CParty: Conditional partition function for density-2 RNA pseudoknots

Abstract RNA molecules fold into biologically important functional structures. Efficient dynamic programming RNA (secondary) structure prediction algorithms restrict the the search space to evade NP-hardness of general pseudoknot prediction. While such prediction algorithms can be extended to provide a stochastic view on RNA ensembles, they are either limited to pseudoknot-free structures or extremely complex. To overcome this dilemma, we follow the hierarchical folding hypothesis, i.e. the bio-physically well-motivated assumption that non-crossing structures fold relatively fast prior to the formation of pseudoknot interactions. Thus, we efficiently compute the conditional partition function (CPF) given a non-crossing structure G for a subset of pseudoknotted structures i.e. density-2 structures G ∪ G ′ for non-crossing disjoint G ′. Notably, this enables sampling from the hierarchical distribution P ( G ′| G ). As our main contribution, we devise the algorithm CParty , which transfers the dynamic programming scheme of HFold (which minimizes free energy of pseudoknots in a realistic model) to a partition function variant by for the first time de-ambiguating its decomposition of density-2 structures. Compared to the only other available pseudoknot partition function algorithm, which covers simple pseudoknots, our method covers a much larger structure class; at the same time, it is significantly more efficient—reducing the time as well as the space complexity by a quadratic factor. Summarizing, we provide a highly efficient, cubic time, algorithm for the stochastic analysis of pseudoknotted RNAs, which enables novel applications. For example, we discuss how the CPF for a pseudoknotted therapeutic target in SARS-CoV-2 provides insights into RNA structure formation kinetic paths. 2012 ACM Subject Classification Applied computing → Computational biology; Theory of computation → Dynamic programming Digital Object Identifier 10.4230/LIPIcs.WABI.2023.23 Funding Hosna Jabbari : [NSERC DG, Microsoft AI for Health]