# Non-Enzymatic Formation of \(N\)-acetylated Amino Acid Conjugates in Urine
## 2 Materials and Methods
### Methods
#### 2.4.4 Molecular Modelling  
Molecular modelling was used to assess the possibility of in vivo formation of \(N\)-AAA conjugates. The maximum activation energy (E\({}_{\text{a}}\)) required for the reaction was calculated and compared with typical E\({}_{\text{a}}\) values of various enzymes. A reaction mechanism proposed by [PERSON] et al. [31] for the non-enzymatic formation of \(N\)-Ac-Ala from pyruvate acid and ammonia served as a starting point. \begin{table}
\begin{tabular}{l l l l} \hline \multicolumn{1}{c}{**2-Keto Acid**} & \multicolumn{1}{c}{**Expected Result**} & \multicolumn{1}{c}{**Actual Product**} & \multicolumn{1}{c}{**Yield (\(\mu\)mol/L)**} \\ \hline \multicolumn{1}{c}{2-Keto-3-methylvaleric acid} & \multicolumn{1}{c}{\(N\)-2-Methylbutyryl-Ile} & \multicolumn{1}{c}{\(N\)-2-Methylbutyryl-Ile} & \multicolumn{1}{c}{Trace–0.6} \\ \hline \multicolumn{1}{c}{2-Ketobutyric acid} & \multicolumn{1}{c}{\(N\)-Propionyl-2-aminobutyric acid} & \multicolumn{1}{c}{\(N\)-Propionyl-2-aminobutyric acid} & \multicolumn{1}{c}{10.12} \\ \hline \multicolumn{1}{c}{2-Ketocapric acid} & \multicolumn{1}{c}{\(N\)-Pentanoyll-\(nor\)-Leu} & \multicolumn{1}{c}{\(N\)-Pentanoyll-\(nor\)leucine} & \multicolumn{1}{c}{14.70} \\ \hline \multicolumn{1}{c}{2-Ketoisocorapric acid} & \multicolumn{1}{c}{\(N\)-Isovaleryl-Leu} & \multicolumn{1}{c}{\(N\)-Isovaleryl-Leu} & \multicolumn{1}{c}{1.35} \\ \hline \multicolumn{1}{c}{2-Ketoisovaleric acid} & \multicolumn{1}{c}{\(N\)-Isobutyryl-Val} & \multicolumn{1}{c}{\(N\)-Isobutyryl-Val} & \multicolumn{1}{c}{20.32} \\ \hline \multicolumn{1}{c}{2-Ketovaleric acid} & \multicolumn{1}{c}{\(N\)-Butyryl-Nva} & \multicolumn{1}{c}{\(N\)-Butyryl-\(Nva\)} & \multicolumn{1}{c}{Trace–1.0} \\ \hline \multicolumn{1}{c}{2-Phenylpyruvate} & \multicolumn{1}{c}{\(N\)-(Phenylacetyl)-Phe} & \multicolumn{1}{c}{\(N\)-(Phenylacetyl)-Phe} & \multicolumn{1}{c}{5.22} \\ \hline \multicolumn{1}{c}{\(p\)-Hydrooxyphenylpyruvate} & \multicolumn{1}{c}{\(N\)-(\(p\)-hydroxyphenylacetyl)-(\(p\)-hydroxy-Phe)} & \multicolumn{1}{c}{No result} & \multicolumn{1}{c}{Not detected} \\ \hline \multicolumn{1}{c}{2-Pyruvate} & \multicolumn{1}{c}{\(N\)-Ac-Ala} & \multicolumn{1}{c}{\(N\)-Ac-Ala} & \multicolumn{1}{c}{2.46} \\ \hline \end{tabular}
\end{table} 
Table 1: \(N\)-AAA conjugate products from a single substrate reaction. Intermediates and products involved in the mechanism were visually represented using the Visualiser module in BIOVIA Materials Studio software (v16.1.0.31 Dassault Systemes, Velizy-Villacoublay, France). Geometric optimisation of these structures was performed using the density functional theory (DFT) module (DMol\({}^{3}\)) in Materials Studio. The calculation model employed was the generalised gradient approximation (GGA) functional PW91, using Ortmann, Bechstedt, and Schmidt (OBS) dispersion correction and a double-numerical basis set with polarisation functions (DNP) basis file 4.4. The molecular modelling parameters were set as follows: An unrestricted electron spin with the initial spin value set to formal spin. The convergence tolerance was set to medium, and the maximum number of iterations was 1 000. The maximum allowable step size for any change in the Cartesian coordinates was 0.3 A, and integration accuracy was set to medium. Direct inversion in interactive subspace (DIIS) was used to speed up the self-consistent field (SCF) convergence, which was set to medium. The DIIS size was set to 6, and the maximum number of SCF iterations to 1000. The maximum angular momentum function was set to octupole, with a density mixing charge of 0.2 and a spin of 0.5. Thermal smearing with a value of 0.005 Ha was selected. All electrons were included in the calculations. The orbital cut-off of the atomic basis set was set to medium quality, and the exact value depended on the elements present in the specific structure. The conductor-like screening model (COSMO) continuum solvation model (CSM) was selected to simulate the solvent environment for the model.