Energy Evaluation for Individual Loops

To assess the free energy contribution of a particular loop \(L\) within a secondary structure, two variants are provided

The bare free energy \(E_L\) (usually in units of deka-calories, i.e. multiples of \(10 \text{cal} \cdot \text{mol}^{-1}\), and
The Boltzmann weight \(q = exp(-\beta E_L)\) of the free energy \(E_L\) (with \(\beta = \frac{1}{RT}\), gas constant \(R\) and temperature \(T\))

The latter is usually required for partition function computations.

Table of Contents

General
Exterior Loops
Hairpin Loops
Internal Loops
Multibranch Loops

General 

Functions to evaluate the free energy of particular types of loops.

Functions

int vrna_eval_loop_pt(vrna_fold_compound_t *fc, int i, const short *pt)

#include <ViennaRNA/eval.h>

Calculate energy of a loop.

SWIG Wrapper Notes:: This function is attached as method eval_loop_pt() to objects of type fold_compound. See, e.g. RNA.fold_compound.eval_loop_pt() in the Python API .

Parameters

fc – A vrna_fold_compound_t containing the energy parameters and model details
i – position of covering base pair
pt – the pair table of the secondary structure

Returns

free energy of the loop in 10cal/mol

int vrna_eval_loop_pt_v(vrna_fold_compound_t *fc, int i, const short *pt, int verbosity_level)

#include <ViennaRNA/eval.h>

Calculate energy of a loop.

Parameters

fc – A vrna_fold_compound_t containing the energy parameters and model details
i – position of covering base pair
pt – the pair table of the secondary structure
verbosity_level – The level of verbosity of this function

Returns

free energy of the loop in 10cal/mol

Exterior Loops 

Functions to evaluate the free energy contributions for exterior (external) loops.

Boltzmann weight (partition function) interface

typedef struct vrna_mx_pf_aux_el_s *vrna_mx_pf_aux_el_t

#include <ViennaRNA/loops/external.h>

Auxiliary helper arrays for fast exterior loop computations.

See also

vrna_exp_E_ext_fast_init(), vrna_exp_E_ext_fast_rotate(), vrna_exp_E_ext_fast_free(), vrna_exp_E_ext_fast()

FLT_OR_DBL vrna_exp_E_ext_stem(unsigned int type, int n5d, int n3d, vrna_exp_param_t *p)

#include <ViennaRNA/loops/external.h>

Evaluate a stem branching off the exterior loop (Boltzmann factor version)

Given a base pair \((i,j)\) encoded by type, compute the energy contribution including dangling-end/terminal-mismatch contributions. Instead of returning the energy contribution per-se, this function returns the corresponding Boltzmann factor. If either of the adjacent nucleotides \((i - 1)\) and \((j+1)\) must not contribute stacking energy, the corresponding encoding must be \(-1\).

See also

vrna_E_ext_stem()

Parameters

type – The base pair encoding
n5d – The encoded nucleotide directly adjacent at the 5’ side of the base pair (may be -1)
n3d – The encoded nucleotide directly adjacent at the 3’ side of the base pair (may be -1)
p – The pre-computed energy parameters (Boltzmann factor version)

Returns

The Boltzmann weighted energy contribution of the introduced exterior-loop stem

vrna_mx_pf_aux_el_t vrna_exp_E_ext_fast_init(vrna_fold_compound_t *fc): #include <ViennaRNA/loops/external.h>

void vrna_exp_E_ext_fast_rotate(vrna_mx_pf_aux_el_t aux_mx): #include <ViennaRNA/loops/external.h>

void vrna_exp_E_ext_fast_free(vrna_mx_pf_aux_el_t aux_mx): #include <ViennaRNA/loops/external.h>

FLT_OR_DBL vrna_exp_E_ext_fast(vrna_fold_compound_t *fc, int i, int j, vrna_mx_pf_aux_el_t aux_mx): #include <ViennaRNA/loops/external.h>

void vrna_exp_E_ext_fast_update(vrna_fold_compound_t *fc, int j, vrna_mx_pf_aux_el_t aux_mx): #include <ViennaRNA/loops/external.h>

Basic free energy interface

int vrna_E_ext_stem(unsigned int type, int n5d, int n3d, vrna_param_t *p)

#include <ViennaRNA/loops/external.h>

Evaluate a stem branching off the exterior loop.

