# The RNA Folding Grammar

The RNA folding grammar as implemented in RNAlib

Specialized Modules:

- Fine-tuning of the Implemented Models
- Unstructured Domains
- Structured Domains
- Secondary Structure Constraints

## Secondary Structure Folding Recurrences

To predict secondary structures composed of the four distinguished loop types introduced before, all algorithms implemented in RNAlib follow a specific recursive decomposition scheme, also known as the RNA folding grammar, or Secondary Structure Folding Recurrences.

However, compared to other RNA secondary structure prediction libraries, our implementation allows for a fine-grained control of the above recursions by constraining both, the individual derivations of the grammar as well as the evaluation of particular loop contributions. Furthermore, we provide a mechanism to extend the above grammar with additional derivation rules, so-called Domains.

## Additional Structural Domains

Some applications of RNA secondary structure prediction require an extension of the regular RNA folding grammar. For instance one would like to include proteins and other ligands binding to unpaired loop regions while competing with conventional base pairing. Another application could be that one may want to include the formation of self-enclosed structural modules, such as G-quadruplexes. For such applications, we provide a pair of additional domains that extend the regular RNA folding grammar, Structured Domains and Unstructured Domains.

While unstructured domains are usually determined by a more or less precise sequence motif, e.g. the binding site for a protein, structured domains are considered self-enclosed modules with a more or less complex pairing pattern. Our extension with these two domains introduces two production rules to fill additional dynamic processing matrices `S` and `U` where we store the pre-computed contributions of structured domains (`S`), and unstructured domains (`U`).

## Structured Domains

Usually, structured domains represent self-enclosed structural modules that exhibit a more or less complex base pairing pattern. This can be more or less well-defined 3D motifs, such as G-Quadruplexes, or loops with additional non-canonical base pair interactions, such as kink-turns.

Note

Currently, our implementation only provides the specialized case of G-Quadruplexes.

## Unstructured Domains

Unstructured domains appear in the production rules of the RNA folding grammar wherever new unpaired nucleotides are attached to a growing substructure (see also Lorenz et al. [2016]):

The white boxes represent the stretch of RNA bound to the ligand and represented by a more or less specific sequence motif. The motif itself is considered unable to form base pairs. The additional production rule `U` is used to precompute the contribution of unpaired stretches possibly bound by one or more ligands. The auxiliary DP matrix for this production rule is filled right before processing the other (regular) production rules of the RNA folding grammar.

## Domain Extension API

For the sake of flexibility, each of the domains is associated with a specific data structure serving as an abstract interface to the extension. The interface uses callback functions to

> - pre-compute arbitrary data, e.g. filling up additional dynamic programming matrices, and

> - evaluate the contribution of a paired or unpaired structural feature of the RNA.

Implementations of these callbacks are separate for regular free energy evaluation, e.g. MFE prediction, and partition function applications. A data structure holding arbitrary data required for the callback functions can be associated to the domain as well. While RNAlib comes with a default implementation for structured and unstructured domains, the system is entirely user-customizable.

See also…

Unstructured Domains, Structured Domains, G-Quadruplexes, Ligands Binding to Unstructured Domains

## Constraints on the Folding Grammar

Secondary Structure constraints can be subdivided into two groups:

> - Hard Constraints

> - Soft Constraints

While Hard-Constraints directly influence the production rules used in the folding recursions by allowing, disallowing, or enforcing certain decomposition steps, Soft-constraints on the other hand are used to change position specific contributions in the recursions by adding bonuses/penalties in form of pseudo free energies to certain loop configurations.

Note

Secondary structure constraints are always applied at decomposition level, i.e. in each step of the recursive structure decomposition, for instance during MFE prediction.

## Hard Constraints API

Hard constraints as implemented in our library can be specified for individual loop types, i.e. the atomic derivations of the RNA folding grammar rules. Hence, the pairing behavior of both, single nucleotides and pairs of bases, can be constrained in every loop context separately. Additionally, an abstract implementation using a callback mechanism allows for full control of more complex hard constraints.

