## 3 Results and Discussion
(**e**) Mean mutual information per residue averaged over the rest of the receptor. (Green dots: 0.25 \(<\) MI \(\leq\) 0.5; red dots: MI \(>\) 0.5). inating feature of polar residues in sharing MI can be attributed to their abundance in loop regions, which displayed a noticeably higher amount of MI than transmembrane regions in addition to their higher amount of rotational degrees of freedom. As illustrated in Figure 4c, the frequency of a residue type in loop regions is slightly proportional to its average shared MI. Almost all polar residues indicated with red dots displayed frequency values above 5%, which represents the random occurrence, whereas only three hydrophobic residues, _Gly_, _Ple_ and _Leu_, had frequencies above 5%. On the other hand, two polar residues _Ser_ and _Thr_, both with hydroxyl groups in their side-chains and frequency values above 7%, displayed low average MI values. Interestingly, _Arg_ and _Lys_, with four rotatable bonds on their positively charged side-chains, displayed slightly different average MI values with respect to each other; with an average MI of 0.23 \(\pm\) 3.64, _Arg_ shared twice as much information as that of _Lys_ despite the  
Figure 4: Mutual information for pairs of distal residues classified as either hydrophobic (blue tones) or polar (pink tones) considering all backbone (\(\phi\), \(\psi\)) and side-chain torsion angles (\(\chi_{k},\ k=0,\ 1,2,3,4\)), averaged over (**a**) residue pairs, (**b**) residue types with the number of side-chain torsion angles \(k\) and (**c**) residue frequency in loop regions versus average MI. fact that both residues were found in nearly equal amounts everywhere in the receptor (-7% in loops and -3% in transmembrane helices, See Supplementary Figure S1). The side-chain of _Arg_ has a positively charged guanidium moiety, which favors \(\pi\)-stacking with aromatic rings and has the potential of forming five hydrogen bonds. As the side-chain of _Arg_ protrudes from the surface of the protein, it has a crucial role in protein-protein interactions. Hence, it is not surprising to see the highest correspondence between _Arg_ and the majority of residues, especially polar ones. Mutual information is a measure of correspondence between two residues \(i\) and \(j\) with respect to their dynamic behaviors, such as positional fluctuations (C\(\alpha\)) or torsional changes happening at the exact same moment. Transfer entropy is another important feature that relates the dynamic states of two residues separated by a time lag parameter \(\tau\). In other words, transfer entropy measures the amount of information transferred from residue \(i\) to residue \(j\) at a later time. Knowing the state of residue \(i\), the state of another residue \(j\) at a distant site can be predicted if there exists an allosteric communication pathway connecting the two sites. Similar to mutual information analysis, net transfer entropy was first calculated based on the backbone C\(\alpha\) atom's positional fluctuations (see Equations (7) and (8) in Section 2). As depicted in Figure 5a, in one of two MD runs, the intracellular loops ICL3, ICL2, TM3, and TM4 moderately appeared as entropy donor sites, whereas the intracellular part of TM1 was detected as a dominant acceptor site. The second MD trajectory displayed a relatively different distribution profile for donor/acceptor sites; ICL3, together with the extracellular part of TM7, appeared as two dominant entropy donor sites, whereas no major acceptor site was detected (See Figure 5b). The maximum amount of information transferred was observed as 16.32 in Run#1 and 18.15 in Run#2. These results clearly indicate alternative communication pathways that can be established via positional fluctuations of C\(\alpha\) atoms for the same system in two separate runs. Figure 5: **(a,b)** Net transfer entropy from residue \(i\) to residue \(j\) (See Equation (8)) based on C\(\alpha\) fluctuations for two independent MD runs.