## 3 Results and Discussion
No G protein was attached, yet ICL3 preserved its initial open conformation as if there was a G protein nearby, although the TM6's upward tilt characterizing the active state was not observed. Clearly, the conformational state of the orthosteric binding site allosterically affects the conformational state of the distant G protein binding site. It might facilitate the opening of the cavity for the initial binding of G protein, yet the fully active state can only be achieved and preserved when there is a G protein nearby interacting with the receptor. In other words, the major conformational shift for the characteristic tilt in TM6 requires an energy boost that a G protein can only provide and thus cannot be achieved in the course of an MD simulation, which is confined to low energy conformational states. Moreover, the absence of an agonist, which is accompanied by only a slight expansion at the unoccupied orthosteric binding site, does not destabilize the active state, which is already securely preserved by a G protein. **Cross-correlations between \(\alpha\)-Carbon displacements disclosed TM6 as the dominating site fluctuating in concert with the rest. ** It is important to highlight distant regions that display positional fluctuations that are correlated with each other, as they might indicate the presence of some potential sites in communication along the allosteric pathway. Thus, the contact map was overlaid with the residue-pair cross-correlation map, as depicted in Figure 2. The contact map was generated by using the heavy atoms with a threshold distance of 6 A. Distant and correlated regions were mainly detected in the second half of the receptor composed of TM5, TM6, ICL3, TM7, and its small extension H8, especially TM6, which incorporated most critical sites for binding intracellular G proteins and small extracellular molecules. Especially, _Phe289_, _Asn_293 on TM6, and _Asn_312 on TM7, which are known to be key residues interacting with the ligand at the orthosteric site, fluctuated in the same direction, with ICL3 having correlation values as high as 0.8. Another set of critical residues at the orthosteric binding sites _Ser_203, _Ser_204, and _Ser_207 located at the extracellular part of TM5 negatively correlated with the distant helical segment TM7 with a \(C_{\rm ij}\) value of around \(-0.5\). Specifically, it is interesting to observe both _Ser_203 and _Ser_207 on one side of the binding cavity fluctuating in opposite directions with _Asn312_ on the opposite side. Moreover, ICL2, the second-most important intracellular loop after ICL3, distantly fluctuated in concert with the second half of the receptor (TM5-H8). Finally, the first transmembrane helix TM1, which incorporated the free amino-terminal tail, mostly fluctuated in the opposite direction from the rest of the receptor, especially the distant helices TM6, TM7, and to some extent with TM3 and TM5, which all incorporated critical key residues at the orthosteric binding site. **Rotamer-based mutual information is mostly observed between loop regions and shared among polar residues. ** Cross-correlation is a metric that ignores the correlated motions in orthogonal directions. Therefore, even perfectly correlated motions important for allosteric signaling may be overlooked if the positional fluctuations are perpendicular to one another. On the other hand, mutual information, a metric in information theory, determines the correspondence between fluctuations of residue pairs, irrespective of their directions. MI was first calculated for the positional fluctuations of backbone C\(\alpha\) atoms, and as anticipated, the highest MI values (max. 4.01) were observed for residues close in space (see the diagonal line in Figure 3a). In addition, it is important to recognize high MI values observed between spatially distant residues as they would likely indicate the existence of an allosteric communication network, which is usually characterized by distant regions with a high degree of correspondence.