Fig. 4.

Comparison of the energy required to share a proton between residues $\left(\mathrm{\Delta }{E}_{\nu =0}\right)$ as a function of the hydrogen-bond donor–acceptor O–O distance $\left(R_{OO}\right)$ compared with the ZPE. (A) $\mathrm{\Delta }{E}_{\nu =0}$ as a function of the O–O distance $\left(R_{OO}\right)$ between O16 and O57 using the tyrosine triad geometry from a crystal structure (details in SI Materials and Methods, section D). A, Inset shows the probability distribution of $R_{OO}$ obtained from the AI-PIMD simulation of ${\mathrm{K}\mathrm{S}\mathrm{I}}^{D40N}$ with ionized Tyr57. The probability is normalized by the maximum value. (B) Potential energy as a function of the proton transfer coordinate ν for $R_{OO}$ = 2.6 Å, indicating values for H and D (O–H and O–D) ZPEs ($ZP{E}_H$ and $ZP{E}_D$, respectively). The position of Tyr32 is fixed as the proton H16 is scanned along $R_{OO}$.