## 3 Results and Discussion
**(c,d)** Net transfer entropy averaged for each residue type categorized as either hydrophobic (blue tones) or polar (pink tones) and the number of side-chain torsion angles \(k\) indicated at the top of each bar. Color code for **(a,b)**: no display for \(\langle netTE\rangle\leq 4\); magenta for \(4<\langle netTE\rangle\leq 8\), green for \(8<\langle netTE\rangle\leq 12\) and red for \(12>\langle netTE\rangle\). Furthermore, net transfer entropy was averaged for each residue type categorized as either hydrophobic or polar, as depicted in Figure 5c,d, where positive and negative \(\langle netTE\rangle\) values correspond to entropy donor and acceptor residues, respectively. Clearly, no correspondence was detected between the number of side-chain torsion angles and the net entropy in both runs. In addition, there is no clear tendency for polar or hydrophobic residues to display either entropy donor or acceptor features. Furthermore, two runs displayed two completely different donor/acceptor profiles with respect to residue types. This is especially noticeable in \(\langle netTE\rangle\) maps illustrated for all residue pairs, such as entropy donor versus entropy acceptor depicted in Supplementary Figure S2. Several residues displayed opposite features, e.g., entropy donor in one run and acceptor in the second run, such as _Pro_, _Cys_, _Val_, _Ile_, _Leu_, _Tyr_, _Met_, _Ser_, _Thr_, _Asn_, _Asp_, _Glu_, and _Lys_. Apparently, fluctuations in \(\mathbb{C}\alpha\) displacements were not driven by residue type, which incorporates the information of both polarity/hydrophobicity and the number of degrees of freedom. Transfer entropy was next determined using backbone torsion angles, \((\varphi,\,\psi)\). As depicted in Figure 6a, ICL3 appeared as the only source of entropy donor to a few isolated acceptor regions detected on mostly loops such as ICL1, ECL1, ECL2, ECL3 and the intracellular part of TM7 adjacent to segment H8. Maximum TE values were determined as 10.86 and 11.54 for two runs, which are well below \(\mathbb{C}\alpha\)-based TE values. Next, the first side-chain torsion angle (\(\chi_{1}\)) was considered together with two backbone angles for identifying the information of the rotameric state transferred from one residue to another in the receptor. As illustrated in Figure 6b, the same loop regions still appeared as entropy donor sites with an increased intensity dominating the future fluctuations of torsional angles everywhere in the receptor. In addition, maximum TE values reached 26.46 and 31.54 in two runs. Unfortunately, the addition of more than one side-chain torsion angle made the computation intractable due to triple joint probability calculations (See Equation (7)), as it roughly required a memory space of \(523,792,501,128\) bytes \((=3^{18}\times N_{Arg}\times N_{Lys}\times 8(\text{bytes/ArrayCell}))\) only for calculating the \(p\left(\Delta R_{j}(t),\,\Delta R_{j}(t-\tau),\,\Delta R_{i}(t-\tau)\right)\) parameter of the transfer entropy equation between all _Arg_ and _Lys_ pairs, which exceeded the maximum amount available for today's computer technology. However, the same analysis was conducted for all possible side-chain torsion angles \(\chi_{k},\,k=1,2,3,4\) only. As anticipated, information transferred from one region to another site increased significantly, with a maximum TE value reaching 61.34 for Run #1 and 63.38 for Run #2 (see Figure 6c). All intra- and extracellular loops that extended slightly towards the neighboring helices were detected as important entropy donor sites. These results clearly represent that the conformational states of the side-chains at loop regions extensively dominated the future conformational states of side-chain torsion angles everywhere in the receptor.