Given a base pair \((i,j)\) encoded by type, compute the energy contribution including dangling-end/terminal-mismatch contributions. Instead of returning the energy contribution per-se, this function returns the corresponding Boltzmann factor. If either of the adjacent nucleotides \((i - 1)\) and \((j+1)\) must not contribute stacking energy, the corresponding encoding must be \(-1\).

See also

vrna_E_exp_stem()

Parameters

type – The base pair encoding
n5d – The encoded nucleotide directly adjacent at the 5’ side of the base pair (may be -1)
n3d – The encoded nucleotide directly adjacent at the 3’ side of the base pair (may be -1)
p – The pre-computed energy parameters

Returns

The energy contribution of the introduced exterior-loop stem

int vrna_eval_ext_stem(vrna_fold_compound_t *fc, int i, int j)

#include <ViennaRNA/loops/external.h>

Evaluate the free energy of a base pair in the exterior loop.

Evalue the free energy of a base pair connecting two nucleotides in the exterior loop and take hard constraints into account.

Typically, this is simply dangling end contributions of the adjacent nucleotides, potentially a terminal A-U mismatch penalty, and maybe some generic soft constraint contribution for that decomposition.

Note

For dangles == 1 || 3 this function also evaluates the three additional pairs (i + 1, j), (i, j - 1), and (i + 1, j - 1) and returns the minimum for all four possibilities in total.

Parameters

fc – Fold compound to work on (defines the model and parameters)
i – 5’ position of the base pair
j – 3’ position of the base pair

Returns

Free energy contribution that arises when this pair is formed in the exterior loop

int vrna_E_ext_loop_5(vrna_fold_compound_t *fc): #include <ViennaRNA/loops/external.h>

int vrna_E_ext_loop_3(vrna_fold_compound_t *fc, int i): #include <ViennaRNA/loops/external.h>

Hairpin Loops 

Functions to evaluate the free energy contributions for hairpin loops.

Basic free energy interface

int vrna_E_hp_loop(vrna_fold_compound_t *fc, int i, int j)

#include <ViennaRNA/loops/hairpin.h>

Evaluate the free energy of a hairpin loop and consider hard constraints if they apply.

This function evaluates the free energy of a hairpin loop

In case the base pair is not allowed due to a constraint conflict, this function returns INF.

Note

This function is polymorphic! The provided vrna_fold_compound_t may be of type VRNA_FC_TYPE_SINGLE or VRNA_FC_TYPE_COMPARATIVE

Parameters

fc – The vrna_fold_compound_t that stores all relevant model settings
i – The 5’ nucleotide of the base pair (3’ to evaluate the pair as exterior hairpin loop)
j – The 3’ nucleotide of the base pair (5’ to evaluate the pair as exterior hairpin loop)

Returns

The free energy of the hairpin loop in 10cal/mol

int vrna_E_ext_hp_loop(vrna_fold_compound_t *fc, int i, int j): #include <ViennaRNA/loops/hairpin.h>
Evaluate the free energy of an exterior hairpin loop and consider possible hard constraints.

Note

This function is polymorphic! The provided vrna_fold_compound_t may be of type VRNA_FC_TYPE_SINGLE or VRNA_FC_TYPE_COMPARATIVE

int vrna_eval_ext_hp_loop(vrna_fold_compound_t *fc, int i, int j): #include <ViennaRNA/loops/hairpin.h>
Evaluate free energy of an exterior hairpin loop.

int vrna_eval_hp_loop(vrna_fold_compound_t *fc, int i, int j)

#include <ViennaRNA/loops/hairpin.h>

Evaluate free energy of a hairpin loop.

