Smooth $\%$MinMax：一种用于密码子优化的可微松弛方法
Smooth $\%$MinMax: A Differentiable Relaxation for Codon Harmonization
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- Department of Chemistry, KAIST（韩国科学技术院化学系）
- School of Chemistry and Chemical Engineering, Highfield Campus, University of Southampton（南安普顿大学化学与化学工程学院）
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中文总结 AI 辅助
针对传统$\%$MinMax等密码子优化指标离散不可微、无法适配梯度驱动神经密码子设计的问题，提出Smooth $\%$MinMax可微松弛方法，实现两类密码子设计的衔接。
中文摘要 AI 辅助
密码子优化旨在为异源表达调整编码序列，同时保留可能影响局部翻译动力学与共翻译蛋白质折叠的天然高频、稀有密码子模式。但广泛使用的优化指标如$\%$MinMax定义在离散密码子序列上，难以直接适配基于梯度的神经密码子设计。本文提出Smooth $\%$MinMax，记为$\%{\rm MinMax}_{(s)}$，是传统硬$\%$MinMax指标（记为$\%{\rm MinMax}_{(h)}$）的可微松弛版本。$\%{\rm MinMax}_{(s)}$用概率加权的同义密码子使用值替代离散密码子使用值，用sigmoid门控插值替代硬$\%$Max/$\%$Min分支。该形式保留了$\%{\rm MinMax}_{(h)}$的符号语义，同时支持针对同义密码子概率与可学习参数的优化。在人源到大肠杆菌的密码子优化实验中，$\%{\rm MinMax}_{(s)}$可高度近似$\%{\rm MinMax}_{(h)}$，并支持同义密码子概率空间内的基于梯度的谱匹配。结果表明$\%{\rm MinMax}_{(s)}$可作为基于谱的密码子优化与神经同义序列设计之间的实用桥梁。
英文摘要
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.
