Partition Function for two hybridized Sequences

Overview

Partition Function Cofolding. More…

// typedefs

typedef struct vrna_dimer_conc_s vrna_dimer_conc_t
typedef struct vrna_dimer_conc_s ConcEnt
typedef struct vrna_dimer_pf_s vrna_dimer_pf_t
typedef struct vrna_dimer_pf_s cofoldF

// structs

struct vrna_dimer_pf_s

// global variables

int mirnatog
double F_monomer[2]

// global functions

vrna_dimer_conc_t* vrna_pf_dimer_concentrations (
    double FcAB,
    double FcAA,
    double FcBB,
    double FEA,
    double FEB,
    const double* startconc,
    const vrna_exp_param_t* exp_params
    )

void vrna_pf_dimer_probs (
    double FAB,
    double FA,
    double FB,
    vrna_ep_t* prAB,
    const vrna_ep_t* prA,
    const vrna_ep_t* prB,
    int Alength,
    const vrna_exp_param_t* exp_params
    )

vrna_dimer_pf_t vrna_pf_dimer (
    vrna_fold_compound_t* vc,
    char* structure
    )

vrna_dimer_pf_t vrna_pf_co_fold (
    const char* seq,
    char* structure,
    vrna_ep_t** pl
    )

Detailed Documentation

Partition Function Cofolding.

To simplify the implementation the partition function computation is done internally in a null model that does not include the duplex initiation energy, i.e. the entropic penalty for producing a dimer from two monomers). The resulting free energies and pair probabilities are initially relative to that null model. In a second step the free energies can be corrected to include the dimerization penalty, and the pair probabilities can be divided into the conditional pair probabilities given that a re dimer is formed or not formed. See [1] for further details.

As for folding one RNA molecule, this computes the partition function of all possible structures and the base pair probabilities. Uses the same global pf_scale variable to avoid overflows.

To simplify the implementation the partition function computation is done internally in a null model that does not include the duplex initiation energy, i.e. the entropic penalty for producing a dimer from two monomers). The resulting free energies and pair probabilities are initially relative to that null model. In a second step the free energies can be corrected to include the dimerization penalty, and the pair probabilities can be divided into the conditional pair probabilities given that a re dimer is formed or not formed.

After computing the partition functions of all possible dimeres one can compute the probabilities of base pairs, the concentrations out of start concentrations and sofar and soaway.

Dimer formation is inherently concentration dependent. Given the free energies of the monomers A and B and dimers AB, AA, and BB one can compute the equilibrium concentrations, given input concentrations of A and B, see e.g. Dimitrov & Zuker (2004)

Typedefs

typedef struct vrna_dimer_conc_s vrna_dimer_conc_t
Typename for the data structure that stores the dimer concentrations, vrna_dimer_conc_s , as required by vrna_pf_dimer_concentration()
typedef struct vrna_dimer_conc_s ConcEnt
Backward compatibility typedef for vrna_dimer_conc_s .
typedef struct vrna_dimer_pf_s vrna_dimer_pf_t
Typename for the data structure that stores the dimer partition functions, vrna_dimer_pf_s , as returned by vrna_pf_dimer()
typedef struct vrna_dimer_pf_s cofoldF
Backward compatibility typedef for vrna_dimer_pf_s .

Global Variables

int mirnatog
Toggles no intrabp in 2nd mol.
double F_monomer [2]
Free energies of the two monomers.

Global Functions

vrna_dimer_conc_t* vrna_pf_dimer_concentrations (
    double FcAB,
    double FcAA,
    double FcBB,
    double FEA,
    double FEB,
    const double* startconc,
    const vrna_exp_param_t* exp_params
    )
Given two start monomer concentrations a and b, compute the concentrations in thermodynamic equilibrium of all dimers and the monomers.

This function takes an array ‘startconc’ of input concentrations with alternating entries for the initial concentrations of molecules A and B (terminated by two zeroes), then computes the resulting equilibrium concentrations from the free energies for the dimers. Dimer free energies should be the dimer-only free energies, i.e. the FcAB entries from the vrna_dimer_pf_t struct.

Parameters:

FcAB Free energy of AB dimer (FcAB entry)
FcAA Free energy of AA dimer (FcAB entry)
FcBB Free energy of BB dimer (FcAB entry)
FEA Free energy of monomer A
FEB Free energy of monomer B
startconc List of start concentrations [a0],[b0],[a1],[b1],…,[an][bn],[0],[0]
exp_params The precomputed Boltzmann factors

Returns:

vrna_dimer_conc_t array containing the equilibrium energies and start concentrations

void vrna_pf_dimer_probs (
    double FAB,
    double FA,
    double FB,
    vrna_ep_t* prAB,
    const vrna_ep_t* prA,
    const vrna_ep_t* prB,
    int Alength,
    const vrna_exp_param_t* exp_params
    )
Compute Boltzmann probabilities of dimerization without homodimers.

Given the pair probabilities and free energies (in the null model) for a dimer AB and the two constituent monomers A and B, compute the conditional pair probabilities given that a dimer AB actually forms. Null model pair probabilities are given as a list as produced by vrna_plist_from_probs() , the dimer probabilities ‘prAB’ are modified in place.

Parameters:

FAB free energy of dimer AB
FA free energy of monomer A
FB free energy of monomer B
prAB pair probabilities for dimer
prA pair probabilities monomer
prB pair probabilities monomer
Alength Length of molecule A
exp_params The precomputed Boltzmann factors
vrna_dimer_pf_t vrna_pf_dimer (
    vrna_fold_compound_t* vc,
    char* structure
    )
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

Parameters:

vc 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.

See also:

vrna_fold_compound() for how to retrieve the necessary data structure

vrna_dimer_pf_t vrna_pf_co_fold (
    const char* seq,
    char* structure,
    vrna_ep_t** pl
    )
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.

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.

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.

See also:

vrna_pf_dimer()