## 2 Results and Discussion  
### Structural Fluctuation and Flexibility  
The RMSDs of heavy atoms from the two ligands, GTP and GDP, in the binding pocket of the WT and mutated HRAS were calculated relative to their initial optimized structure to understand their dynamics in HRAS (Figure S1). The RMSDs of GTP fluctuate between 0.16 A and 3.12 A in the active form of HRAS (Figure S1A), while those of GDP range from 0.06 A to 4.72 A in the inactive state of HRAS (Figure S1B). This result shows that the stability of GTP in active HRAS is higher than that of GDP in inactive HRAS. The frequency distribution of RMSDs for GTP and GDP are presented in Figure 2A,B, respectively. In WT HRAS, A59E, and K117R HRAS mutants (Figure 2A), the RMSDs of heavy atoms for GTP are distributed with peaks at 0.67 \(\pm\) 0.01, 0.91 \(\pm\) 0.01, and 0.74 \(\pm\) 0.00 A, and the average RMSDs are 0.72, 1.07, and 0.81 A. Moreover, the averaged RMSDs of GTP in the A59E and K117R HRAS are 0.35 and 0.09 A larger than those in the WT one. Thus, the A59 Eand K117R mutations slightly weaken the structural stability of GTP in HRAS compared to the WT HRAS, and the influence of A59E is stronger than that of K117R. As for GDP, the distribution of RMSDs has one peak of 0.91 \(\pm\) 0.01 and 1.02 A \(\pm\) 0.01 in the WT and A59E HRAS, respectively, but two peaks of 1.08 \(\pm\) 0.01 and 2.25 \(\pm\) 0.02 A for the K117R HRAS (Figure 2B). The average RMSDs are 1.08, 1.16, and 1.99 A for the GDP-bound WT, A59E, and K117 HRAS, respectively. These results indicate that A59E and K117R mutations reduce the structural stability of GDP in HRAS compared to the WT HRAS, and the effect of K117R is more significant than that of A59E. The RMSFs of the C\(\alpha\) atoms in HRAS were computed in order to understand the impacts of A59E and K117R on the structural flexibility of HRAS (Figure 2C,D). The structural domains corresponding to the alterations in the RMSFs are depicted in Figure S2. It can be observed that the SW1, SW2, and the loop L2 showed high flexibility (Figures 2C,D and S2). The difference in RMSFs between the WT and mutated HRAS was estimated using the equation \(\alpha\)RMSF = \(RMSF_{mutant}-RMSF_{WT}\) (Figure S2), where \(\alpha\)RMSF, \(RMSF_{mutant}\) and \(RMSF_{WT}\) indicate the RMSF difference and RMSFs of mutants and WT HRAS, respectively. In the case of GTP-bound WT and mutated HRAS, K117R strengthens the structural flexibility of the switch domain SW1 in the GTP-bound active HRAS by referencing the WT HRAS (Figure 2C); differently, A59E weakens the structural flexibility of the SW1-L (the loop part of the SW1) but strengthens that of the SW1-\(\beta\), namely, the \(\beta\) part of the SW1 (Figures S2 and S3). A59E slightly enhances the structural flexibility of the switch domain SW2 in the GTP-bound active HRAS, but K117R highly reduces the structural flexibility of this domain compared to the GTP-bound WT one (Figures S2 and S3). In addition, A59E increases the structural flexibility of the P-loop, while K117R produces the opposite effect on the structural flexibility of the L2 loop. For the GDP-bound WT and mutated HRAS, although A59E enhances the structural flexibility of the \(\alpha\)1-L compared to the WT HRAS, it weakens that of the SW1-\(\beta\) (Figure S2). K117R abates the structural flexibility of the \(\alpha\)1-L, but highly strengthens that of the SW1-L and the loop L2 by comparison with the GDP-bound WT HRAS (Figures S2 and S3). Furthermore, K117R increases the structural flexibility of the P-loop, and residues 84-98 and A59E strengthen the structural flexibility of the L2 loop compared to the GDP-bound WT HRAS (Figure 2D). The MSAs (molecular surface areas) of the GTP- and GDP-bound forms of HRAS were estimated to evaluate the extent to which HRAS is exposed to solvents (Figure S4). It is  
Figure 2: Structural fluctuations and flexibility. RMSDs of heavy atoms for GTP (**A**) and GDP (**B**); RMSFs of the GTP-bound complexes (**C**) and GDP-bound complexes (**D**).