**3. Materials and Methods**

The nucleotide sequences of *H. sapience*, *M. musculus,* and *Rattus norvegicus* genes were downloaded from Ensembl (Release 91) [36]. The nucleotide sequences of *A. thaliana* (TAIR10), *Arabidopsis lyrata*, *Drosophila melanogaster* (BDGP6) genes were obtained from Ensembl, too. Ensembl also provided the orthologous relationships between *H. sapience* and *M. musculus* as well as those of *M. musculus* and *R. norvegicus*. The sequences of *S. cerevisiae* and *Saccharomyces paradoxus* were obtained from the Saccharomyces Genome Database [37], while those of *Drosophila pseudoobscura* genes were downloaded from FlyBase [38]. The orthologs of the two *Arabisopsis* species, the two yeast species, and the two *Drosophila* species were selected by bidirectional best hit analysis. The proteins were classified by subcellular localizations based on the Gene-Ontology (GO) annotations in UniProt (Release 2017\_05) [39]. Specifically, the following GO IDs were used for subcellular classifications: nucleus: GO:0005634; cytoplasm: GO:0005829; mitochondria: GO:0005739; endoplasmic reticulum/Golgi apparatus: GO:0005783, GO:0005794, and GO:0005793; plasma membrane: GO:0005886; secreted: GO:0005576 and GO:0005615; immune-related: GO:0002376.

From the coding sequences, the signal peptides were removed based on UniProt annotations because they are unclassifiable as SDs or IDRs due to their absence in mature proteins. The remaining amino acid sequences of orthologs were aligned by MAFFT [40] and the corresponding nucleotide sequences were aligned according to the MAFFT results. dn/ds values were then computed using the codeml program (model M0) in PAML (version 4.9d) [41]. Statistical differences between two quantities were tested by Mann-Whitney's *U*-test, while statistical significance of correlations was evaluated by Spearman's rank correlation by means of in-house programs.

Number of PPIs and expression levels were taken from the BioGRID (version 3.4.158) [42] and the PaxDb (version 4.1) [43] databases, respectively. BioGRID is a curated database of interactions including protein-protein interactions obtained by two-hybrid studies, affinity purification coupled to mass spectrometry, and other methods, while PaxDB contains whole genome protein abundance information obtained by integrating numerous datasets using scores and ranks. Each protein was divided into SDs and IDRs by three methods: DISOPRED3 [29], DICHOT [30] and POODLE-L [31]. Briefly, DISOPRED3 assigns IDRs based on sequence profiles and other sequence-derived features, DICHOT classifies proteins into SDs and IDRs using sequence characteristics, alignments to existing protein structures, and sequence divergence, while POODLE-L is a prediction method for long IDRs that makes use of support-vector machine with 10 kinds of simple physico-chemical properties of

amino acids. Based on the overall MAFFT alignments, the alignments of the corresponding sections were made. The evolution rate of each section was then determined as above.
