A model for open-close control of cation channels in the plasma membrane of retinal rod outer segments

A model for open-close control of cation channels in the plasma membrane of retinal rod outer segments is presented. A channel is assumed to open when 3 cGMP molecules bind to it and close as soon as one of the 3 cGMP molecules is released from it. The calcium ion (divalent cation) is a modulator of the channel conductance. The channel conductance is low when Ca2+ binds to it, while it is high when it is free from Ca2+. From the above assumptions, the reaction scheme of channels with cGMP and Ca2+ is created and the fraction of channels in the open and closed states was calculated using equations for this scheme. The kinetic constants used in the model are estimated from the experimental results of many studies and from the theories. From this estimation, it was found that at the physiological concentrations of intracellular and extracellular Ca2+, almost all channels are bound with Ca2+ and are in the low conductance state. The present model accounts for the reported dose(cGMP)-response(membrane current or conductance) relationship, where the Hill coefficient decreases as the cGMP concentration increases. The dark-level cGMP concentration of 8.13 microM is estimated from the model. This is in good agreement with the reported values. Moreover, the model predicts the invariance of current noise at relatively low Ca2+ concentrations when the cGMP concentration is raised from the dark level to a saturation level. The dynamic properties (opening and closing actions) of the channels in the present model are also in good agreement with the reported observations. The burst mode opening and closing of a channel is predicted by the present model, and it was found that the number of openings in a burst is controlled by the forward and backward rate constants between a channel protein and cGMP molecules. The simulated waveform of a single channel is similar to the reported observations.