Mathematical Modeling of Neurons and Endocrine Cells

National Institute Of Diabetes And Digestive And Kidney Diseases

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Abstract

We have studied the complex kinetics of the P2X7 receptor, a ligand-gated ion channel activated by extracellular ATP. This receptor is found in pituitary cells and also in macrophages. Brief single stimulations at low agonist concentrations activate small currents and are associated with cell growth and proliferation, whereas repeated stimuli or high agonist concentrations activate much larger currents and lead to cell blebbing and death. Two hypotheses have been put forward to account for the large currents. One is that the pore of P2X7R dilates and the other is that it interacts with another membrane protein that has a large pore. Together with the Stojilkovic lab (NICHD) we developed a mathematical model of the receptor kinetics based on the former hypothesis, dilation of a single pore. The model assumes that there are three ATP binding sites, consistent with the recently obtained structure for the related P2X4 receptor, which has three subunits and three likely binding sites. The structure is assumed to be symmetrical when no ATP is bound and all three sites have high affinity. If one ATP binds, a conformational change is assumed to reduce the affinity of the remaining sites, and more so if a second ATP binds. However, once three ATP molecules are bound, the receptor is postulated to make a slow transition to a large conductance, dilated state that is considered to be "sensitized". The slow transition corresponds to the slow increase of current seen at intermediate ATP concentrations. The sensitized state can return to the unsensitized state only very slowly, so repeated stimulations lead to accumulation of sensitized receptors. When ATP is removed, sensitized receptors go to a closed but still sensitized state. Reapplication of ATP results in rapid opening back to the sensitized state. This accounts for the experimental observation that there is no slow component of current once a receptor has been sensitized by prior exposure to ATP. The model has eight states and is able to account for most of the experimental observations. The number of parameters has been reduced by assuming that the receptor with three ATP's bound returns to a symmetric conformation that has the same rates as the unexposed receptor. A paper is in press.