In the present article, we selected different non-canonical amino acids (see Tables S1–6) that had been previously investigated and published in an experimental study [16]. The work presented by Kubyshkin [16] focused on examining the experimental lipophilicity of non-standard amino acid derivatives originating from methionine, phenylalanine, tyrosine, tryptophan, lysine, and proline using the n-octanol/water system. In our study, non-taking into account the standard versions of amino acids, a total of 57 non-canonical amino acids have been investigated. This includes 7 modifications of methionine, 4 of lysine, 9 of phenylalanine, 4 of tyrosine, 25 of proline, and 8 of tryptophan.

For each molecule, we considered two variants regarding the N- and C-terminal capping groups. These end fragments are responsible for mimicking the peptide bond which confers rigidity to these regions, as well as, aiming to mimic the physicochemical behavior of the amino acid when present inside a protein, rather than in an individual state. Our study included in parallel both variants for all amino acids, in order to preserve the original capping groups from our previous study [10], but also to compare with those used by Kubyshkin [16] in his experimental study (see Figure 1).

Figure 1 shows the first variant, known as “Model 1”, which involves the introduction of an N-methyl (NME) group at the N-terminal end and an acetyl (ACE) group at the C-terminal end of the derivatives. “Model 2” uses the capping groups of the experimental data published in Kubyshkin’s [16] article, which presents slight modifications. While the C-terminal group remains the same, the N-terminal end features an O-methyl (OME) group instead of the NME group.

This a priori small change presumes to have a reasonable impact on the hydrophobicity of the studied compounds. Since the NH to O modification supposes the loss of a hydrogen bond donor interaction and translates into an increase of lipophilicity, like the experimental values of N-methylacetamide (logP = –1.05) and methyl acetate (logP = 0.18) reported by Hansch et al. in 1995 support [18].

Using the DataWarrior software [19], within the framework of Model 1 diverse simple descriptors were calculated to better capture the chemical diversity of the studied sets. Thanks to that it could be highlighted that, the molecular weights of the explored molecules lie in the range of 168 to 339 g/mol (see Figure S2). The total number of rotatable bonds varies from one to nine (see Figure S3). Additionally, the count of hydrogen bond acceptors spans from four to seven (see Figure S4), while hydrogen bond donors range from one to four (see Figure S5). In the context of Model 2, which involves substituting the NH group with an oxygen atom in one of the capping groups, there is an approximate one-unit increase in molecular weight. Simultaneously, there is a decrease of one unit in the count of hydrogen bond donor, while the number of acceptors remains unchanged. For more detailed information check Tables S7–12 in the Supplementary material.

Concerning their lipophilicity, if we consider the difference of each non-standard amino acid compared to the original, based on experimental values reported by Kubyshkin [16] for methionine derivatives, four of them are slightly more lipophilic, and three are more hydrophilic, with variations ranging from plus 0.80 units (most lipophilic) to minus 1.92 (most hydrophilic). In the case of lysine, all derivatives are more hydrophilic than the canonical, with the most marked difference being 2.43 units. Moving to tyrosine, among the four cases, except for a single case (Dopa) that is slightly more hydrophilic, all others are more lipophilic, despite moving in a narrow range from 0.50 (most hydrophilic) to 0.69 (most lipophilic).

For phenylalanine, five derivatives are more lipophilic, three are more hydrophilic, and one has the same experimental logP value. The variation range spans 2.29 units, from the most hydrophilic to the most lipophilic. A similar situation is observed for tryptophan derivatives, where out of the eight cases, only two derivatives with polar groups (5-amino and 5-hydroxy) are more hydrophilic than the standard residue (1.46 units less than the most hydrophilic and 1.17 units more than the most lipophilic, resulting in a range of 2.63 units). Among the 25 proline cases, except for six instances, all are more lipophilic, with the most lipophilic being 1.59 units greater than standard proline and the most hydrophilic being 0.93 units less lipophilic.

We decided not to include some tyrosine derivatives containing iodine atoms in our study. This decision was based on the limitations of the DFT-based integral equation formalism polarizable continuum model/Miertus-Scrocco-Tomasi (IEFPCM/MST) continuum solvation method used for estimating solvation energies, as it lacks parameterization for iodine atoms. However, this method does include parameterization for other halogen atoms like fluorine, chlorine, and bromine, which present minimal differences experimentally when compared to iodine derivatives. Hence, we included molecules containing these three halogen atoms in our study. A similar criterion was taken in the exclusion of selenomethionine from the analysis since the selenium atom is also not included in the IEFPCM/MST current parametrization [20].

