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
%MinMax(s), a differentiable relaxation of the conventional hard
%MinMax metric, denoted as
%MinMax(h).
%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
%MinMax(h), while enabling optimization with respect to the synonymous-codon probabilities and learnable parameters. In human-to-Escherichia coli codon harmonization experiments,
%MinMax(s) closely approximates
%MinMax(h) and supports gradient-based profile matching in synonymous-codon probability space. These results suggest
%MinMax(s) as a practical bridge between profile-based codon harmonization and neural synonymous-sequence design.