## 2 Materials and Methods
\tag{2}\]  
Contact percentages over the MD trajectory were calculated with \(\sum_{n=1}^{nconf}M_{i,j}/nconf\) and the threshold was set to 75% of the whole trajectory to recognize stable contacts. **Mutual Information (MI). ** Mutual information based on \(\alpha\)-Carbon positional fluctuations between residue pairs \(i\) and \(j\) was calculated using the following expression:  
\[MI(i,j)=\sum_{k}p\big{(}\Delta R_{i}(t_{k}),\Delta R_{j}(t_{l})\big{)}log_{2} \frac{p\big{(}\Delta R_{i}(t_{k}),\Delta R_{j}(t_{l})\big{)}}{p(\Delta R_{i} (t_{k})).\ p\big{(}\Delta R_{j}(t_{l})\big{)}} \tag{3}\]  
where \(p\big{(}\Delta R_{i}(t_{k}),\Delta R_{j}(t_{l})\big{)}\) represents the joint probability of observing the fluctuation of residue \(i\) in state \(k\) and that of residue \(j\) in state \(l\). Mutual information is a non-negative and symmetric quantity, and zero if the fluctuations of residue \(i\) are independent of the fluctuations of residue \(j\). To calculate the probability of occurrence, \(p\big{(}\Delta R_{i}(t_{k}),\Delta R_{j}(t_{l})\big{)}\), the number of states \(k\) and \(l\), also described as the number of bins, \(N_{bins}\), were determined for each residue separately using Shannon's entropy criterion. The number of bins (or states)for each residue was determined as the value for which Shannon's entropy reaches its maximum. The convergence criterion was expressed as:  
\[\frac{\left|H(N_{bins}+1)_{i}-H(N_{bins})_{i}\right|}{H(N_{bins})_{i}}<0.02 \tag{4}\]  
where \(H(N_{bins})_{i}\) is the Shannon entropy for residue \(i\) with \(N_{bins}\). Similarly, mutual information based on fluctuations in backbone and side torsion angles were expressed as:  
\[MI_{i,j}=\sum_{\Theta_{i}}\sum_{\Theta_{j}}p(\Theta_{i},\ \Theta_{j})\ log_{2} \Bigg{(}\frac{p\left(\Theta_{i},\ \Theta_{j}\right)}{p(\Theta_{i}),\ p\left(\Theta_{j} \right)}\Bigg{)} \tag{5}\]  
where \(p\left(\Theta_{i},\ \Theta_{j}\right)\) denotes the joint probability of observing the joint state \(\left(\Theta_{i},\ \Theta_{j}\right)\) of residues \(i\) and \(j\). Here, \(\Theta_{i}\) and \(\Theta_{j}\) represent the rotameric states of backbone \(\varphi,\ \psi\) and side-chain dihedrals \(\chi_{i},\ i=1,2,3,4\) in residues \(i\) and \(j\), respectively. Based on the distribution of rotameric states, the number of discrete rotameric states (or bins) for backbone dihedrals was set to 3, whereas for side-chain dihedrals, the number of states varied between 0 and 6 according to the rotamer library [36]. **Transfer Entropy. ** Transfer entropy is defined as the reduction in uncertainty in future states of residue \(j\) at \(t+\tau\) by knowing the states of residue \(i\) at time \(t\). Based on [PERSON]'s work [18], it was defined by [PERSON] et al. [22; 23] as;  
\[TE_{i\to j}(\tau)=H\big{(}\Delta R_{j}(t)\big{|}\Delta R_{j}(t-\tau)\big{)}-H \big{(}\Delta R_{j}(t)\big{|}\Delta R_{j}(t-\tau),\Delta R_{i}(t-\tau)\big{)} \tag{6}\]  
where \(H\big{(}\Delta R_{j}(t)\big{|}\Delta R_{j}(t-\tau)\big{)}\) is the conditional entropy of residue \(j\) at time \(t\) given the values of \(\Delta R_{j}\) at time \(t-\tau\). The second term \(H\big{(}\Delta R_{j}(t)\big{|}\Delta R_{j}(t-\tau),\Delta R_{i}(t-\tau)\big{)}\) is the conditional entropy of residue \(j\) at time \(t\) given the values of \(\Delta R_{i}\) and \(\Delta R_{j}\) at time \(t-\tau\).