Time and space efficient RNA-RNA interaction prediction via sparse folding

In the past years, a large set of new regulatory ncRNAs have been identified, but the number of experimentally verified targets is considerably low. Thus, computational target prediction methods are on high demand. Whereas all previous approaches for predicting a general joint structure have a complexity of O(n⁶) running time and O(n⁴) space, a more time and space efficient interaction prediction that is able to handle complex joint structures is necessary for genome-wide target prediction problems. In this paper we show how to reduce both the time and space complexity of the RNA-RNA interaction prediction problem as described by Alkan et al. [1] via dynamic programming sparsification - which allows to discard large portions of DP tables without loosing optimality. Applying sparsification techniques reduces the complexity of the original algorithm from O(n⁶) time and O(n⁴) space to O(n⁴ψ(n)) time and O(n ²ψ(n)+n³) space for some function ψ(n), which turns out to have small values for the range of n that we encounter in practice. Under the assumption that the polymer-zeta property holds for RNAstructures, we demonstrate that ψ(n) = O(n) on average, resulting in a linear time and space complexity improvement over the original algorithm. We evaluate our sparsified algorithm for RNA-RNA interaction prediction by total free energy minimization, based on the energy model of Chitsaz et al. [2], on a set of known interactions. Our results confirm the significant reduction of time and space requirements in practice.