Table 1.

Calculated pK_a’s for model Asp, Glu and His

Model	Ref	Hybrid	GRF	PME
Asp	4.0	3.8±0.02	3.5±0.17	4.0±0.09
Glu	4.4	4.1±0.01	4.1±0.13	4.5±0.09
His	6.5	6.9±0.01	6.8±0.10	6.5±0.02
His-Nδ	6.6	–	–	6.7±0.03
His-Nε	7.0	–	–	6.9±0.03
Lys	10.4	10.4±0.02	10.4±0.12	10.4±0.04

Average pK_a’s and standard deviations based on five independent sets of pH-replica CpHMD simulations. Reference pK_a’s refer to the experimentally measured pK_a’s of blocked single amino acids.⁵¹ The microscopic pK_a’s of His-N^δ and His-N^ε are taken from Ref.⁵² All these values are identical to the previous CpHMD work.^6–8,25 The hybrid-solvent simulation used 5 replicas, each of which was sampled for 10 ns with λ-update every 10 MD steps. The GRF-based simulation used 10 pH replicas, each of which was sampled for 10 ns.²⁵ The PME-based simulation used 5 pH replicas, each of which was sampled for 5 ns. The PMF functions with parameters slightly adjusted to minimize the deviations from the reference pK_a’s were used (see Table S5).