As shown in Ref., well balanced acceptance ratio, while avoiding bottlenecks in the replica diffusion, do not guarantee an ideal flux in the HREM simulation of conformationally complex systems. In Figure of the Supporting Information (SI), we report the flux as a function of the nodes for the HREM simulations sampled during the 16 ns HREM simulations with (green) and without (dark green) the balancing of the scaling factors according to Eq. 4. As the figure shows, the equalization of the acceptance ratio using Eq. 4 produced only a modest improvement on the flux. The mean absolute deviation with respect to the ideal flux is 0.06 and 0.09 for the balanced and unbalanced HREM simulation, evidencing the fact that well behaving short-time properties such as P acc equalization do not necessarily imply an ideal or near-to-ideal flux across the replica progression. In Figure of the SI, we show the results for variance S (see Eq. 6) obtained in the two HREM simulations. The variance S(k) are similar with no significant gains when using the adaptive scheme based on P acc equalization, hence confirming the moderate impact of P acc on-the-fly balancing on replica flow.