Mathematical Modeling of Neurons and Endocrine Cells

嘌呤能受体 我们之前已经描述过(参见2010和2012年的报告和参考文献中的回顾。#2)与斯托伊尔科维奇实验实验室(NICHD)合作开发的P2X7受体的动力学模型。该受体是一种由细胞外ATP激活的配体门控离子通道，广泛表达于脑垂体细胞和巨噬细胞。在低浓度的ATP下，这种配体门控的钙通道的作用与P2X家族的其他成员很相似，但长时间或反复暴露于高浓度的ATP会导致它扩张，并阻止大量的钙内流。这种不寻常和复杂的行为导致了人们的假设，即正常和超常电流是由两个不同的通道引起的，但这个模型--一个有8个状态的马尔可夫状态模型--表明，一个通道可以同时扮演这两个角色。 当钙离子浓度较小时，P2X7既可以作为一种传统的钙离子通道，也可以作为细胞生长和分化模式与钙离子大量内流时细胞程序性死亡模式之间的转换。这可能是免疫系统如何在对炎症做出适当反应和过度反应之间保持平衡的重要部分。P2X7受体的多态性被认为是1型糖尿病模型NOD小鼠的易感基因。 相比之下，在维持ATP的情况下，通过P2X2受体的电流会迅速关闭，但模型和实验表明，该受体仍然会扩张，因为它在受到ATP刺激后获得了引导大型有机阳离子的能力。该模型显示扩张被脱敏作用所掩盖(参考文献1)。#1,2012年报告)。在参考文献中。#1，我们回到了P2X7受体并增加了脱敏，这是一个已知存在但在第一次迭代中被忽略的特征，以保持对扩张和记忆的关键特征的关注。这两种受体的模型在结构上非常相似，但在转移率上有所不同。更新的P2X7模型现在同时表现出扩张和脱敏，但与P2X2相比，扩张占主导地位。这两个模型之间的相似性支持了我们的总体假设，即P2X受体具有共同的核心功能，但在数量上不同，以实现不同的末端行为。 通过将模型扩展到P2X4(参考文献)，我们进一步检验了这一假设。#3)。我们发现，我们对P2X7和P2X2使用的相同模型也可以应用，只是对P2X4也进行了量化修改。特别是，我们已经证明，像P2X2一样，天生只表现出强烈脱敏作用的P2X4，在药物伊维菌素存在的情况下也可以表现出扩张。P2X4参与疼痛通路，这种对通道如何调节的增强知识可能有助于设计通过加强脱敏或抑制扩张来缓解疼痛的药物。

Purinergic Receptors We have previously described (see 2010 and 2012 reports and review in Ref. # 2) 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 switch between a mode of cell growth and differentiation, when calcium is small, and a mode of programmed cell death, when calcium influx is large. This could be an important part of how the immune system maintains a balance between responding appropriately and 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, 2012 report). In Ref. # 1, we returned to the P2X7 receptor and added desensitization, a feature that was known to be present but was neglected in the first iteration in order to keep the focus on the key features of dilation and memory. The models of the two receptors are structurally very similar but differ quantitatively in the transition rates. The updated P2X7 model now exhibits both dilation and desensitization, but, in contrast to P2X2, dilation dominates. 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. # 3). 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.