Mathematical Modeling of Neurons and Endocrine Cells

神经元和内分泌细胞的数学模型

基本信息

批准号：
8553369
负责人：
Arthur Sherman
金额：
$ 12.42万
依托单位：
NATIONAL INSTITUTE OF DIABETES AND DIGESTIVE AND KIDNEY DISEASES
依托单位国家：
美国
项目类别：
财政年份：
资助国家：
美国
起止时间：
至
项目状态：
未结题

来源：
https://reporter.nih.gov/project-details/8553369
关键词：
Accounting Action Potentials Address Area Automobile Driving Behavior Beta Cell Biological Sciences Biophysics Calcium Calcium Channel Calcium-Activated Potassium Channel Cations Cell Death Cell Differentiation process Cell secretion Cells Chemicals Classification Classification Scheme Collaborations Communities Complex Coupled Development Educational workshop Endocrine Endoplasmic Reticulum Equation Equilibrium Exhibits Exocytosis Exposure to Family France Future Gated Ion Channel Genetic Polymorphism Hodgkin Disease Hormones Hypothalamic structure Immune System Part Inbred NOD Mice Inflammation Insulin Insulin-Dependent Diabetes Mellitus Ion Channel Ion Pumps Kinetics Lead Ligands Mathematics Mediating Mediator of activation protein Membrane Memory Modeling National Institute of Child Health and Human Development Nerve Neuroendocrinology Neurons Nobel Prize Organelles P2X-receptor Pattern Pituitary Gland Play Purinoceptor Reporting Role Scheme Second Messenger Systems Signaling Protein Societies Specificity Structure of beta Cell of islet Susceptibility Gene System Time Universities Work abstracting base cell growth cell type desensitization extracellular falls indexing interest lactotroph macrophage markov model mathematical model meetings member neglect programs receptor salivary acinar cell second messenger tool

Accounting Action Potentials Address Area Automobile Driving Behavior Beta Cell Biological Sciences Biophysics Calcium Calcium Channel Calcium-Activated Potassium Channel Cations Cell Death Cell Differentiation process Cell secretion Cells Chemicals Classification Classification Scheme Collaborations Communities Complex Coupled Development Educational workshop Endocrine Endoplasmic Reticulum Equation Equilibrium Exhibits Exocytosis Exposure to Family France Future Gated Ion Channel Genetic Polymorphism Hodgkin Disease Hormones Hypothalamic structure Immune System Part Inbred NOD Mice Inflammation Insulin Insulin-Dependent Diabetes Mellitus Ion Channel Ion Pumps Kinetics Lead Ligands Mathematics Mediating Mediator of activation protein Membrane Memory Modeling National Institute of Child Health and Human Development Nerve Neuroendocrinology Neurons Nobel Prize Organelles P2X-receptor Pattern Pituitary Gland Play Purinoceptor Reporting Role Scheme Second Messenger Systems Signaling Protein Societies Specificity Structure of beta Cell of islet Susceptibility Gene System Time Universities Work abstracting base cell growth cell type desensitization extracellular falls indexing interest lactotroph macrophage markov model mathematical model meetings member neglect programs receptor salivary acinar cell second messenger tool

