arXiv:2607.03881v1 Announce Type: 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
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