{"ID":5937974,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-07T13:42:41.749155092Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.03881","arxiv_id":"2607.03881","title":"Smooth $\\%$MinMax: A Differentiable Relaxation for Codon Harmonization","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.","short_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 disc...","url_abs":"https://arxiv.org/abs/2607.03881","url_pdf":"https://arxiv.org/pdf/2607.03881v1","authors":"[\"Yoonho Jeong\",\"Hyunwoo Choi\",\"Ryan Fernandez Medina Hariri\",\"Eok Kyun Lee\",\"Seung Seo Lee\",\"Insung S. Choi\"]","published":"2026-07-04T13:54:06Z","proceeding":"q-bio.QM","tasks":"[\"q-bio.QM\",\"cs.LG\"]","methods":"[]","has_code":false}