Mathematical Modeling of Neurons and Endocrine Cells

National Institute Of Diabetes And Digestive And Kidney Diseases

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Abstract

Purinergic Receptors We have previously described (see 2010 and 2012 reports and review in Ref. # 1) a kinetic model, developed in collaboration with the Stojilkovic experimental lab (NICHD), of the P2X7 receptor. This receptor is a ligand-gated ion channel activated by extracellular ATP and is expressed ubiquitously, including in pituitary cells and macrophages. At low concentrations of ATP, this ligand-gated calcium channel acts much like other members of the P2X family, but prolonged or repeated exposure to high ATP concentrations causes it to dilate and gate a massive influx of calcium. This unusual and complex behavior had led to proposals that the normal and super-normal currents are due to two different channels, but the model, a Markov state model with 8 states, showed that a single channel could play both roles. P2X7 can act both as a conventional calcium channel and as a signaling molecule promoting cell growth and differentiation, when calcium influx is low, and promoting programmed cell death, when calcium influx is high. This could be an important part of how the immune system maintains a balance between activating in response to pathogen vs.over-reacting to inflammation. A polymorphism in the P2X7 receptor has been proposed as a susceptibility gene for the NOD mouse, a model for type 1 diabetes. The current through the P2X2 receptor, in contrast, rapidly shuts off in the face of maintained ATP but the model and experiments showed that the receptor nonetheless dilates, because it gains the ability to conduct large organic cations after stimulation with ATP. The model showed that the dilation was masked by desensitization (Ref. # 1 in the 2012 report). In the 2014 report we discussed opposite behavior in P2X7: desensitization is masked by dilation. The models of the two receptors are structurally very similar but differ quantitatively in the transition rates. The similarity between the two models lends support to our overall hypothesis that P2X receptors have a common core of features but differ quantitatively to achieve different end behaviors. We have tested this hypothesis further by extending the model to P2X4 (Ref. # 2). We found that the same model we used for P2X7 and P2X2 can be applied, with only quantitative modifications to P2X4 as well. In particular, we have shown that P2X4, which natively only shows strong desensitization, like P2X2, can also show dilation when in the presence of the drug ivermectin. P2X4 is involved in pain pathways, and this enhanced knowledge of how the channel is regulated may help in the design of drugs that can relieve pain by strengthening desensitization or inhibiting dilation.