Where ∆𝐺 𝑖𝑗 𝑝 refers to electrostatic interactions between the i th amino acid in the ionized form and all other j th amino acid when they are assigned to be charged, as determined by the titration PDLD calculation. This correction is necessary because the intrinsic pKa deviates from the actual pKa by how the solvation of the i th amino acid is influenced by the presence of all other ionized residues in the protein at a given pH. The total energetics of the m th combination of protonation state can be expressed by Eqn. (7): (7) Where ∆𝐺 𝑚 denotes the free energy change of the protein transitioning from a hypothetical reference state, where all amino acids are neutral, to the m th ionization state.