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    We developed LinearCDSfold, a novel dynamic programming algorithm for designing coding sequences (CDS) that optimizes both secondary structure stability and codon adaptation index. This method offers accurate and efficient CDS design, outperforming existing tools in speed.

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    Area of Science:

    • Computational Biology
    • Bioinformatics
    • Synthetic Biology

    Background:

    • Existing dynamic programming algorithms like CDSfold focus on minimizing minimum free energy (MFE) for coding sequence (CDS) design.
    • Modifying these algorithms to jointly optimize secondary structure stability and codon adaptation index (CAI) has been challenging.

    Purpose of the Study:

    • To modify the CDSfold dynamic programming algorithm for the joint optimization of CDS secondary structure stability and CAI.
    • To develop an efficient computational tool for high-quality CDS design.

    Main Methods:

    • Modified a dynamic programming algorithm to exactly solve the joint CDS design problem in O(L^3) time and O(L^2) space.
    • Accelerated the algorithm using beam search for approximate CDS design in O(L) time, implemented as LinearCDSfold.
    • Compared LinearCDSfold's performance against state-of-the-art tools LinearDesign and DERNA.

    Main Results:

    • LinearCDSfold achieves comparable accuracy to LinearDesign and DERNA in terms of MFE and CAI when using exact search.
    • LinearCDSfold demonstrates significantly faster runtime than DERNA, despite similar theoretical complexity.
    • Beam search in LinearCDSfold enables rapid design of high-quality approximate CDS with excellent MFE and CAI.

    Conclusions:

    • The modified DP algorithm successfully addresses the challenge of jointly optimizing CDS secondary structure stability and CAI.
    • LinearCDSfold provides an accurate and efficient tool for CDS design, with a fast approximate design option.
    • This work advances computational methods for synthetic biology and genetic engineering.