. Author manuscript; available in PMC: 2015 May 23.

Published in final edited form as: Biochemistry. 2015 Feb 6;54(6):1307–1313. doi: 10.1021/bi5012833

Table 2.

Comparison of experimental and simulated microscopic pK_as using the microscopic model illustrated in Scheme 2 for apo and cCMP-bound RNase A.

	$p K_{a, B}^{A H^{+}}$	$p K_{a, B}^{A}$	ΔpK_a,B	$p K_{a, A}^{B H}$	$p K_{a, A}^{B^{-}}$	ΔpK_a,A
*Apo-RNase A with His12(B* )/His119(A)

Expt.^a	5.87	6.18	0.31	6.03	6.34	−0.31
Microscopic model	5.88 (0.14)	6.05 (0.15)	0.17	6.13 (0.05)	6.30 (0.10)	−0.17

*Apo-RNase A with Lys41(B* )/His119(A)

Microscopic model	8.29 (0.14)	9.26 (0.07)	0.97	6.23 (0.07)	7.21 (0.21)	−0.97

*cCMP-RNase A with His119(B* )/His12(A)

Expt. (3′-UMP)^a	7.95	7.85	−0.1	6.45	6.35	0.1
Microscopic model	7.20 (0.12)	6.99 (0.20)	−0.21	8.12 (0.17)	7.92 (0.16)	0.21

*cCMP-RNase A with His119(B* )/Lys41(A)

Microscopic model	7.17 (0.12)	7.41 (0.40)	0.24	9.40 (0.18)	9.64 (0.16)	−0.24

The calculated microscopic pK_a values are derived from the thermodynamic cycle illustrated in Scheme 2, which contains three free parameters that were fit to the acid/base fractions f_(AH⁺/B^-), f_(AH⁺/BH), f_(A/BH), and f_(A/B^-). The pK_a shifts are defines as $Δ p K_{a, A} = p K_{a, A}^{B H} - p K_{a, A}^{B^{-}}$ , and $Δ p K_{a, B} = p K_{a, B}^{A} = p K_{a, B}^{A H^{+}}$ . Note the constraint of the thermodynamic cycle in Scheme 2 ensures ΔpK_a,A+ΔpK_a,B=0, and a positive value for ΔpK_a,B indicates anticooperative coupling of protonation states (i.e., protonation of the acid site disfavors protonation of the base), whereas a negative value of ΔpK_a,B indicates cooperative coupling (i.e., protonation of the acid site favors protonation of the base). Statistical error estimates, shown in parentheses, were obtained as standard deviations derived from values computed from data in 5 ns intervals over the 60 ns of production. Results were compared with the experimental (Expt.) values obtained from NMR

Taken from Ref. 36 in order to validate the model. In order to explore the degree to which this weak coupling persists with other plausible general base and acid pairs, the general base was replaced by Lys41 for each case and the resulting microscopic pK_a values were determined.