Molecular contacts, conformational search

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. 

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