Balancing Minimum Free Energy and Codon Adaptation Index for Pareto Optimal RNA Design

Xinyu Gu, Yuanyuan Qi, Mohammed El-Kebir

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The problem of designing an RNA sequence v that encodes for a given target protein w plays an important role in messenger RNA (mRNA) vaccine design. Due to codon degeneracy, there exist exponentially many RNA sequences for a single target protein. These candidate RNA sequences may adopt different secondary structure conformations with varying minimum free energy (MFE), affecting their thermodynamic stability and consequently mRNA half-life. In addition, species-specific codon usage bias, as measured by the codon adaptation index (CAI), also plays an essential role in translation efficiency. While previous works have focused on optimizing either MFE or CAI, more recent works have shown the merits of optimizing both objectives. Importantly, there is a trade-off between MFE and CAI, i.e. optimizing one objective is at the expense of the other. Here, we formulate the Pareto Optimal RNA Design problem, seeking the set of Pareto optimal solutions for which no other solution exists that is better in terms of both MFE and CAI. We introduce DERNA (DEsign RNA), which uses the weighted sum method to enumerate the Pareto front by optimizing convex combinations of both objectives. DERNA uses dynamic programming to solve each convex combination in O(|w|3) time and O(|w|2) space. Compared to a previous approach that only optimizes MFE, we show on a benchmark dataset that DERNA obtains solutions with identical MFE but superior CAI. Additionally, we show that DERNA matches the performance in terms of solution quality of LinearDesign, a recent approach that similarly seeks to balance MFE and CAI. Finally, we demonstrate our method's potential for mRNA vaccine design using SARS-CoV-2 spike as the target protein.

Original languageEnglish (US)
Title of host publication23rd International Workshop on Algorithms in Bioinformatics, WABI 2023
EditorsDjamal Belazzougui, A�da Ouangraoua
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772945
StatePublished - Aug 2023
Externally publishedYes
Event23rd International Workshop on Algorithms in Bioinformatics, WABI 2023 - Houston, United States
Duration: Sep 4 2023Sep 6 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference23rd International Workshop on Algorithms in Bioinformatics, WABI 2023
Country/TerritoryUnited States


  • Multi-objective optimization
  • RNA sequence design
  • dynamic programming
  • mRNA vaccine design
  • reverse translation

ASJC Scopus subject areas

  • Software


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