Specification of a latent space strategy guides the search and selection of sequences. The regular distribution of stable sequences in the latent space (Fig. ) led us to develop the straight-line evolutionary strategy. This strategy encodes the query sequence (DhaA in our case) into its latent representation and then follows the straight line connecting that point to the origin of the latent space (Fig. ), mimicking the mapping of ancestral dependencies into the latent space. The line is divided into equal intervals, whose boundaries are then selected for reconstruction by the decoder. In the experiments, we selected 100 intervals. To represent the designed sequences, we analyzed several statistical parameters for the individual designed sequences: the average reconstruction match, similarity to the query sequence, similarity to the closest sequence in the latent space from the training set, and the number of insertions/deletions compared to the original sequence. The values obtained were plotted and visually inspected to identify variants with interesting statistical values. The generated profiles were then used to select suitable variants for subsequent experimental characterisation (Fig. ). Fig. : The straight-line evolutionary strategy for Model 1. (A) Straight evolutionary strategy reconstructed 100 sequences along the trajectory from query embedding to the latent space origin (black dashed line). The embeddings of experimentally validated Babkova's ancestors (points 0-5) and engineered DhaA variants (yellow to pink spectrum points) are mapped closer to the latent space origin, supporting the idea behind our ancestral generation strategy. (B) A detailed view of DhaA variants engineered to improve their stability almost perfectly aligned along the straight-line trajectory to the origin of the latent space. The degree of stability improvement is depicted by the color bar on the right. While there is no strong correlation between the positions in the latent space and the stability gain of variants up to 28˚C, some of the most stable points are situated closer to the origin. (C) The statistical profile of 100 sequences from the straight evolutionary strategy. The vertical lines represent sequences selected for experimental characterization for the first and second rounds (Table ) where dashed line variants were successfully expressed.