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DERNA: Pareto Optimal RNA Design for mRNA Vaccine Development

• Simultaneously Optimize MFE and CAI: Balance thermodynamic mRNA stability with species-specific translation efficiency.

• Exact Pareto Front Enumeration: Execute a systematic multi-objective sweep to uncover a diverse landscape of non-dominated RNA sequences.

• Proven Vaccine Design Potential: Generate alternative mRNA sequences for complex targets like the SARS-CoV-2 spike protein with superior stability characteristics.

Pareto Optimal mRNA Design

The design of an RNA sequence v that encodes a target protein sequence w is a cornerstone of messenger RNA (mRNA) vaccine and therapeutic development. Due to codon degeneracy, single protein sequences correspond to an exponentially large space of potential synonymous mRNA sequences. Selecting the right sequence dictates two critical properties:

1. Thermodynamic Stability (MFE): Candidates fold into distinct secondary structures. Sequences achieving the Minimum Free Energy (MFE) display enhanced structural integrity and longer biological half-lives.

2. Translation Efficiency (CAI): Organisms display specific codon usage biases. The Codon Adaptation Index (CAI) quantifies this bias against highly expressed reference genes; higher CAI correlates with rapid ribosomal translation.

While optimizing one objective typically comes at the strict expense of the other, DERNA (DEsign RNA) models this trade-off as a formal multi-objective optimization challenge: the PARETO OPTIMAL RNA DESIGN (PORD) problem. Instead of outputting a single compromised sequence, DERNA mathematically enumerates the Pareto front—the set of optimal solutions where no alternative sequence can improve one metric without degrading the other.

How DERNA Works

DERNA handles multi-objective constraints by leveraging the weighted sum method to optimize convex combinations of both metrics:

Objective = λ x MFE(v,P) - (1-λ) x CAI(v,w)

Here, λ in [0,1] explicitly dictates the prioritization between structure and expression.

Dynamic Programming Core

For any fixed λ value (the Balanced RNA Design or BRD problem), DERNA extends the classical Zuker and Stiegler secondary structure prediction recurrence. It simultaneously handles codon selection for each input amino acid and tracks CAI contributions across codon boundaries to eliminate double-counting. DERNA evaluates the thermodynamic contributions of all 5 structural elements:

• Stacking elements

• Hairpin loops

• Bulge loops

• Internal loops

• Multibranch loops

By storing 4 parallel dynamic programming tables (O, E, M, and N), each single instance is solved exactly in O(|w|^3) time and O(|w|^2) space.

Algorithmic Sweep

To map the continuous Pareto front, DERNA initiates an automated queue-driven parameter sweep over λ. It recursively samples intermediate values, dynamically tightening the sampling density wherever unique structural variants emerge, ensuring a mathematically rigorous exploration of the design space.

Performance and Validation

Peerless Solution Quality

When strictly prioritizing structural stability (λ -> 1), DERNA identifies solutions that match the exact absolute minimum MFE of single-objective tools like CDSfold, yet uncovers sequences with vastly superior CAI scores. This guarantees maximized translation speed without dropping a single kcal/mol of thermodynamic mRNA stability.

Exact vs. Heuristic Search

In benchmarks against alternative frameworks like LinearDesign, DERNA demonstrates matching, high-fidelity solution profiles. However, while other tools implement closed-source, heuristic fixed-size beam searches that risk missing true thermodynamic minima, DERNA provides an exact, fully open-source global search architecture.

Case Study: SARS-CoV-2 Spike Protein

When deployed on the 1273-amino-acid SARS-CoV-2 spike protein, DERNA successfully analyzed the complete sequence landscape. Compared directly to deployed public vaccine configurations:

• At a matching CAI of 0.95, DERNA discovered an alternative sequence with an MFE of -1955.2 kcal/mol, dramatically outperforming the Pfizer-BioNTech vaccine mRNA structure (-1217 kcal/mol).

• At a matching CAI of 0.98, DERNA found a design yielding an MFE of -1724.8 kcal/mol, significantly beating the Moderna vaccine sequence profile (-1369.2 kcal/mol).

These custom structural arrangements offer a direct path toward extended mRNA functional half-lives in vivo.

What is Tamarind Bio?

Tamarind Bio is a pioneering no-code bioinformatics platform built to democratize access to powerful computational tools for life scientists and researchers. Recognizing that many cutting-edge machine learning models and structural biology algorithms are often difficult to deploy, use, and scale, Tamarind provides an intuitive, web-based environment.

The platform completely abstracts away the complexities of high-performance computing, software dependencies, and command-line interfaces. By managing complex GPU/CPU orchestration, cloud parallelization, and data compliance behind the scenes, Tamarind Bio empowers biologists, chemists, and therapeutic developers to focus entirely on their scientific questions and drastically accelerate their discovery workflows.

How to Use DERNA on Tamarind Bio

Running an exact multi-objective RNA design project requires no programming or local high-performance hardware:

1. Access the Tool: Log in to the Tamarind Bio platform and select DERNA from the available tools.

2. Input Protein Sequence: Paste your target primary amino acid sequence (FASTA text format or raw sequence) into the designated target area.

3. Select Optimization Mode: Choose whether to run a comprehensive Pareto Front Sweep to acquire a diverse library of candidates, or input a Fixed Balance parameter if your stability-to-expression target is already predetermined.

4. Configure Constraints: Upload a custom species-specific codon frequency CSV file if working with non-standard model organisms, or leave it set to human default settings.

5. Launch and Parallelize: Click Submit. Tamarind Bio manages the dynamic programming grid arrays across cloud environments automatically.

6. Analyze and Export: Interactively inspect your custom generated Pareto front graph. Filter candidates based on explicit MFE and CAI percentiles, visualize predicted loop secondary structures, and download optimized FASTA sequence files ready for in vitro synthesis.

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