TABLE 2.

Hopping rates estimated from the simulations

	kr − kl (#/ns)	kr + kl (#/ns)	kl (#/ns)	kr (#/ns)	kr/kl
sim1	−3.9 ± 0.3	5.7 ± 1.4	4.8 ± 0.7	0.9 ± 0.7	0.19	0.27
sim2	−1.9 ± 0.6	5.1 ± 1.4	3.5 ± 0.8	1.6 ± 0.8	0.46	0.52
sim3	2.0 ± 0.3	4.0 ± 0.4	1.0 ± 0.3	3.0 ± 0.3	3.1	1.9
sim4	2.3 ± 0.3	4.6 ± 0.4	1.1 ± 0.2	3.5 ± 0.2	3.1	3.7

For each channel, the trajectory of the collective coordinate X for water molecules in the defined region (length L = 15 Å) was obtained as described in the text. k_r − k_l was calculated from the total displacement of X in 4 ns, according to Eq. 19. To calculate k_r + k_l, the 4-ns trajectory of X was divided into 20 subtrajectories, each of 200 ps duration. For each t, the variance of the displacements in the 20 subtrajectories during time t was computed, and k_r + k_l was calculated from the slope of the variance-t curve, according to Eq. 20. k_r, k_l, and k_r/k_l were obtained from k_r − k_l and k_r + k_l. The last column (^* of the table is the predicted value of k_r/k_l, calculated from exp(−Δμ/k_BT) (Eq. 6), using T = 310 K and Δμ taken from Table 1.