Joint protein, mRNA, DNA sequence design and optimization with nucleotide-level Potts models

Protein design generates amino acid sequences first and then translates them into DNA post-hoc. Control over the nucleotide sequence via codon choice at design time is thus limited. We introduce NuCaliby, a structure-conditioned model that jointly designs a protein's amino acid, mRNA, and DNA sequences at nucleotide resolution. It predicts a Potts model over a nucleotide graph, trained using amino acid supervision by marginalizing over synonymous codons. Its energy-based formulation supports composable inference-time guidance from both differentiable and non-differentiable objectives. NuCaliby preserves residue-level designability on par with Caliby while learning codon-aware nucleotide couplings directly from structure. Under organism-specific tRNA adaptation guidance, NuCaliby improves adaptation to host tRNA pools beyond synonymous sequence space while preserving protein designability. NuCaliby also embeds functional RNA motifs, directly into coding sequences, a problem that is combinatorially infeasible with extensive sampling alone. In wet lab experiments NuCaliby produces expressible and soluble proteins on par with state of the art methods, although it enables more complex nucleotide-level control and optimization. Together, these results extend protein design beyond the residue level, enabling joint optimization across the central dogma of molecular biology.