SWIG Wrapper Notes:: This function is attached as method eval_hp_loop() to objects of type fold_compound. See, e.g. RNA.fold_compound.eval_hp_loop() in the Python API .

Note

This function is polymorphic! The provided vrna_fold_compound_t may be of type VRNA_FC_TYPE_SINGLE or VRNA_FC_TYPE_COMPARATIVE

Parameters

fc – The vrna_fold_compound_t for the particular energy evaluation
i – 5’-position of the base pair
j – 3’-position of the base pair

Returns

Free energy of the hairpin loop closed by \( (i,j) \) in deka-kal/mol

static int E_Hairpin(int size, int type, int si1, int sj1, const char *string, vrna_param_t *P)

#include <ViennaRNA/loops/hairpin.h>

Compute the Energy of a hairpin-loop.

To evaluate the free energy of a hairpin-loop, several parameters have to be known. A general hairpin-loop has this structure: where X-Y marks the closing pair [e.g. a (G,C) pair]. The length of this loop is 6 as there are six unpaired nucleotides (a1-a6) enclosed by (X,Y). The 5’ mismatching nucleotide is a1 while the 3’ mismatch is a6. The nucleotide sequence of this loop is “a1.a2.a3.a4.a5.a6”

See also

scale_parameters(), vrna_param_t

Note

The parameter sequence should contain the sequence of the loop in capital letters of the nucleic acid alphabet if the loop size is below 7. This is useful for unusually stable tri-, tetra- and hexa-loops which are treated differently (based on experimental data) if they are tabulated.

Warning

Not (really) thread safe! A threadsafe implementation will replace this function in a future release!

Energy evaluation may change due to updates in global variable “tetra_loop”

Parameters

size – The size of the loop (number of unpaired nucleotides)
type – The pair type of the base pair closing the hairpin
si1 – The 5’-mismatching nucleotide
sj1 – The 3’-mismatching nucleotide
string – The sequence of the loop (May be NULL, otherwise mst be at least \(size + 2\) long)
P – The datastructure containing scaled energy parameters

Returns

The Free energy of the Hairpin-loop in dcal/mol

Boltzmann weight (partition function) interface

static FLT_OR_DBL exp_E_Hairpin(int u, int type, short si1, short sj1, const char *string, vrna_exp_param_t *P)

#include <ViennaRNA/loops/hairpin.h>

Compute Boltzmann weight \(e^{-\Delta G/kT} \) of a hairpin loop.

Note

multiply by scale[u+2]

Warning

Not (really) thread safe! A threadsafe implementation will replace this function in a future release!

Energy evaluation may change due to updates in global variable “tetra_loop”

Parameters

u – The size of the loop (number of unpaired nucleotides)
type – The pair type of the base pair closing the hairpin
si1 – The 5’-mismatching nucleotide
sj1 – The 3’-mismatching nucleotide
string – The sequence of the loop (May be NULL, otherwise mst be at least \(size + 2\) long)
P – The datastructure containing scaled Boltzmann weights of the energy parameters

Returns

The Boltzmann weight of the Hairpin-loop

FLT_OR_DBL vrna_exp_E_hp_loop(vrna_fold_compound_t *fc, int i, int j)

#include <ViennaRNA/loops/hairpin.h>

High-Level function for hairpin loop energy evaluation (partition function variant)

See also

vrna_E_hp_loop() for it’s free energy counterpart

Note

This function is polymorphic! The provided vrna_fold_compound_t may be of type VRNA_FC_TYPE_SINGLE or VRNA_FC_TYPE_COMPARATIVE

Internal Loops 

Functions to evaluate the free energy contributions for internal (interior) loops.

Basic free energy interface

int vrna_E_int_loop(vrna_fold_compound_t *fc, int i, int j): #include <ViennaRNA/loops/internal.h>

int vrna_eval_int_loop(vrna_fold_compound_t *fc, int i, int j, int k, int l)

#include <ViennaRNA/loops/internal.h>

Evaluate the free energy contribution of an interior loop with delimiting base pairs \((i,j)\) and \((k,l)\).