All molecules were designed using Avogadro software (version 1.1.1) [21]. Then, we employed OpenBabel 2.4.0 genetic algorithm to stochastically conduct a preliminary generation of the preferred conformations of the amino acids based on energy score [22]. Due to the structural complexity of some molecules (with several rotatable bonds ranging from 1 to 9), we limited the generation of conformers to a maximum of 100 structures, to make a balance between a complete conformational landscape of them, but at the same time deal with an acceptable number of conformers.

Then, generated geometries of the conformers in both water and n-octanol were optimized using the B3LYP/6-31G(d) level of theory [23–25]. The influence of solvent on the geometric parameters was considered by employing the IEFPCM/MST model [26–28], integrated into a local version of Gaussian16 [29]. The minimum energy state of optimized geometries in each solvent was confirmed by inspecting the vibrational frequencies, excluding those conformations presenting negative ones. Afterward, thermal corrections were introduced to estimate the relative free energy of the conformers in water and n-octanol. Also, single-point energy calculations were carried out in the gas phase to evaluate the solvation free energy of each conformation. Those redundant conformers that after visual inspection converged in the same geometry were eliminated to avoid weight imbalance between both solvents. Obtaining a final conformational distribution in both solvents (like the one highlighted in Figure S6). Finally, the logP value was estimated by considering the Boltzmann-weighted distribution of the conformational families obtained in water and n-octanol.

To ensure that the logP values obtained from our computations were exclusively influenced by the inherent characteristics of their side chains rather than the capping groups, a reference framework was implemented. This involved considering the computationally predicted logP value for glycine, a molecule lacking a heavy atom side chain, but still marked by the influence of capping groups. In the context of the derivatives estimated in Model 1 (incorporating the ACE and NME capping groups), an adjustment was introduced by adding +0.17 logP units to the calculated value. This value originated from the disparity observed between the glycine amino acid value as reported by Zamora et al. [10] in their 2019 publication and the experimental value documented by Fauchère and Pliska [30] on their published scale. Conversely, within the framework of Model 2 (incorporating the ACE and OME capping groups), a correction was made by subtracting –0.78 logP units. This value reflected the difference existing between the logP value computed using the IEFPCM/MST approach and the experimental value detailed in Kubyshkin’s article [16]. Additionally, the structural models used in our previous work [10] did not contain the terminal methylated amide present in Model 1 of this work. However, the effect of methylation is well-known, leading to an increase of logP values by approximately 0.60 units (see Table S13) where we report the computed values for the 20 canonical amino acids using the capping group of the methylated amide). Furthermore, previous research conducted by our group has already explored models featuring methyl groups for hydration computations [31]. Consequently, for the present work, we decided to add a methyl group to better mimic the protein environment and facilitate comparison with the ester model (Model 2) used by Kubyshkin [16].

The canonical residue methionine is an essential amino acid for its antioxidant effect by reacting with oxidizing species [32], therefore, the tuning of its properties, e.g., lipophilicity, may be relevant to enhance its bioactivity. To this end, Figure 2 shows a consistent behavior between Models 1 and 2. Notably, most lipophilic moieties exhibit a congruent (response about the standard methionine residue values). In Model 1, the logP value is near zero, while in Model 2 there is a slightly augmented lipophilicity (0.27). More detailed values can be observed in Table S14.

Nonstandard residues ethionine (Eth), norvaline (Nva), norleucine (Nle), and trifluoronorleucine (Tfnle) exhibited a more lipophilic profile than methionine, with logP values moving between 0.20 and 1.82, considering both models. This behavior is logical, attributable to the aliphatic nature of these derivatives (Nle, Nva, and Eth), or the addition of halogen moieties, exemplified by Tfnle.

In the case of hydrophilic derivatives, methionine sulfoxide (MetO) and azidohomoalanine (Aha) a consistent pattern is observed. The introduction of functional groups such as azide or sulfoxide provoked a discernible alteration in the lipophilic profile of methionine, culminating in marked negative values, moving between –0.90 and –1.20, considering both models. This is to be expected due to the high polarity of the oxygen and nitrogen atoms that confer hydrogen bond acceptor properties.

One of the most evident divergences between both approximations arises in the case of methoxinine (Mox), characterized by the replacement of the sulfur atom with an oxygen moiety relative to the standard methionine structure. Model 1 gives a sub-zero value of –0.65, whereas Model 2 manifests a migration towards an apolar value of 0.46. This small incongruity may be ascribed, at least in part, to the presence of an O-methyl capping group in Model 2, different from the NME capping group featured in Model 1. The computational method IEFPCM/MST elucidates a propensity to increase lipophilicity concerning Model 1, accentuated by the alteration of a nitrogen-hydrogen moiety to oxygen, resulting in the loss of a donor hydrogen bond interaction, a structural modification that IEFPCM/MST tends to penalize towards a more lipophilic value.

