Table 1.

Expectation values for 〈ε_tot〉 and the ratios and obtained from packing density and pathway analyses^*

		Wild type	M51L	M51K	M51A	M51C
	(Experiment)	1.0	0.68	0.49	0.13	—
〈εtot〉 × 103	(Pathway analysis)	0.90 ± 0.03	0.47 ± 0.03	0.61 ± 0.02	0.65 ± 0.02	0.73 ± 0.02
	(Pathway analysis)	1.0	0.36 ± 0.04	0.52 ± 0.04	0.57 ± 0.04	0.76 ± 0.05
εtot × 103	(Packing density)	0.70 ± 0.03	0.42 ± 0.04	0.51 ± 0.03	0.62 ± 0.05	1.03 ± 0.05
	(Packing density)	1.0	0.56 ± 0.09	0.76 ± 0.07	0.89 ± 0.15	2.29 ± 0.26
Phb		0.53	0.15	0.19	0.18	0.16
τ (ns-1)		0.40	0.57	0.60	0.65	0.68

^*The uncertainties account for the sampling errors of the computational protocol (see SI Text). Experimental rates k_ET were obtained from k₃ (at 30 °C) in table 3 of ref. 15 (M51C was not reported). P_hb is the unit-normalized likelihood that a water molecule is simultaneously hydrogen bonded to both the MADH Ser β 56 O and amicyanin His 95 HE2 atoms during our simulations. The turnover τ of the bridging water molecule is defined as the number of different water molecules that participate in pathway A₁ divided by the length of the simulation in nanoseconds.