Alignment of RNA molecules: Binding energy and statistical properties of random sequences

A new statistical approach to the problem of pairwise alignment of RNA sequences is proposed. The problem is analyzed for a pair of interacting polymers forming an RNA-like hierarchical cloverleaf structures. An alignment is characterized by the numbers of matches, mismatches, and gaps. A weight function is assigned to each alignment; this function is interpreted as a free energy taking into account both direct monomer-monomer interactions and a combinatorial contribution due to formation of various cloverleaf secondary structures. The binding free energy is determined for a pair of RNA molecules. Statistical properties are discussed, including fluctuations of the binding energy between a pair of RNA molecules and loop length distribution in a complex. Based on an analysis of the free energy per nucleotide pair complexes of random RNAs as a function of the number of nucleotide types c , a hypothesis is put forward about the exclusivity of the alphabet c = 4 used by nature.