepts vrna_fold_compound_t of type VRNA_FC_TYPE_SINGLE, and VRNA_FC_TYPE_COMPARATIVE. Also, this function may return INF / 100. in case of contradicting constraints or numerical over-/underflow. In the latter case, a corresponding warning will be issued to `stdout`.

    Parameters:

      - fc – [inout] The fold compound data structure

      - structure – [inout] A pointer to the character array where position-wise pairing propensity will be stored. (Maybe NULL)

    Returns:

      The ensemble free energy \(G = -RT \cdot \log(Q) \) in kcal/mol

  vrna_dimer_pf_t vrna_pf_dimer(vrna_fold_compound_t *fc, char *structure)
    #include <ViennaRNA/part_func.h>

    Calculate partition function and base pair probabilities of nucleic acid/nucleic acid dimers.

    This is the cofold partition function folding.

    SWIG Wrapper Notes:

      This function is attached as method `pf_dimer()` to objects of type `fold_compound`. See, e.g. `RNA.fold_compound.pf_dimer()` in the Python API.

    See also

    vrna_fold_compound() for how to retrieve the necessary data structure

    Note

    This function may return INF / 100. for the `FA`, `FB`, `FAB`, `F0AB` members of the output data structure in case of contradicting constraints or numerical over-/underflow. In the latter case, a corresponding warning will be issued to `stdout`.

    Parameters:

      - fc – the fold compound data structure

      - structure – Will hold the structure or constraints

    Returns:

      vrna_dimer_pf_t structure containing a set of energies needed for concentration computations.

  FLT_OR_DBL *vrna_pf_substrands(vrna_fold_compound_t *fc, size_t complex_size)
    #include <ViennaRNA/part_func.h>
  FLT_OR_DBL vrna_pf_add(FLT_OR_DBL dG1, FLT_OR_DBL dG2, double kT)
    #include <ViennaRNA/part_func.h>

  Simplified global partition function computation using sequence(s) or multiple sequence alignment(s)

  float vrna_pf_fold(const char *sequence, char *structure, vrna_ep_t **pl)
    #include <ViennaRNA/part_func.h>

    Compute Partition function \(Q\) (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.

    See also

    vrna_pf_circfold(), vrna_pf(), vrna_fold_compound(), vrna_fold_compound_t

    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.

    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_ep_t to store pairing probabilities (Maybe NULL)

    Returns:

      The ensemble free energy \(G = -RT \cdot \log(Q) \) in kcal/mol

  float vrna_pf_circfold(const char *sequence, char *structure, vrna_ep_t **pl)
    #include <ViennaRNA/part_func.h>

    Compute Partition function \(Q\) (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.

    Folding of circular RNA sequences is handled as a post-processing step of the forward recursions. See Hofacker and Stadler [2006] for further details.

    See also

    vrna_pf_fold(), vrna_pf(), vrna_fold_compound(), vrna_fold_compound_t

    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.

    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_ep_t to store pairing probabilities (Maybe NULL)

    Returns:

      The ensemble free energy \(G = -RT \cdot \log(Q) \) in kcal/mol

  float vrna_pf_alifold(const char **sequences, char *structure, vrna_ep_t **pl)
    #include <ViennaRNA/part_func.h>

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

    This simplified interface to vrna_pf() computes the partition function and, if required, base pair probabilities for an RNA sequence alignment 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.

    See also

    vrna_pf_circalifold(), vrna_pf(), vrna_fold_compound_comparative(), vrna_fold_compound_t

    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.

    Parameters:

      - sequences – RNA sequence alignment

      - 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_ep_t to store pairing probabilities (Maybe NULL)

    Returns:

      The ensemble free energy \(G = -RT \cdot \log(Q) \) in kcal/mol

  float vrna_pf_circalifold(const char **sequences, char *structure, vrna_ep_t **pl)
    #include <ViennaRNA/part_func.h>

    Compute Partition function \(Q\) (and base pair probabilities) for an alignment of circular RNA sequences using a comparative method.

    This simplified interface to vrna_pf() computes the partition function and, if required, base pair probabilities for an RNA sequence alignment 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.

    Folding of circular RNA sequences is handled as a post-processing step of the forward recursions. See Hofacker and Stadler [2006] for further details.

    See also

    vrna_pf_alifold(), vrna_pf(), vrna_fold_compound_comparative(), vrna_fold_compound_t

    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.

    Parameters:

      - sequences – Sequence alignment of circular RNAs

      - 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_ep_t to store pairing probabilities (Maybe NULL)

    Returns:

      The ensemble free energy \(G = -RT \cdot \log(Q) \) in kcal/mol

  vrna_dimer_pf_t vrna_pf_co_fold(const char *seq, char *structure, vrna_ep_t **pl)
    #include <ViennaRNA/part_func.h>

    Calculate partition function and base pair probabilities of nucleic acid/nucleic acid dimers.

    This simplified interface to vrna_pf_dimer() computes the partition function and, if required, base pair probabilities for an RNA-RNA interaction 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.

    See also

    vrna_pf_dimer()

    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_dimer(), and the data structure vrna_fold_compound_t instead.

    Parameters:

      - seq – Two concatenated RNA sequences with a delimiting ‘&’ in between

      - 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_ep_t to store pairing probabilities (Maybe NULL)

    Returns:

      vrna_dimer_pf_t structure containing a set of energies needed for concentration computations.

  Functions

  vrna_ep_t *vrna_plist_from_probs(vrna_fold_compound_t *fc, double cut_off)
    #include <ViennaRNA/utils/structures.h>

    Create a vrna_ep_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:

      - fc – [in] The fold compound

      - cut_off – [in] The cutoff value

    Returns:

      A pointer to the plist that is to be created

  struct vrna_dimer_pf_s
    #include <ViennaRNA/part_func.h>

    Data structure returned by vrna_pf_dimer()

    Public Members

    double F0AB

      Null model without DuplexInit.

    double FAB

      all states with DuplexInit correction

    double FcAB

      true hybrid states only

    double FA

      monomer A

    double FB

      monomer B

  struct vrna_multimer_pf_s

    Public Members

    double F_connected

      Fully connected ensemble (incl. DuplexInititiation and rotational symmetry correction.

    double *F_monomers

      monomers

    size_t num_monomers

      Number of monomers.