Although the influence of capping groups is notably adjusted by the previously commented corrections in the methodological section, certain Model 2 values are corrected starting from an overestimated lipophilic value, and therefore exhibiting an inclination towards greater lipophilicity. This tendency is also observed in Eth and Tfnle cases, that present a difference of 1–1.2 logP units between Models 1 and 2.

According to correspondence with experimental data (Table S14), in Model 1, apart from Aha (+1.09 logP units), which contains a chemical group that tends to present difficulties in their estimation, all methionine cases maintain differences lower than 1 logP unit. Instead, in Model 2, two cases are above 1 unit of difference, more specifically Tfnle (1.10 units) and Mox (1.11 units), probably ascribed to the presence of groups that exaggerate their lipophilic profile.

In our study, we analyzed modifications of the main aromatic residues, tyrosine, phenylalanine, and tryptophan. These residues have several functions that maintain the structure and function of proteins. Interactions with cations are essential for maintaining bioactive protein conformations [33]. Thus, any structural modification of these residues will have an impact on both their lipophilicity and aromaticity and thus on the structure/activity relationships.

This amino acid represents the most frequently post-translationally modified so it is no coincidence its impact on protein regulation and function [34]. The reference logP value for standard lysine is taken from Zamora et al. [10], which gives an approximate logP of –0.40 for the amide model (the derived experimental logP from the Fauchère’s experimental [30] logD_7.4 = –3.07 and using a pKa = 10.0 yields an experimental logP of –0.47) and 0.17 for the N-acetyl-L-amino-acid-N-methyl amide (Model 1) residue (see Table S13). Based on that, as can be seen in Figure 6, most lipophilic nonstandard residue is S-allylcysteine (Sac), which have almost identical values in one each model, around ~1.30, respectively. Absolute values can be checked in Table S18.

However, discrepancies manifest in the two other cases. Concerning N-propargyloxycarbonyl-lysine [(Pro)Lys], Model 1 considers it slightly polar (–0.45), whereas Model 2 positions it distinctly as more apolar (0.57), but in both cases more apolar compared to coded lysine (1.11). Let us mention that, these differences, although not negligible, are within the range found even in experimental measurements.

According to N-acetyl-lysine [(Ac)Lys], Model 1 denotes an extremely hydrophilic characterization of –1.64, while Model 2 persists in –0.39. Chemically insight underscores the incorporation of an ACE group, analogous to (Boc)Lys and [(Pro)Lys], that should provoke a slight increase in the lipophilicity. Consequently, Model 1 tends to excessively accentuate the hydrophilic trait of this residue, while Model 2’s depiction is more aligned with a hydrophobic profile. However, the tendency is to be more hydrophilic than the standard version of the amino acid.

In this case, the comparison with experimental data shows that all cases in both Models almost have a perfect fitting, presenting a difference of lower than 1 unit. In Model 1, the most deviated case has a 0.75 units divergence while in Model 2 is 0.68 units.

In the context of proline residues, their examination was previously undertaken by Matamoros et al. in 2022 [35], employing the SMD solvation approach [36], In the current study, we subject these residues to analysis via our IEFPCM/MST methodology. As illustrated in Figure 7 and detailed in Table S19, the outcomes affirm the comparable efficacy of our approach, thus rendering it well-suited and eminently applicable for extending our scale of lipophilicity.

Regarding proline, in general, all cases maintain a difference with respect to the experimental value, lower than 2 units of logP in both models. Only dehydroproline (Dhp) in Model 1, presents a deviation of 2.26 logP units, presenting an excessive hydrophilic profile due to the capacity of performing hydrogen bond interaction of the NH group.

Regarding the correlation between experimental and computational estimations, Figures 8 and 9 reveal a noteworthy similarity between the two models. Both exhibit a correlation coefficient (R²) that is moderately acceptable—0.73 for Model 1 and 0.71 for Model 2. Also, the root mean square error (RMSE) for Model 1 is 0.7, while Model 2 stands at 0.9. Furthermore, additional statistical parameters such as MSE and mean unsigned error (MUE) also indicate a consistent pattern across both models. Despite the subtle differences, Model 1 demonstrates a stronger correlation and exhibits lower error when compared to the experimental values. This observation aligns coherently with our previously published findings that utilized similar capping groups as those in Model 1.

Delving into specifics, it becomes evident that indistinctly of the model considered, all methionine and tyrosine residues (yellow and green colored dots in Figures 8 and 9, respectively) consistently exhibit present values with a discrepancy not higher than 1.2 logP units. Similarly, in the case of lysine is even better, remaining below than 1 logP unit in all cases (blue colored dots in Figures 8 and 9). This can be translated into the fact that there is hardly any difference between the experimental values and those reproduced computationally. It’s worth noting that a deviation near 1 logP unit can often be attributed to inherent errors within the method itself.

