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This research introduces a differentiable relaxation of the %MinMax metric to enable gradient-based optimization for neural codon design, bridging discrete sequence analysis with machine learning workflows. By replacing hard constraints with sigmoid-gated interpolations, the method facilitates direct training on synonymous-codon probabilities while preserving native translation dynamics. This advancement is significant for computational biology applications where AI models must optimize protein expression profiles across species boundaries.
Smooth $\%$MinMax: A Differentiable Relaxation for Codon Harmonization
arXiv:2607.03881v2 Announce Type: replace-cross Abstract: Codon harmonization aims to adapt the coding sequences for heterologous expression while preserving the native-like patterns of frequent and rare codons that may influence local translation dynamics and co-translational protein folding. However, widely used harmonization metrics, such as $\%$MinMax, are defined on discrete codon sequences and are, therefore, not readily compatible with gradient-based neural codon design. Here, we introduce Smooth $\%$MinMax, denoted as $\%{\rm MinMax}_{(s)}$, a differentiable relaxation of the conventional hard $\%$MinMax metric, denoted as $\%{\rm MinMax}_{(h)}$. $\%{\rm MinMax}_{(s)}$ replaces the discrete codon-usage values with probability-weighted synonymous-codon usage values and replaces the hard $\%$Max/$\%$Min branch with a sigmoid-gated interpolation. This formulation preserves the signed interpretation of $\%{\rm MinMax}_{(h)}$, while enabling optimization with respect to the synonymous-codon probabilities and learnable parameters. In human-to-Escherichia coli codon harmonization experiments, $\%{\rm MinMax}_{(s)}$ closely approximates $\%{\rm MinMax}_{(h)}$ and supports gradient-based profile matching in synonymous-codon probability space. These results suggest $\%{\rm MinMax}_{(s)}$ as a practical bridge between profile-based codon harmonization and neural synonymous-sequence design.
Abstract:Codon harmonization aims to adapt the coding sequences for heterologous expression while preserving the native-like patterns of frequent and rare codons that may influence local translation dynamics and co-translational protein folding. However, widely used harmonization metrics, such as $\%$MinMax, are defined on discrete codon sequences and are, therefore, not readily compatible with gradient-based neural codon design. Here, we introduce Smooth $\%$MinMax, denoted as $\%{\rm MinMax}_{(s)}$, a differentiable relaxation of the conventional hard $\%$MinMax metric, denoted as $\%{\rm MinMax}_{(h)}$. $\%{\rm MinMax}_{(s)}$ replaces the discrete codon-usage values with probability-weighted synonymous-codon usage values and replaces the hard $\%$Max/$\%$Min branch with a sigmoid-gated interpolation. This formulation preserves the signed interpretation of $\%{\rm MinMax}_{(h)}$, while enabling optimization with respect to the synonymous-codon probabilities and learnable parameters. In human-to-Escherichia coli codon harmonization experiments, $\%{\rm MinMax}_{(s)}$ closely approximates $\%{\rm MinMax}_{(h)}$ and supports gradient-based profile matching in synonymous-codon probability space. These results suggest $\%{\rm MinMax}_{(s)}$ as a practical bridge between profile-based codon harmonization and neural synonymous-sequence design.
Quantitative Methods (q-bio.QM); Machine Learning (cs.LG)
arXiv:2607.03881 [q-bio.QM]
(or arXiv:2607.03881v2 [q-bio.QM] for this version)
https://doi.org/10.48550/arXiv.2607.03881 Focus to learn more arXiv-issued DOI via DataCite
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