*2.6. ECs Could Not Be Identified for Very Small Interfaces with no H-Bonds or Salt Bridges*

By comparing the interfaces of the complexes with and without ECs (the latter group comprised all the 30 non-redundant complexes that did not provide high-scoring ECs by Gremlin) for their interface areas, H-bond and salt bridge densities, we did not find any significant difference (Figure 3). However, it became evident that ECs could not be detected for interfaces <600 Å<sup>2</sup> (for transient complexes this threshold rather seems as 1000 Å2) in size, not even for exceptionally widely conserved interactions. ECs could also not be identified for interfaces without any assigned H-bonds or salt bridges (Figure 3C).

**Figure 3.** Comparison of interface areas and bonds for EC and no-EC interfaces. (**A**) Comparison of EC and non-EC interface areas with Mann–Whitney U test. (**B**) Density plot of the interfaces in the two groups. (**C**) Comparison of the normalized numbers of H-bonds and salt bridges between EC and non-EC interfaces with Mann–Whitney U test, with the corresponding *p*-values indicated. In the boxplots, stars (\*) indicate the average values of the datasets.

#### *2.7. EC Interfaces Are Enriched in Negatively Charged Residues*

We have also calculated the amino acid and amino acid group compositions of the trimmed protein segments (analyzed sequence ranges), all interfaces (all IFs), interfaces without any detectable EC pairs (No-EC IFs), EC-carrying interfaces (EC IFs) and EC residues for the IDPs and partners separately. Comparing EC IFs and ECs to all IFs, we found no significant differences either for IDPs (Figure 4, Supplementary Figure S2) or their partners (Supplementary Figure S3), although the enrichment of the EC-carrying interfaces of IDPs in negative residues was nearly significant (*p* = 0.0519). We have to note though that we had only 28 IDP- and 30 partner EC residues, which is suboptimal for rigorous statistical analysis. Due to the small sample size, even seemingly very large differences were not statistically significant, for instance, IDP EC residues were not found to be enriched in positive amino acids compared to all IDP interface residues, despite having almost two times as high fraction of positives (28.6% vs. 14.5%; Figure 4). When comparing the compositions of EC interfaces to those of no-EC interfaces, we found that the EC-carrying interfaces of IDPs harbor significantly more negatively charged residues (*p* = 0.0101), in particular glutamates (*p* = 0.0240), than the IDP interfaces with no ECs (Figure 4, Supplementary Figure S2). For the partner interfaces no significant differences were found (Supplementary Figure S3).

**Figure 4.** The amino acid group compositions of IDP EC-carrying interfaces and ECs. The amino acid group compositions of trimmed protein segments (analyzed sequence ranges), all interfaces (all IFs), interfaces with no ECs (no-EC IFs), EC-carrying interfaces (EC IFs) and EC residues of IDPs. Both EC-carrying interfaces and EC residues have been compared to all IFs. Also, EC interfaces were compared to no-EC interfaces. P-values are only indicated for amino acid group proportion differences that were found significant by the built-in test of equal proportions of R.
