## 3 Results and Discussions
### Root Mean Square Deviation (RMSD) Analysis  
RMSD is an important parameter for observing and analyzing the degree of conformational change and stability of proteins, and its calculation formula is as follows:  
\[RMSD=\sqrt{\frac{1}{N_{atm}}{\sum_{A}^{N_{atm}}}{\left({r_{A}-r_{A}^{ref}} \right)}^{2}}\]  
In the above equation, \(A\) represents the number of atoms, \(N_{atm}\) represents the number of atoms in the selected range, and the superscript ref represents the reference structure. In this paper, the RMSD of the whole and partially changing fragments of the simulated protein under the action of electric fields in different directions is calculated, as shown in Figure 2, to study the conformational changes, stability, and convergence of the proteins during the simulation [30]. Firstly, we calculate the RMSD value of the protein in the 310 K, 0 v/nm state and set it as the reference value. According to Figure 2a, the RMSD reference value of the protein fluctuated at around 0.25 nm, and the overall dynamic was stable. After applying the electric field, the RMSD curve of the protein could be seen to shift, and the change was clear. This phenomenon indicates that the protein changes its original spatial position and the conformation changes under the action of the electrostatic field. In the above analysis, we observed that the secondary structure of some regions of the protein except residues 4-19 (residues 61-88, 139-149, 169-180 residues) also changed significantly. So, the RMSD parameter graph of residues 61-88, 139-149, and 169-180 under the action of electric fields in different directions was drawn. From Figure 2b-d, it can be seen that the above three segment residues changed significantly under the action of electrostatic fields in different directions. After applying an electric field of 0.5 v/nm at different amounts and directions, the RMSD curve of residues 61-88 increased to a certain height sharply and maintained dynamic stability. This indicates that the secondary structure of the protein fragment changes under the influence of the electric field and deviates significantly from the initial position, maintaining the current conformation to maintain equilibrium after a period of deformation. When the 0.5 v/nm electrostatic field was applied to the z axis and x, z-axis, respectively, the RMSD of residues 61-88 underwent a second mutation at about 20 ns to 30 ns at the start of the reaction and remained dynamically stable after the second mutation. This is because protein molecules  
Figure 1: Conformational changes in proteins at different amounts and directions of electric fields. have an interaction force that maintains the initial structure, and the destruction of this force requires a certain period of continuous action, sometimes divided into several stages. In addition, the RMSD value of residues 61-88 was finally dynamically stabilized at about 0.5 nm after the electric field was applied to the z-axis alone, while the final value was about 1.3 nm when the electric field was applied to the x and z-axis simultaneously. It can be seen that the stability of protein molecules is anisotropy, and the application of electric fields in different directions has different effects on the protein structure. It can be found from the changes in the RMSD curve in Figure 2c for residues 139-149 that although the RMSD value is significantly higher than the reference value under the action of the electric field, the curves of each group do not undergo clear bending or rising but increase as a whole. This phenomenon shows that the structure of residues 139-149 is very stable, and the movement of protein molecules is intensified under the action of the electric field, but no clear deformation occurs. In addition, the different structures of proteins in different directions have different effects on the reaction time and degree, just like residues 169-180.