Extended "Constant Field" equations: an electrodiffusion model of NMDA receptors

Ion channels are experimentally divided into Ohmic and non-Ohmic channels. Similarly, a theoretical dichotomy exists in the flux equations of these channels. The "constant field" or "Goldman-Hodgkin and Katz" current equation is a commonly accepted analytic model of electrodiffusion in channels. This equation, however, seems to have some shortcomings, such as the inability to explain the nonlinear relation between the single channel current and the membrane potential in non-Ohmic channels. In this study, we introduce the "general" and "extended" versions of this equation that are applicable to both Ohmic and non-Ohmic channels. Our results showed the ability of these equations to simulate the NMDA receptor current, as a non-Ohmic channel, not only in the symmetric "uni-ionic" solutions but also in the asymmetric "bi-ionic" solutions of sodium and calcium ions. Our equations reveal for the first time that sodium ions like calcium ions are able to block the NMDA receptors current. It seems that the previously identified cation binding-sites have a prominent role in changing the diffusion coefficient inside the channel. We also propose the concentration-dependent change in the asymmetry of diffusion coefficient as a remarkably effective mechanism for shaping the channel's I-V curve.