To estimate the overall redox potential of the cysteine residues of the putative Zn(II) binding domain of P2X4R (C126, C132, C149 and C159), two models were constructed. One was a fully oxidized model, the state observed in the experimental structure [21], where the C126-C149 and C132-C159 pairs form disulfide bridges. The other was a fully reduced model, where the aforementioned cysteines are in their thiol form. The C116 and C165 residues, which are away from the putative Zn(II) site, were left in their experimental forms, forming a disulfide bridge, in both models.

The obtained oxidized and reduced models were fully optimized with the semiempirical GFN2-xTB method [31], employing the ALPB continuum solvent model for water, as implemented in the xtb program [32,33]. Frequencies were obtained at the same level of theory for the full models, and free energies were estimated from the electronic, solvation and vibrational contributions. Thus, the Gibbs free energy for the half reaction of the putative zinc site reduction was obtained.

While the GFN2-xTB method is not parameterized for electronic energies, and does not produce accurate bond-breaking energies, the errors of the GFN methods are known to be, to a large extent, systematic [31,34]. To mitigate the systematic part of these errors, the other half reaction was chosen as the oxidation of glutathione, where a disulfide bridge is also formed. Thus, the full reaction consists of of the oxidation of four glutathione molecules to reduce the four cysteine residues of the putative Zn(II) site. The free energy for the glutathione oxidation half reaction was estimated with the same methodology described. The oxidized and reduced glutathione molecules were optimized and had their frequencies calculated with GFN2-xTB and the ALPB solvent model for water.

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