*4.2. Parametrization of Phosphorylated Amino Acids*

We used five different hydrophobicity-predictor programs to estimate the hydrophobicity of phosphorylated residues. These programs calculate the logarithmic value of the equilibrium partition coefficient *P*, i.e., the ratio of concentrations in a mixture of two immiscible phases, water, and 1-octanol, as a measure for hydrophobicity. They use experimental log *P* values of fragments (small groups of atoms) to calculate the log *P* for bigger molecules by adding the individual contributions from the constituting fragments, based on the structure additivity principle for hydrophobicity [55]. There are several challenges in incorporating the log *P* estimates for the complete molecules directly in our 1 BPA model, which are: (i) the error from the estimate of the log *P* values for the fragments accumulate while calculating the log *P* for the entire molecule; and (ii) each of the hydrophobicity-predictor programs are trained with different experimental data, and therefore generate different estimates of log *P* for a given molecular structure. In order to have the hydrophobicity values comparable to our 1BPA model, first we rescaled and then normalized the log *P* estimates for all amino acids obtained from a hydrophobicity-predictor program *k*, so that hydrophobicity of any amino acid *i* (i.e., *εk*,*i*) falls in the range from 0 to 1. Here, 0 and 1 corresponds to the hydrophobicity of the most hydrophilic and most hydrophobic amino acids, according to hydrophobicity-predictor program *k*. Next, to minimize the error we decided to incorporate the change in *εk*,*<sup>i</sup>* values of the phosphorylatable residues (obtained from the five hydrophobicity-predictor programs) compared to the 1BPA model, for which the hydrophobicity values are extracted from three different partition coefficient measurements [35]. To account for the variation in the prediction of *εk*,*<sup>i</sup>* by the different hydrophobicity-predictor programs, a weighted average approach is considered. The weights are assigned to individual predictor programs based on their accuracy in predicting the *εk*,*<sup>i</sup>* values of the amino acids in their native state, as used in [35]. Thus, the assigned weight for hydrophobicity-predictor program *k* for amino acid *i* can be written as,

$$w\_{k,i} = \frac{\left(1/\Delta\varepsilon\_{k,i}\right)^2}{\sum\_{k=1}^5 \left(1/\Delta\varepsilon\_{k,i}\right)^2},\tag{2}$$

where Δ*εk*,*<sup>i</sup>* = *εk*,*<sup>i</sup>* − *ε*1BPA,*<sup>i</sup>* represents the difference between the hydrophobicity for an amino acid in its native state used in our 1BPA model [35] and the hydrophobicity-predictor programs (see Tables S3 and S4 for the source data). Next, the change in hydrophobicity upon phosphorylation is calculated as

Δ*εk*,*i*-phos = *εk*,*i*-phos − *ε*1BPA,*i*, where "*i*-phos" represents the amino acid *i* in its phosphorylated state. Finally, using the weights for the hydrophobicity-predictor programs (see Table S4) we computed the hydrophobicity for the phosphorylated amino acid as *ε*p,*<sup>i</sup>* = *ε*1BPA,*i*+∑<sup>5</sup> *<sup>k</sup>*=<sup>1</sup> *wk*,*<sup>i</sup>* Δ*εk*,*i*-phos. The amino acids Serine (S), Histidine (H), Tyrosine (Y), and Threonine (T) undergo phosphorylation [18,19], and the introduction of a phosphate group results in the introduction of a −2e charge, as shown in Table 1. The phosphorylation of these amino acids results in a more hydrophilic atomic composition, which can be seen in Table 1. As a reference, the prediction of the hydrophobicity of amino acid *i* in the native state, *ε*weighted,*<sup>i</sup>* = *ε*1BPA,*<sup>i</sup>* + ∑<sup>5</sup> *<sup>k</sup>*=<sup>1</sup> *wk*,*<sup>i</sup>* Δ*εk*,*i*, is also shown in Table 1. Note that the subscript *i* is dropped from *ε*p,*<sup>i</sup>* and *ε*weighted,*<sup>i</sup>* in Table 1 for clarity.

**Supplementary Materials:** Supplementary materials can be found at http://www.mdpi.com/1422-0067/20/3/ 596/s1.

**Author Contributions:** Conceptualization, A.M. and P.R.O.; methodology, A.M., W.S.; software, A.M.; validation, A.M.; formal analysis, A.M.; investigation, A.M..; writing—original draft preparation, A.M.; writing—review and editing, A.M., W.S., L.M.V., E.V.G., and P.R.O.; visualization, A.M..; supervision, P.R.O. and E.V.G.; project administration, P.R.O.; funding acquisition, P.R.O.

**Funding:** This research was funded by the Zernike Institute for Advanced Materials (University of Groningen), the UMCG, and NWO ECHO (grant number: 711.013.008 to A.M., P.R.O., and L.M.V.).

**Acknowledgments:** We acknowledge the use of the Peregrine cluster (University of Groningen) and the Cartesius cluster (SURFsara, funding grant by NWO) for the large scale simulations carried out during this project.

**Conflicts of Interest:** The authors declare no conflict of interest.
