## 2 Results and Discussion
### Analyses of GTP- and GDP-HRAS Interaction Networks  
The interaction networks between GTP and GDP with HRAS were analyzed using the protein-ligand interaction profiler (PLIP) server [76] (Figure 6). The hydrogen bonding interactions (HBIs) of GTP and GDP with HRAS were also identified using the CPPTRAprogram (Table 1; Figure 6A,B). We investigated the role of Mg\({}^{2+}\) in the binding of ligands to HRAS (Figure 6C,D). The frequency distributions of the distances involved in the non-bonded interactions of GTP and GDP with residues are shown in Figure 7, and the time courses of these distances are provided in Figure S7. The frequency distributions of the distances involved in the Mg\({}^{2+}\)-mediated interactions in the GTP- and GDP-bound systems are plotted in Figure 7, while the time evolution of these distances is displayed in Figure S8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{\({}^{\mathbf{a}}\)**Hydrogen Bonds**} & \multicolumn{3}{c}{\({}^{\mathbf{b}}\)**Occupancy (\%)**} \\
**Residues** & **GTP/GDP** & **WT** & **A59E** & **K117R** \\ \hline G13-N-H & O3G/O1B & 96.9/96.2 & 95.2/86.1 & 85.8/75.4 \\ V14-NH & -/O3B & -/14.2 & -/34.3 & -/82.1 \\ G15-N-H & O2B/O3B & 99.7/96.3 & 99.6/96.7 & 98.7/95.4 \\ K16-N-H & O2B/O3B & 99.9/99.8 & 99.9/95.6 & 99.9/90.8 \\ S17-N-H & O1B/O2B & 96.4/62.9 & 98.4/82.3 & 92.3/69.1 \\ A18-N-H & O2A/O2A & 99.7/94.9 & 99.7/89.1 & 99.8/41.2 \\ Y32-N-H & -/O1B & -/-29.8 & -/-5.4 & -/1.3 \\ Y32-OH-HH & O3G/- & 86.6/- & 69.2/- & 59.7/- \\ T35-N-H & O1G/- & 65.1/- & 45.6/- & 42.9/- \\ V29-O & O2’-HO2’/O2’-H2’ & 65.4/39.7 & 49.6/39.7 & 15.1/9.8 \\ D30-O & O3’-H3T/O3’-H3’ & 62.3/33.7 & 50.8/7.4 & 15.3/9.3 \\ N116-ND2-HD21 & N7/N7 & 95.4/89.7 & 95.0/88.3 & 84.1/78.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hydrogen bonding interactions of GTP/GDP with the WT and mutated HRAS. Figure 6: Geometric positions of key interactions. **(A)** GTP–residue interactions, **(B)** GDP–residue interactions, **(C)** the interactions of magnesium ion Mg\({}^{2+}\) with GTP and residues, and **(D)** the interactions of Mg\({}^{2+}\) with GDP and residues. The HBIs are shown in solid green lines, salt bridge interactions are shown in dashed purple lines, and the \(\pi\)–\(\pi\) interactions are shown in solid orange lines. Atoms are colored according to their elements. The residues in the P-loop, including G13, G15, K16, S17, and A18 in WT HRAS, formed HBIs with GTP and GDP (Figure 6A,B), respectively. These interactions had high occupancies, exceeding 60.0% (Table 1), indicating their high stability throughout the GaMD simulations of GTP- and GDP-bound WT HRAS. S17 formed a weaker HBI with GDP compared to GTP. In contrast to the GTP-associated WT HRAS, GDP formed an additional HBI with V14, but its occupancy was only 14.2%. Additionally, GTP and GDP also formed HBIs with the residues N116, K117, and D119 in loop L3, as well as residues S145, A146, S17, and S187, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{\({}^{\mathbf{a}}\)**Hydrogen Bonds**} & \multicolumn{3}{c}{\({}^{\mathbf{b}}\)**Occupancy (\%)**} \\
**Residues** & **GTP/GDP** & **WT** & **A59E** & **K117/R** \\ \hline K117-NZ-HZ1 & O4\({}^{\prime}\)/O4\({}^{\prime}\) & 15.6/18.2 & 16.0/15.4 & -/- \\ D119-OD1 & N1-H1/N1-H1N & 99.9/95.4 & 90.5/84.1 & 82.6/94.0 \\ D119-OD2 & N2-H21/N2-H21 & 99.9/88.7 & 89.1/77.5 & 79.4/89.5 \\ S145-OG-HG & N1/O6 & 52.8/61.9 & 53.0/54.3 & 52.4/63.5 \\ A146-N-H & O6/O6 & 56.6/56.1 & 55.3/51.1 & 67.8/50.5 \\ K147-N-H & O6/O6 & 87.1/91.7 & 86.7/82.6 & 70.2/92.8 \\ \hline \hline \end{tabular} \({}^{\mathbf{a}}\) Hydrogen bonds were analyzed with an acceptor-donor distance of \(\sim\)3.5 Å and an acceptor-H-donor angle of \(>\)120\({}^{\circ}\). \({}^{\mathbf{b}}\) Occupancy (%) is defined as the percentage of simulation time for which a specific hydrogen bond existed.  
\end{table} 
Table 1: _Cont._  
Figure 7: Frequency distribution of distances.