## 3 Results and Discussion
### Role of Water Molecules  
For the first \(\sim\)30 ns of the bR-graphene simulation, there were \(\sim\)90 interfacial water molecules between bacteriorhodopsin and graphene. The number of water molecules then began to decrease at around 40 ns when bR was close to the graphene surface and ultimately stabilized at around 60 molecules once bR and graphene were at an optimal distance from one another (Figure 6a). The RMSD of the interfacial water molecules, however, was practically stable throughout the simulation (Figure 6b), which is a sign of stable adsorption of bR on the graphene surface and indicates that the interfacial water molecules were also crucial in regulating the interface. Comparing the presence and absence of graphene, there were more water molecules at the active site in the presence of graphene (Figure 6c) compared to the control (Figure 6d). From Figure 3d (Section 3.2), the number of hydrogen bonds around the active site also increased at \(\sim\)40 ns in the presence of graphene, which can also be attributed to the favorable interactions between bR and graphene. Furthermore, it is understood that water molecules play a key role in the transportation of protons from one amino acid site to another during the photocycle. This is largely due to the hydrogen bonding of water molecules to the proton donor and acceptor groups [36]. As a result, more H bonds and increased water molecules around the active site means a greater probability that the photocycle is achieved. Figure 6: Role of water molecules at the interface of bR and graphene: (**a**) Number of interfacial water molecules between bR and graphene (within 5Å) during the 100 ns simulation; (**b**) Root Mean Square Deviation (RMSD) of interfacial water molecules between bR and graphene; (**c,d**) End of run screenshots showing the number of water molecules around the retinal in the presence and absence of graphene. Analysis of the Number of Atoms Adsorbed and the Optimal Distance of bR from the Surface of Graphene  
The distance between graphene and the retinal changes with time and reduces to \(\sim\)22 A from the initial distance of \(\sim\)34 A at 0 ns (a 12 A approach due to the adsorption of bR on graphene surface) (Figure 7a). The conformational rearrangement of the retinal is the direct result of the adsorption of bR onto graphene. Moreover, an average number of bR atoms including hydrogen atoms (\(\sim\)11 atoms) are present at a 3 A distance from the graphene surface. This number of atoms constantly increases as the cut-off distance increases up to 12 A (Figure 7b). The attractive energy between these atoms and the surface of graphene also continuously increases with the distance ranging from 2 A to 6 A and becomes stable after 10 A (Figure 7c). A comparison was done with and without hydrogen atoms to understand the interactions between heavy atoms (oxygen, carbon and nitrogen) as the heavy atoms are more stable. Figure 7d shows the optimal distance between the bR and graphene, where a minimum number of atoms interact with maximum energy and, hence, play a crucial role in stabilizing the interface. It was found that this optimal cut-off distance is \(\sim\)4.2 A. To further understand the nature of the interactions between graphene and bR, a thorough analysis was done to identify the type of residues adsorbed on the surface of graphene. As shown in Table 3, the interactions were largely due to the non-polar (hydrophobic) residues supporting the conformational changes in the bR and the resulting changes in the dihedral angles and energies. Figure 7: Optimal distance analysis between bR and graphene: (**a**) Distance between the center of the masses of graphene and retinal; (**b**) Number of atoms of bR with respect to cut-off distance; (**c**) Total interaction energy between bR and graphene with respect to cut-off distance; (**d**) Optimal distance between bR and graphene where minimum number of atoms drive the interactions at the interface.