Smooth %MinMax: A Differentiable Relaxation for Codon Harmonization
Authors: Yoonho Jeong, Hyunwoo Choi, Ryan Fernandez Medina Hariri, Eok Kyun Lee, Seung Seo Lee, Insung S. Choi
Organizations: Department of Chemistry, KAIST, Daejeon 34141, Korea. · School of Chemistry and Chemical Engineering, Highfield Campus, University of Southampton, Southampton SO17 1BJ, United Kingdom.
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.
Multimodal ΔΔG predictors integrating protein language models with inverse-folding representations achieve strong in-distribution accuracy on the Megascale dataset but exhibit limited robustness on out-of-distribution (OOD) proteins, persistent forward-reverse bias on paired-mutation benchmarks, and under-representation of rare stabilizing mutations. Existing approaches address these limitations primarily through additional architectural components, leaving optimization-level intervention comparatively underexplored. We introduce a constraint-aware optimization framework combining Balanced Mean Squared Error, a Siamese anti-symmetric regularizer, and a novel OOD-margin consistency loss on the per-position feature representation, requiring no architectural changes to the SPURS backbone. Across eleven benchmarks and three random seeds, the framework improves Spearman correlation on S669 from 0.486 to 0.540 (σ=0.002 across seeds), matching the published SPURS baseline (0.50) without architectural modification, and on S461 from 0.653 to 0.711, with consistent smaller gains on five additional OOD datasets. A controlled diagnostic on Ssym reveals that anti-symmetric training does not eliminate systematic forward-reverse bias, indicating that gains arise through implicit regularization rather than exact thermodynamic constraint enforcement.
Equivariant graph neural network (GNN) methods for antibody complementarity-determining region (CDR) design achieve the highest sequence recovery but suffer from severe vocabulary collapse. The current best GNN methods over-predict very few amino acids, such as tyrosine and glycine, while ignoring functionally important residues. We trace this failure to GNN encoders learning amino acid distributions de novo from limited structural data, discarding substitution patterns encoded in evolutionary databases. To resolve this, we propose EvoStruct, which bridges a frozen protein language model (PLM) with 3D structural context from an E(3)-equivariant GNN via a cross-attention adapter. Unlike prior PLM-structure adapters for general protein design, EvoStruct targets the vocabulary collapse problem specific to CDR design through progressive PLM unfreezing and R-Drop consistency regularization. On the CHIMERA-Bench dataset, EvoStruct achieves the highest amino acid recovery and lowest perplexity among several antibody design methods, improving sequence recovery by 16% and reducing perplexity by 43% relative to the best GNN baselines, while recovering 2.3x greater amino acid diversity and the highest binding-pair correlation with ground truth.
The growing energy demand for computation is becoming increasingly unsustainable. Thermodynamic computing, which harnesses physical thermal fluctuations as a computational resource rather than suppressing them, offers orders-of-magnitude energy savings for probabilistic and combinatorial tasks. Pharmaceutical R&D, heavily reliant on computational optimization and sampling, is a natural application domain. Here we present what is, to our knowledge, the first concrete pharmaceutical application mapped to thermodynamic hardware with energy estimates grounded in prototype measurements. We reduce mRNA codon optimization, a combinatorial problem routinely solved in drug development, to sampling from an Ising model, making it directly executable on a thermodynamic sampling unit (TSU). Benchmarking three approaches (Potts sampling, Ising sampling, and a genetic algorithm baseline) on the SARS-CoV-2 spike protein, we find that all achieve comparable optimization quality (scores ~234-240), but energy estimates based on validated hardware models indicate that a TSU could solve this problem using approximately 10e6 times less energy than a conventional GPU. All code is released under an open-source license.