PKProbDesign: RNA inverse folding including pseudoknots by optimizing thermodynamic folding probability

Motivation: RNA inverse folding, the design of RNA sequences that fold into specified target secondary structures, is a central problem in RNA design, with applications in functional RNA engineering, synthetic biology, and nucleic-acid therapeutics. This task becomes especially challenging for pseudoknotted target structures because pseudoknots break the nested structure assumed by standard thermodynamic folding models. Existing pseudoknot inverse-folding methods often rely on structure-predictor-based objectives. These methods do not directly optimize the probability that a sequence folds into the specified pseudoknotted target structure. Such optimization requires an evaluator that can assign a folding probability to the specified target within a pseudoknot-aware ensemble. Results: We present PKProbDesign, a sampling-based inverse-folding framework that directly optimizes a thermodynamic folding-probability objective for pseudoknotted targets. For each target, sampled sequences are scored by combining the folding probability of a pseudoknot-free scaffold with the conditional folding probability of the remaining extension component. On 254 unique density-2 PseudoBase++ targets, PKProbDesign achieved the highest pseudo-joint folding probability on 245 targets, compared with 6 for DesiRNA, 3 for MODENA, and none for antaRNA. Conclusions: PKProbDesign demonstrates that pseudoknot inverse folding can be formulated with target folding probability as its objective rather than structure-prediction agreement alone. By combining scaffold decomposition with conditional folding-probability evaluation based on CParty, the method provides a practical folding-probability-based approach to designing sequences for density-2 pseudoknotted targets. Availability: The source code of PKProbDesign is available at https://github.com/TakumiOtagaki/PKProbDesign.