sentence: More detailed calculations of the kinetic rate constants , including calculating the diffusion coefficient for the proton and its mean first passage time , are included in the SI.The pK of E148 was estimated using the equation for calculating the equilibrium constant of binding of the substrate at the binding site of the protein , based on the one-dimensional PMF for the substrate moving along the channel axis with the cylindrical potential applied at the channel entrance : 3where the substrate is the excess proton and the binding site is E148 .