See also…

Hard Constraints

## Soft Constraints API

For the sake of memory efficiency, we do not implement a loop context aware version of soft constraints. The static soft constraints as implemented only distinguish unpaired from paired nucleotides. This is usually sufficient for most use-case scenarios. However, similar to hard constraints, an abstract soft constraints implementation using a callback mechanism exists, that allows for any soft constraint that is compatible with the RNA folding grammar. Thus, loop contexts and even individual derivation rules can be addressed separately for maximum flexibility in soft-constraints application.

See also…

Soft Constraints, Incorporating Ligands Binding to Specific Sequence/Structure Motifs, SHAPE Reactivity Data

  Typedefs

  typedef int (*vrna_grammar_rule_f)( vrna_fold_compound_t *fc, int i, int j, void *data)
    #include <ViennaRNA/grammar.h>
  typedef void (*vrna_grammar_rule_f_aux)( vrna_fold_compound_t *fc, int i, int j, void *data)
    #include <ViennaRNA/grammar.h>
  typedef FLT_OR_DBL (*vrna_grammar_rule_f_exp)( vrna_fold_compound_t *fc, int i, int j, void *data)
    #include <ViennaRNA/grammar.h>
  typedef void (*vrna_grammar_rule_f_aux_exp)( vrna_fold_compound_t *fc, int i, int j, void *data)
    #include <ViennaRNA/grammar.h>
  typedef void (*vrna_grammar_cond_f)( vrna_fold_compound_t *fc, unsigned char stage, void *data)
    #include <ViennaRNA/grammar.h>
  typedef void (*vrna_grammar_data_free_f)(void *data)
    #include <ViennaRNA/grammar.h>

    Free auxiliary data.

    Param data:

      The auxiliary data to be free’d

  typedef struct vrna_gr_aux_s vrna_gr_aux_t
    #include <ViennaRNA/grammar.h>

  Functions

  int vrna_gr_set_aux_f( vrna_fold_compound_t *fc, vrna_grammar_rule_f cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_exp_f( vrna_fold_compound_t *fc, vrna_grammar_rule_f_exp cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_c( vrna_fold_compound_t *fc, vrna_grammar_rule_f cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_exp_c( vrna_fold_compound_t *fc, vrna_grammar_rule_f_exp cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_m( vrna_fold_compound_t *fc, vrna_grammar_rule_f cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_exp_m( vrna_fold_compound_t *fc, vrna_grammar_rule_f_exp cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_m1( vrna_fold_compound_t *fc, vrna_grammar_rule_f cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_exp_m1( vrna_fold_compound_t *fc, vrna_grammar_rule_f_exp cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux( vrna_fold_compound_t *fc, vrna_grammar_rule_f_aux cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_aux_exp( vrna_fold_compound_t *fc, vrna_grammar_rule_f_aux_exp cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_data( vrna_fold_compound_t *fc, void *data, vrna_grammar_data_free_f free_data)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_set_cond( vrna_fold_compound_t *fc, vrna_grammar_cond_f cb)
    #include <ViennaRNA/grammar.h>
  int vrna_gr_reset( vrna_fold_compound_t *fc)
    #include <ViennaRNA/grammar.h>
  struct vrna_gr_aux_s

    Public Members

    vrna_grammar_cond_f cb_proc

      A callback for pre- and post-processing of auxiliary grammar rules.

    vrna_grammar_rule_f cb_aux_f
    vrna_grammar_rule_f cb_aux_c
    vrna_grammar_rule_f cb_aux_m
    vrna_grammar_rule_f cb_aux_m1
    vrna_grammar_rule_f_aux cb_aux
    vrna_grammar_rule_f_exp cb_aux_exp_f
    vrna_grammar_rule_f_exp cb_aux_exp_c
    vrna_grammar_rule_f_exp cb_aux_exp_m
    vrna_grammar_rule_f_exp cb_aux_exp_m1
    vrna_grammar_rule_f_aux_exp cb_aux_exp
    void *data
    vrna_grammar_data_free_f free_data