Smooth %MinMax: A Differentiable Relaxation for Codon Harmonization

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 %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.

Source: arXiv cs.LG | 2026-07-07