## 2 Materials and Methods  
### Internal Angles as Local Probes of the Protein Main and Side-Chain Conformational Changes  
Local conformational changes of the main chain of human GSTA1 were analyzed using coarse-grained angles (CGAs) \((\theta,\gamma)\), which can be represented by a unit vector in spherical coordinates, where \(\gamma\) is the azimuth angle and \(\theta\) the polar angle [25]. For a residue \(i\) along the amino-acid sequence (see Figure 2A), \(\theta_{i}\) is the bond angle formed by the virtual bonds joining three successive C\({}^{\alpha}\) atoms (\(i-1\), \(i\) and \(i+1\)) and \(\gamma_{i}\) is the dihedral angle formed by the virtual bonds joining four successive C\({}^{\alpha}\) atoms (\(i-1\), \(i\), \(i+1\) and \(i+2\)). The first pair of CGA \((\theta,\gamma)\) along the sequence is \((\theta_{2},\gamma_{2})\) and the last one is \((\theta_{N-2},\gamma_{N-2})\), where \(N\) is the total number of residues. The convention for \(\gamma\) angles is the following: each angle varies between \(-180^{\circ}\) and \(+180^{\circ}\), with \(\gamma=0^{\circ}\) being chosen when C\({}_{i-1}^{\alpha}\) is cis to C\({}_{i+2}^{\alpha}\), and the clockwise rotation of C\({}_{i+1}^{\alpha}-C_{i+2}^{\alpha}\) is positive when looking from C\({}_{i}^{\alpha}\) to C\({}_{i+1}^{\alpha}\). Because the length of the \(C^{\alpha}-C^{\alpha}\) virtual bond between two consecutive residues is nearly constant, the main-chain conformation is entirely described by the main-chain bond angles \(\theta\) and the main-chain torsional angles \(\gamma\) (Figure 2A). These CGAs \((\theta,\gamma)\), which represent the torsion and curvature of the protein main chain and form a complete set of order parameters for protein folding [26], are part of coarse-grained protein models [27] and were used to analyze large conformational changes of proteins [28], protein folding, and dynamics in all-atom simulations [25; 29; 30] and conformational ensemble of intrinsically disordered proteins [31]. Moreover, local conformational changes of the side chains of human GSTA1 were analyzed using side-chain dihedral angles (SCAs) \(\chi^{k}\). SCAs capture the rotation around \(C-C\) or \(C-N\) bonds of the side chain from its \(C^{\beta}\) to its extremity. Each SCA is built from the coordinates of four successive atoms along the side chain of an amino acid. First of all, dihedral angle \(\chi^{1}\) is made of \(N-C^{\alpha}-C^{\beta}-X\), where \(X\) depends on the amino acid. \(X\) can be \(S^{7}\) (Cys), \(O^{7}\) (Ser, Thr), or \(C^{7}\) for all the other amino acids except Gly and Ala, for which \(\chi^{1}\) dihedral angle is not defined. Second, \(\chi^{2}\) corresponds to the rotation around the bond \(C^{\beta}-C^{7}\) and is not defined for amino acids Gly, Ala, Cys, Ser, Thr, and Val. Third, \(\chi^{3}\), corresponding to the rotation around the bond \(C^{7}-C^{\delta}\) or \(C^{7}-S^{\delta}\) (Met), is only defined for amino acids Gln, Glu, Met, Arg, and Lys. Finally, \(\chi^{4}\) are only defined for Arg and Lys amino acids and correspond to the rotation around the bond \(C^{\delta}-C^{\epsilon}\) (Lys) or \(C^{\delta}-N^{\epsilon}\) (Arg), and \(\chi^{5}\) is only defined for Arg and corresponds to the rotation of the side chain around the bond \(N^{\epsilon}-C^{\zeta}\) (Figure 2A). Figure 2: (**A**) Cartoon representation of CGAs \((\theta,\gamma)\) and SCAs (\(\chi^{k}\)) used as local probes to track local conformational changes in hGSTA1 from MD. C\({}^{\alpha}\) atoms are shown with black spheres. The main chain and side chains of each residue are shown in sticks. (**B**) Time series of CGAs \(\theta\) (**top panel**), \(\gamma\) (**middle panel**), and SCA \(\chi^{1}\) (**bottom panel**) for residue 84, as an example, recorded during run 1 of hGSTA1 in its APO form. (**C**) Effective free-energy surface \(V(\theta,\gamma)_{84}\) computed from time series shown in panel (**B**). Effective free-energy profiles of each internal coordinate \(\theta_{84}\) and \(\gamma_{84}\) are also presented.