Table 1 Acronym list of the computational models

RUM

Mutations are introduced by randomly selecting positions and assigning with uniform probability one nucleotide.

BPR

Mutations with the Base-Pair Replacement method are introduced following the WT structure: at paired positions, both nucleotides are mutated simultaneously into G–C, G–U, or A–U pairs; otherwise, mutations are random.

BPR + 3D

Mutations are introduced as in BPR except positions involved in tertiary interactions (detected by analyzing the tertiary structure), which are kept unchanged.

SB

Mutations are introduced with the MCMC algorithm following the Structure-Based (SB) score, which penalizes mispairing under the thermodynamic folding model.

SB-3D

Mutations are introduced as in SB except positions involved in tertiary interactions (detected by analyzing the tertiary structure), which are kept unchanged.

PRO

Mutations are introduced by randomly selecting positions and assigning nucleotides according to the frequency of the mutation observed in the MSA.

DCA T = 1

Mutations are introduced with the MCMC algorithm at T = 1 following the DCA model trained on the MSA of homologs, ensuring designs match single and pairwise frequencies observed in the MSA.

DCA T = 0.3

Mutations are introduced with the MCMC algorithm at T = 0.3 following the DCA model, which concentrates the sampling onto the most likely sequences under the DCA model.

DCA-SB

Mutations are introduced with the MCMC algorithm at T = 0.3 following the DCA model combined with the SB score, optimizing simultaneously the DCA score and the folding into the WT fold.

VAE

Mutations are introduced with the neural network called Variational AutoEncoder (VAE), which is trained on the MSA of homologs. Similarly to DCA, it is trained to maximize the likelihood of the observed MSA.

CHI

Chimeric sequences are derived from natural sequences aligned to Azoarcus by replacing deletions with Azoarcus nucleotides, using only aligned positions to maintain the same length.