  A new statistical method of alignment of two heteropolymers which can form
hierarchical cloverleaf-like secondary structures is proposed. This offers a
new constructive algorithm for quantitative determination of binding free
energy of two noncoding RNAs with arbitrary primary sequences. The alignment of
ncRNAs differs from the complete alignment of two RNA sequences: in ncRNA case
we align only the sequences of nucleotides which constitute pairs between two
different RNAs, while the secondary structure of each RNA comes into play only
by the combinatorial factors affecting the entropc contribution of each
molecule to the total cost function. The proposed algorithm is based on two
observations: i) the standard alignment problem is considered as a
zero-temperature limit of a more general statistical problem of binding of two
associating heteropolymer chains; ii) this last problem is generalized onto the
sequences with hierarchical cloverleaf-like structures (i.e. of RNA-type).
Taking zero-temperature limit at the very end we arrive at the desired "cost
function" of the system with account for entropy of side cactus-like loops.
Moreover, we have demonstrated in detail how our algorithm enables to solve the
"structure recovery" problem. Namely, we can predict in zero-temperature limit
the cloverleaf-like (i.e. secondary) structure of interacting ncRNAs by knowing
only their primary sequences.
