Abstract

Motivation: RNA inverse folding, the design of RNA sequences that fold into specified target 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 disrupt the nested structure assumed by standard thermodynamic folding models. Existing pseudoknot inverse-folding methods often rely on structure-predictor-based objectives. Direct optimization of the thermodynamic folding probability of a specified pseudoknotted target remains limited. This requires an evaluator that can assign target-specific folding probabilities within a pseudoknot-aware ensemble and can be used as an optimization signal. Results: We present PKProbDesign, a sampling-based inverse-folding framework that directly optimizes a thermodynamic folding-probability objective for pseudoknotted targets. For each target, candidate sequences are scored by combining the folding probability of a pseudoknot-free sca[ff]old with the conditional folding probability of the remaining extension component. On 354 PseudoBase++ targets, PKProbDesign achieved the highest folding probability on 221 targets, compared with 117 for DesiRNA and 16 for MODENA. Conclusions: PKProbDesign demonstrates that pseudoknot inverse folding can be formulated around target folding probabilities rather than structure-prediction agreement alone. By combining sca[ff]old decomposition with HFold/CParty-consistent conditional-ensemble evaluation, the method provides a practical probability-based framework for designing sequences for density-2 pseudoknotted targets. Availability: The source code of PKProbDesign is available at https://github.com/TakumiOtagaki/ PKProbDesign.