Ab initio molecular orbital study of the interaction of Li, Na and K with the pore components of ion channels: Consideration of the size, structure and selectivity of the pore of the channels

Ab initio molecular orbital calculations were made for the various types of structures of the pore of the ion channel and the results were applied to the permeability model by Hille, an extension of the Eyring rate theory. In Hille's model, ion passage through the channel is regarded as a kinetic process. Accordingly, it is thought that the interaction energy between cation and ligand, the easier the passage is, due to the lower activation energy. The calculated interaction energy was in the order Li+ greater than Na+ greater than K+ for all models. The optimum size of the pore determined from the interaction energy depends on the structure of the filter. The size for the pentagon was largest, followed by the hexagon and tetragon. On the other hand, the size depends hardly at all on the kind of ligand molecules. In the case of the tetragon, the sizes for the Na and K channels were nearly the same as those estimated from the model building and inhibitor-blocking experiment. The interaction energy between the ionized carboxyl group and the cation was extremely large, clearly reflecting the experimental fact that the carboxyl group in the pore has an important role in making the passage of the cation through the channel easier by dehydrating the water molecules. By analysis of the interaction energy, it was revealed that the contribution of the electrostatic energy was predominant, although the contributions of the other effects might not be negligible. Among these effects, the value of the charge transfer energy is largest, and this is noteworthy in connection with the selective transmission of cations through the overlap of orbitals. It is concluded that the quantum-chemical indices such as interaction energy and the electronic charge calculated by the sophisticated ab initio method help to shed light on the nature of the pore of the ion channel.