A physical model of potential energy profiles of ions going through a biological membrane channel

To attempt to explain what determines a single particle (an ion or an ion group) penetration of a cell membrane channel, a physical model of potential energy profiles V₂(x) of a channel is proposed, based on the authors´ previous study of one dimensional (1-D) steady state Schrodinger equation in a single particle system and in a time independent field. In this model, a V₂(x) is simplified as an effective constant height of potential energy barrier V₂ in a channel to obtain analytical solutions in mathematics. This model elucidates that: (1) Ion selectivity of a channel is determined by V₂. V₂ is divided into a V_2c for a cation and V_2a for an anion. V_2c and V_2a may be or may be not the same value depending on electrical characteristics of the particles and the channel. It is called a cation channel if a V_2c is much lower than a V_2a and vice versa. It is called a cation-anion cotransporter if a V_2e and a V_2a are equal or almost equal. (2) Whether a particle can penetrate through a channel is mostly determined by the repulsion energies (barriers) rather than the attraction energies (wells). (3) A channel´s conformation can be changed when the channel is stimulated strongly enough. The variation of the conformation could influence V₂(x) and V₂, and eventually result in open or close of the channel