Conformational search space

Here, we consider RNA three-dimensional structure as the assembly of its constituent nucleotides in three-dimensional space. We introduce a RNA conformational search space defined by molecular contacts (or constraints). The molecular contacts are used in operators that position and orient the nucleotides in three-dimensional space. 

In the following, we first present how contact graphs define the conformational search space of RNAs, to position and orient all nucleotides in three-dimensions. Then, a database of spatial relations based on molecular contacts, as observed among pairs of nucleotides in known structures, is introduced. 

RNA Conformational Search Space Defined by Molecular Contacts. The premise to use molecular contacts in defining the conformational space of RNAs relies on the fact that molecular contacts contain all the information critical to the global fold of the molecule. Consider the best characterized case of an RNA double-helix. The spatial relation between two bases involved in a Watson-Ciick pairing can be used, in conjunction with a canonical base stacking geometry, as a good approximation to position and orient double-helical strands in three-dimensions. 

The number of spanning trees, pairs of nucleotide contacts and homogeneous transformation matrices associated with a contact graph determine the conformational search space size of a RNA. The number of homogeneous transformation matrices associated with a molecular contact type is given by the number of occurrences observed in all available RNA three-dimensional structures in the Protein DataBank (PDB) (7), Nucleic acids DataBase (NDB) (5) and other personally communicated structures. 

The development of RNA three-dimensional structure determination methods requires three essential components. First is a computer representation, or a data structure, of RNA three-dimensional structural knowledge and data. Second is an RNA conformational search space that includes three-dimensional structures consistent with the computer representation. The implementation of a conformational search space includes the following tasks (i) the creation of a set of operators to manipulate the RNA three-dimensional structures (ii) the definition of a metric to evaluate RNA three-dimensional structures (iii) the design of an efficient method for applying the chosen metric and (iv) the design of an efficient method for generating the next three-dimensional structure to consider. Third is an inference engine which searches the conformational search space for three-dimensional structures that fit input descriptions. 

A conformational search space is a set of three-dimensional structures that we are interested in searching. 

The three-dimensional structures of a conformational search space are defined by a series of parameters and its size by the product of the numbers of allowed values that can be assigned to each parameter. The three-dimensional structures in a conformational search space are related to each others by operators that modify the value of each parameter. 

The size of a conformational search space defined by spatial relations among nitrogen bases is smaller than a conformational search space defined by backbone torsion angles. Mainly because of the theoretical flexibility of the backbone, a conformational search space defined by backbone torsion angles produces a very large number of three-dimensional structures of high uncertainty in the position and orientation of the nitrogen bases. 

The adenines of the pairs were superimposed to evaluate the distribution of the stacked guanines. Mainly because of weaker stabilizing forces, the conformational freedom of two stacked bases is larger than that of paired bases. The most important variation comes from the ba.se overlapping. Neverthele.ss, ba.se stacking information also reduces the conformational. search space of RNA three-dimensional structures and thus should be used as much as possible in their determination. 

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