Abstract
Protein design typically generates amino acid sequences first and then translates them into DNA post-hoc limiting control over the nucleotide sequence via codon choice at design time. We introduce NuCaliby, a structure-conditioned model that jointly designs amino acid, mRNA, and DNA sequences of a protein at nucleotide resolution. NuCaliby predicts a Potts model over a nucleotide graph, trained using amino acid supervision by marginalizing over synonymous codons. It preserves residue-level designability on par with the original Caliby model. Its energy-based formulation supports composable inference-time guidance from sequence-level objectives through proposal construction and candidate acceptance, allowing the incorporation of biological proxies into the coding nucleotide sequence. Under organism-specific tRNA adaptation guidance, NuCaliby improves adaptation to host tRNA pools beyond synonymous sequence space, trading-off self-consistency. NuCaliby also embeds specified RNA motif sequences directly into coding sequences, avoiding the combinatorial growth required for the same task at the amino-acid level. In wet lab experiments, NuCaliby produces expressible and soluble proteins on par with state of the art methods, while enabling more complex nucleotide-level control and optimization. Together, these results extend protein design beyond the amino acid level, enabling joint optimization across the central dogma of molecular biology. The code and model weights are available here: https://github.com/blazejba/NuCaliby