12914
Biochemistry 2005, 44, 12914
Corrections
Agonists and Partial Agonists of Rhodopsin: Retinals with Ring Modifications, by Reiner Vogel,* Friedrich Siebert, Steffen Lu¨deke, Amiram Hirshfeld, and Mordechai Sheves*, Volume 44, Number 35, September 6, 2005, pages 11684-11699. There is an error in the calculation of the enthalpy change ∆H and the entropy change ∆S of the Meta I-Meta II equilibrium in the Supporting Information due to incorrect use of the Henderson-Hasselbalch equation. Correctly, the equation is
This can be simplified to
∆S ) R × 2.303
T∆S at 20 °C pKa pKa ∆H ∆S (J at 20 °C at 0 °C ∆pKa (kJ/mol) mol-1 K-1) (kJ/mol)
(4)
Inserting this expression into eq 3 of the Supporting Information yields the following expression for ∆H (with ln 10 ≈ 2.303)
pK2 - pK1 ) ∆H ) -R × 2.303 1 1 T2 T1 T1T2 (5) R × 2.303(pK1 - pK2) T 1 - T2 which is not affected by the error. Evaluating eq 2 at T2 and insertion of eqs 4 and 5 yield the following expression for the change of entropy of the transition
∆H ) T
[
T1T2
R × 2.303 pK2 + (pK1 - pK2) (T1 - T2)T2
(6)
which is independent of pH. The values for ∆S stated in Table 1 in the paper are therefore shifted uniformly and by 134 J mol-1 K-1 too low. The corrected version of Table 1 is given.
which yields Keq ) 10pK, and therefore
∆S ) R ln Keq +
)
pK1T1 - pK2T2 T1 - T2
Table 1: Enthalpy and Entropy Changes in the Meta I-Meta II Equilibria of Selected Pigmentsa
[MII] [MII] pK ) pH + log10 ) log10 Keq ) log10 [MI] [MI][H+]
ln Keq ) (ln 10)pK
(
]
native acyclic-1 acyclic-2 16,17-demethyl 16,17,18-demethyl opsinb
7.7 4.8 5.0 5.8 5.2 -
6.6 4.0 4.1 4.8 4.5 -
1.1 0.8 0.9 1.0 0.7 -
84 61 69 77 54 48
434 301 331 372 282 236
127 88 97 109 83 69
a
∆pKa is the difference between the pKa values measured at 0 and 20 °C. The estimated error margins for ∆H and ∆S are 15 kJ/mol and 54 J mol-1 K-1, respectively. b Opsin conformational equilibrium; see the text for details.
The experimental values for the thermodynamic parameters of the Meta I-Meta II equilibrium of the native pigment at 20 °C are 84 kJ/mol for ∆H, 127 kJ mol-1 for T∆S, and thus -43 kJ/mol for ∆G. The absolute shift of the ∆S values by 134 J mol-1 K-1 affects the synthetic pigments in the same way as the native pigment. Our conclusions regarding the single pigments are based on changes in ∆S and are therefore not affected by the error. BI058026W 10.1021/bi058026w Published on Web 09/02/2005