SWIG Wrapper Notes:: This function is attached as method eval_int_loop() to objects of type fold_compound. See, e.g. RNA.fold_compound.eval_int_loop() in the Python API .

Note

This function is polymorphic, i.e. it accepts vrna_fold_compound_t of type VRNA_FC_TYPE_SINGLE as well as VRNA_FC_TYPE_COMPARATIVE

int vrna_E_ext_int_loop(vrna_fold_compound_t *fc, int i, int j, int *ip, int *iq): #include <ViennaRNA/loops/internal.h>

int vrna_E_stack(vrna_fold_compound_t *fc, int i, int j): #include <ViennaRNA/loops/internal.h>

Boltzmann weight (partition function) interface

FLT_OR_DBL vrna_exp_E_int_loop(vrna_fold_compound_t *fc, int i, int j): #include <ViennaRNA/loops/internal.h>

FLT_OR_DBL vrna_exp_E_interior_loop(vrna_fold_compound_t *fc, int i, int j, int k, int l): #include <ViennaRNA/loops/internal.h>

Multibranch Loops 

Functions to evaluate the free energy contributions for mutlibranch loops.

Boltzmann weight (partition function) interface

typedef struct vrna_mx_pf_aux_ml_s *vrna_mx_pf_aux_ml_t

#include <ViennaRNA/loops/multibranch.h>

Auxiliary helper arrays for fast exterior loop computations.

See also

vrna_exp_E_ml_fast_init(), vrna_exp_E_ml_fast_rotate(), vrna_exp_E_ml_fast_free(), vrna_exp_E_ml_fast()

FLT_OR_DBL vrna_exp_E_mb_loop_fast(vrna_fold_compound_t *fc, int i, int j, vrna_mx_pf_aux_ml_t aux_mx): #include <ViennaRNA/loops/multibranch.h>

vrna_mx_pf_aux_ml_t vrna_exp_E_ml_fast_init(vrna_fold_compound_t *fc): #include <ViennaRNA/loops/multibranch.h>

void vrna_exp_E_ml_fast_rotate(vrna_mx_pf_aux_ml_t aux_mx): #include <ViennaRNA/loops/multibranch.h>

void vrna_exp_E_ml_fast_free(vrna_mx_pf_aux_ml_t aux_mx): #include <ViennaRNA/loops/multibranch.h>

const FLT_OR_DBL *vrna_exp_E_ml_fast_qqm(vrna_mx_pf_aux_ml_t aux_mx): #include <ViennaRNA/loops/multibranch.h>

const FLT_OR_DBL *vrna_exp_E_ml_fast_qqm1(vrna_mx_pf_aux_ml_t aux_mx): #include <ViennaRNA/loops/multibranch.h>

FLT_OR_DBL vrna_exp_E_ml_fast(vrna_fold_compound_t *fc, int i, int j, vrna_mx_pf_aux_ml_t aux_mx): #include <ViennaRNA/loops/multibranch.h>

Basic free energy interface

int vrna_E_mb_loop_stack(vrna_fold_compound_t *fc, int i, int j)

#include <ViennaRNA/loops/multibranch.h>

Evaluate energy of a multi branch helices stacking onto closing pair (i,j)

Computes total free energy for coaxial stacking of (i.j) with (i+1.k) or (k+1.j-1)

int vrna_E_mb_loop_fast(vrna_fold_compound_t *fc, int i, int j, int *dmli1, int *dmli2): #include <ViennaRNA/loops/multibranch.h>

int E_ml_rightmost_stem(int i, int j, vrna_fold_compound_t *fc): #include <ViennaRNA/loops/multibranch.h>

int vrna_E_ml_stems_fast(vrna_fold_compound_t *fc, int i, int j, int *fmi, int *dmli): #include <ViennaRNA/loops/multibranch.h>

Energy Evaluation for Individual Loops

General

Exterior Loops

Hairpin Loops

Internal Loops

Multibranch Loops

General 

Exterior Loops 

Hairpin Loops 

Internal Loops 

Multibranch Loops 