Analyzing free energy relationships for proton translocations in enzymes: Carbonic anhydrase revisited

The nature of proton transfer (PT) in proteins is explored by considering the catalytic cycle of carbonic anhydrase III. Special attention is paid to the free energy relationship established by Silverman and co-workers (Silverman, D. N.; Tu, C.; Chen, X.; Tanhauser, S. M.; Kresge, A. J.; Laipis, P. J. Biochemistry 1993, 34, 10757-10762). The free energy surfaces for the PT process is analyzed in the framework of the modified Marcus theory of Warshel and co-workers (Warshel, A.; Hwang, J. K.; Angstromqvist, J. Faraday Discuss. 1992, 93, 22), using realistic values of the relevant reorganization energy and the off-diagonal mixing term. It is found that the free energy relationship reflects a much more complex situation than that deduced from an empirical fit to the standard two-state Marcus formula. Apparently, the PT process involves three or more parabolic free energy surfaces rather than the two assumed in the Marcus treatment. Furthermore, PT processes involve large off-diagonal mixing terms that lead to apparent reorganization energies which are much smaller than the actual reorganization energies. Because our analysis reproduced the experimental trend using nonadjustable molecular parameters (derived by actual molecular simulations), we believe that this analysis is much more consistent than alternative phenomenological fitting approaches. The present approach provides a general framework for studies of proton translocations in proteins and justifies the approach used in our recent study of proton transport in bacterial reaction centers and aquaporin.