## 2 Materials and Methods
### Free-Energy Surface, Free-Energy Profile, and Similarity Index  
Effective 2D Free-Energy Surfaces (FESs) \(V(\theta_{i},\gamma_{i})\) were computed for each pair of CGA \((\theta_{i},\gamma_{i})\) by using  
\[V(\theta_{i},\gamma_{i})=-k_{B}T\log P(\theta_{i},\gamma_{i}) \tag{1}\]  
where \(k_{B}\) is the Boltzmann constant, \(T\) is the temperature, and \(P(\theta_{i},\gamma_{i})\) is the probability density function (PDF) of CGA pair \((\theta_{i},\gamma_{i})\). Two-dimensional PDFs were computed on a sphere, using CGA time series (Figure 2B) extracted from concatenated MD trajectories for each hGSTA1 binding-state: APO (2 runs of 900 ns), GSH (2 runs of 900 ns), and GS-R (1 run of 1200 ns). An example of free-energy surface for CGA pair \((\theta_{84},\gamma_{84})\) (Gly83-Lys84-Asp85-Ile86) is shown in Figure 2C.  
Then, to quantify the modifications between two FESs of identical CGA pair \((\theta_{i},\gamma_{i})\) due to different ligand-binding form of hGSTA1, i.e., APO vs. GSH, GSH vs. GS-R, or GS-R vs. APO, as shown in Figure 1C, we computed the similarity index \(H\) between their associated 2D PDFs using  
\[H_{1|2}(\theta_{i},\gamma_{i})=\frac{2\int_{0}^{\pi}\text{sin}\theta_{i}d\theta _{i}\int_{-\pi}^{+\pi}P_{1}(\theta_{i},\gamma_{i})P_{2}(\theta_{i},\gamma_{i} )d\gamma_{i}}{\int_{0}^{\pi}\text{sin}\theta_{i}d\theta_{i}\int_{-\pi}^{+\pi}P _{1}(\theta_{i},\gamma_{i})^{2}d\gamma_{i}+\int_{0}^{\pi}\text{sin}\theta_{i}d \theta_{i}\int_{-\pi}^{+\pi}P_{2}(\theta_{i},\gamma_{i})^{2}d\gamma_{i}} \tag{2}\]  
where \(P_{1}(\theta_{i},\gamma_{i})\) is the PDF of CGA pair \((\theta_{i},\gamma_{i})\) in binding form 1 and \(P_{2}(\theta_{i},\gamma_{i})\) is the PDF of CGA pair \((\theta_{i},\gamma_{i})\) in binding form 2. The similarity index \(H\) varies between 0 (dissimilar) and 1 (identical). We consider similarity between 2 FESs to be (i) large if \(H>0.70\), (ii) moderate if \(0.30\leq H<0.70\), and (iii) low if \(H<0.3\), as per a previous work [28].  
Similarly, effective 1D free-energy profiles (FEPs) \(V(\chi_{i}^{k})\) were computed for each SCA \(\chi_{i}^{k}\) (\(k=1,...,5\)) by using  
\[V(\chi_{i}^{k})=-k_{B}T\log P(\chi_{i}^{k}) \tag{3}\]  
where \(P(\chi_{i}^{k})\) is the PDF of the dihedral angle \(\chi_{i}^{k}\). One-dimensional PDFs were computed on a circle from time series extracted from MD (Figure 2B) using concatenated MD trajectories, as performed for 2D PDFs (see above). An example of free-energy profile for side-chain dihedral angle \(\chi_{84}^{1}\) (Lys) is shown in Figure 2D. Moreover, modifications between two FEPs of identical side-chain dihedral angle \(\chi_{i}^{k}\) due to different ligand-binding forms of GST were quantified using the similarity index \(H\) between their associated 1D PDFs [28]:  
\[H_{1|2}(\chi_{i}^{k})=\frac{2\int_{-\pi}^{+\pi}P_{1}(\chi_{i}^{k})P_{2}(\chi_ {i}^{k})d\chi_{i}^{k}}{\int_{-\pi}^{+\pi}P_{1}(\chi_{i}^{k})^{2}d\chi_{i}^{k} +\int_{-\pi}^{+\pi}P_{2}(\chi_{i}^{k})^{2}d\chi_{i}^{k}} \tag{4}\]  
where \(P_{1}(\chi_{i}^{k})\) is the PDF of SCA \((\theta_{i},\gamma_{i})\) in binding form 1, and \(P_{2}(\chi_{i}^{k})\) is the PDF of SCA \((\chi_{i}^{k})\) in binding form 2. The same scale of similarity, as described above for FESs, is used to quantify similarities (large, moderate, and low).