As regards the other derivatives, in general trend is maintained, however, certain cases with notably substantial discrepancies have come to light. In the case of the phenylalanine derivatives (orange-colored dots in Figures 8 and 9), the Aha derivative (4-N₃-Phe) in Model 1, presents a deviation of 2.13 units from the experimental value, though this deviation is somewhat mitigated in Model 2 (1.32 units). An underlying explanation could be associated with the azide group present within the side chain. Despite the group’s net charge being neutral, there exists a subtle polarization distributed across its nitrogen atoms. This charge distribution potentially contributes to deviations and fluctuations in accurately estimating the compound’s lipophilicity [37–42]. The difference of 0.81 units in the assessment of the identical residue across Model 1 and Model 2 might arise from the distinct origins of their unadjusted initial values. In Model 1, the original value comes from a measurement involving the NME capping group, introducing a hydrogen bond interaction that doesn’t occur with the OME capping in Model 2. Consequently, this residue could potentially be overestimated as hydrophilic, driven by the presence of the NME capping group. This last aspect is also observed in the most deviated case from the proline dataset (red dots in Figures 8 and 9), Dhp in the case of Model 1 deviates 2.26 units more hydrophilic than the experimental one.

Another pattern observed in deviated cases is the presence of bromine atoms, more specifically, in the case of phenylalanine and tryptophan residues (orange and grey colored dots in figures 8 and 9, respectively), 4-Br-Phe, 5-Br-Trp and 6-Br-Trp present a more marked difference. While the rest of the residues present a deviation around 1 logP unit, these cases move around 1.34 and 2.29, between both models. The bromine atom is a relatively heavy atom compared to other lighter halogens like fluor and chlorine (deviations around 0–0.8 logP units) and it has unique electronic properties due to its larger size and higher atomic number. These factors can influence the interactions of bromine with its surrounding environment, including solvent molecules and other atoms in a molecule.

Another potential source of mismatch between experimental and computational results can be attributed to the fact that IEFPCM/MST method is an implicit solvation model, that treats the solvent as a continuous dielectric medium, simplifying the simulation and reducing the computational cost. This approach permits to be more efficient but sometimes can oversimplify the solvent behavior and fail to capture specific solvent-solute interactions accurately. Contrary to that explicit solvation models represent individual solvent molecules, which can sometimes permit a detailed description of these interactions. For instance, the polarized structure-specific backbone charge (PSBC) explicit model has been successful in predicting both the experimental folding of helical peptides [41] and β-sheet structures [42] thanks to considering the polarizability of backbone hydrogen bonds by implementing the partial charges of backbone hydrogen-bond donor and acceptor atoms during peptide folding simulations. However, despite their differences some bibliography holds that for predicting solvation energies and partition coefficients, both methods can perform quite reasonable results [43, 44].

Acetylation is a relevant post-translational modification that is mainly carried out in both the ε-amine on the side chain of lysine and in the α-amine of the N-terminus in peptides and proteins [45]. In health and pathological states, the reversible acetylation of lysine residues plays a crucial role in regulating cellular and developmental processes. These facts make the correct identification of acetylated peptides and proteins a constantly developing field in modern proteomics [46]. In this context, experimental studies have analyzed the impact of peptide acetylation on chromatographic retention time in reversed phase-high performance liquid chromatography (RP HPLC) in order to create predictive models that suggest an efficient way for the separation of these peptides that will allow their identification [46].

Table 1 reports the experimental hydrophobicity index (ΔHI) obtained by Mizero and collaborators [47], calculated as the difference between the hydrophobicity index for modified (acetylated) and non-modified peptide pairs expressed in % acetonitrile (% ACN). As can be seen, it is evident that the greater the change in the degree of acetylation in the lysines of the peptide pairs, the greater the amount of organic solvent (% ACN) will be necessary.

Figure 10 depicts the derivative of the change in the hydrophobic index with respect to the change in (Ac)Lys residues in the modified/non-modified pairs [ΔΔHI/Δ(Ac)Lys] from which the slope permit to obtain the increase in hydrophobicity due to the acetylation of a lysine residue (~1.70 units).

In order to further evaluate the reliability of the predictions of the calculations performed in this work, Table 2 reports the increase of hydrophobicity under the acetylation of lysine residues (ΔlogP_Ac) using our computations but also those obtained of ChemAxon [48] and milogP [49]. Let us mention that HPLC separation systems are carried out under acidic conditions (pH around 2). Therefore, our reported value of –3.07 refers mainly to the partitioning of the ionic species (logD₂) and not to the neutral species (logP). For acetylated lysine, the reported value corresponds to the logP. Thus, since our prediction (~1.43 logP units) is close to that obtained experimentally (see Figure 10), it can be used to efficiently predict experimental HPLC conditions to separate acetylated peptides and thus, be used for proteomic studies.