*2.1. Structural Order–Disorder Properties of RTT and RTT-like Causing Proteins during Chordate Evolution*

We retrieved 97, 113, and 108 chordates sequences of MeCP2, CDKL5, and FOXG1, respectively, and constructed a heat map of the structural order–disorder propensity for each protein of these genes according to aligned sequences and taxonomic position in the phylogenetic tree (Supplementary Table S1 and Figure 1). This analysis was conducted in order to investigate the evolutionary patterns of structural properties. The results showed that all proteins harbored both ordered and disordered regions; by comparing their distribution to domain and non-domain regions, we found that the catalytic domain and non-domain regions of CDKL5 were ordered and disordered, respectively (Figure 1B). While most regions of MeCP2 were predicted to be disordered, some ordered structures were observed in the MBD (Figure 1A). Furthermore, FOXG1 showed a varied distribution of ordered–disordered regions corresponding to domain and non-domain regions, with the former predicted to be fully ordered (Figure 1C). Although insertions and deletions were frequently detected in disordered regions, particularly in MeCP2 and FOXG1 (Figure 1A,C), the structural order–disorder of all proteins showed to be stable in chordates, excluding a few conformational transitions of FOXG1 and CDKL5 in mammals and fishes, respectively. This indicated that the disordered regions of MeCP2, CDKL5, and FOXG1 tend to be functional either as an entropic chain, transient binding site, or permanent binding site in chordates. Additionally, insertions and deletions were frequently detected in disordered regions. This is caused by their flexibility, which makes sequence alignment difficult; a tendency of linear motifs to lie among the flexible disordered regions; and the permutation of functional modules with respect to others during evolution that is possible in disordered regions, such as SUMO modification sites in *Drosophila melanogaster* and human p53 that are located before and after the oligomerization domain, respectively [26,34].

**Figure 1.** The order–disorder propensity of RTT and RTT-like causing proteins in chordates. Heat maps of the order–disorder propensity were generated according to the taxonomic positions in the phylogenetic tree (rows) and multiple sequence alignment (columns). The heat maps show a color gradient of blue (ordered) to red (disordered), with white as the boundary between the two and black as gaps. Colored boxes between the trees and heat maps indicate the taxonomic group, and bars above the heat maps indicate domain position in the multiple sequence alignment, with light blue and black areas indicating the domain and absence of a domain, respectively. (**A**–**C**) Heat maps for MeCP2 (**A**), CDKL5 (**B**), and FOXG1 (**C**) are shown. MBD, TRD, NID, FBD, GBD, JBD, NLS, and NES indicate methyl-CpG-binding domain, transcriptional repression domain, NCoR/SMRT interaction domain, forkhead binding domain, Groucho-binding domain, JARID1B binding domain, nuclear localization signal, and nuclear export signal, respectively.