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项目摘要

Purinergic Receptors We have previously described (see 2010 report) 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. In neurons, P2X7 may act mostly as a conventional calcium channel, but in macrophages, the small current mode may promote cell growth and differentiation whereas the large current mode may lead to cell death. 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. We have now extended the model to describe the rather different behavior of the P2X2 receptor (Ref. # 1). The current through this receptor rapidly shuts off in the face of maintained ATP but is nonetheless thought to dilate, because it gains the ability to conduct large organic cations after stimulation with ATP. The model showed how desensitization could occur simultaneously with dilation. With the help of the model, we were able to identify not one but two distinct mechanisms of desensitization, one calcium-dependent and one calcium-independent. Each of these adds 4 states to the Markov model for a total of 16. The model showed that the calcium-dependent desensitization must be mediated by an effector molecule that exhibits hysteresis in order to account for the observed kinetics. Although a kinetic model cannot by itself identify molecules, the predicted kinetics should help guide the search. The P2X2R model includes the P2X7R as a sub-model, albeit with modified rate constants. The similarity will be heightened by adding calcium-independent desensitization to the P2X7R model, a feature which 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. These connections should help elucidate the evolutionary and developmental unity of the P2X family. In the coming period, we plan to push this approach further by modeling other members of the P2X family. Classification of Bursting Oscillations Bursting oscillations, which are widely found in neurons and endocrine cells, consist of silent and active (spiking) periods alternating on a time scale typically of seconds to tens of seconds. These are often mediated by the rise and fall of intracellular calcium, which modulates the spiking activity through calcium-activated potassium channels, but many other channel mechanisms are possible. Mathematically, we abstract from the channels involved to focus on the transitions, known as bifurcations, between spiking and silence. In addition to modeling the bursting electrical oscillations in particular cell types, we have had a long-standing interest in classifying the various burst mechanisms based on the types of these transitions. This makes it possible to establish the simplest models that can account for each of the known patterns, where simplicity is indexed by the minimum number of parameters required to define the set of transitions. In general, cells use redundant parametrizations because they have to explore parameter space through the mechanisms at their disposal, such as ion channels and pumps, but the minimal mathematical description is still important for our understanding. We can now report major progress, in collaboration with Krasimira Tsaneva-Atanosova of the University of Bristol and Hinke Osinga of the University of Auckland, that largely completes the program of analysis of bursting begun in this lab by former chief John Rinzel 25 years ago. See Ref. # 2. This work was also presented as an invited plenary talk at the 2012 Life Sciences meeting of the Society for Industrial and Applied Mathematics. One application of the classification scheme is to understand the connections between the bursting patterns exhibited by different cells types. A key motivating example was the comparison between pituitary somatotrophs and lactotrophs vs. pancreatic beta cells. Both classes of cells exhibit bursts of action potentials from a depolarized plateau, which is potent at driving calcium entry into the cells for secretion of their respective hormones. We had shown in previous work that in the pituitary models the spikes were transients due to slow attraction to the upper steady state that defines the plateau, whereas in the beta cells the spikes are sustained oscillations that would persist if calcium were fixed rather than slowly varying. The two types of cells are developmental and evolutionary cousins, so it was expected that the distinct burst mechanisms would be related. However, whereas it has been known for a while that the beta-cell type burst pattern can be generated with only three parameters, we found that the pituitary pattern requires four parameters, further underscoring the fundamental differences between the two. Nonetheless, both types appear within the extended four-parameter scheme as neighbors and each can be converted into the other varying only one of the parameters. We and others had found previously that each of several biophysically identifiable parameter, including the threshold for activation of the calcium channels, can mediate such a conversion. The abstract mathematics is thus gratifyingly confirmatory of the biophysics, but this raises other questions. If activity patterns lie nearby in parameter space, how are cells able to maintain their identities and not drift from one to another? We believe this is a deep question and we hope to be able to address it in the future. In addition to the specific projects described here, we were involved in organizing a highly successful workshop on modeling in neuroendocrinology, in Tours, France. This was the third semi-annual meeting on this topic involving both theorists and experimentalists, and the nascent interdisciplinary community that has grown out of the meetings now appears to be well-established and self-sustaining.

嘌呤能受体我们先前已经描述了P2X7受体的Stojilkovic实验实验室（NICHD）合作开发的动力学模型。该受体是由细胞外ATP激活的配体门控离子通道，并在垂体细胞和巨噬细胞中被普遍表达。在低浓度的ATP下，该配体门控钙通道的作用与P2X家族的其他成员一样，但延长或反复暴露于高ATP浓度，导致其扩张并大量大量钙涌入。这种不寻常且复杂的行为导致提出正常和超正常电流是由于两个不同的通道引起的，但是该模型是具有8个状态的马尔可夫州模型，表明一个通道可以扮演两个角色。在神经元中，P2X7可能主要充当常规的钙通道，但是在巨噬细胞中，小电流模式可能促进细胞的生长和分化，而大型电流模式可能导致细胞死亡。这可能是免疫系统如何在适当反应和反应过度反应之间保持平衡的重要组成部分。已经提出了P2X7受体中的多态性作为NOD小鼠的易感基因，该基因是1型糖尿病的模型。现在，我们扩展了该模型，以描述P2X2受体的相当不同的行为（参考文献＃1）。面对维持的ATP时，通过该受体的电流迅速关闭，但仍被认为是扩张的，因为它具有在用ATP刺激后进行大型有机阳离子的能力。该模型显示了如何与扩张同时发生脱敏。借助模型，我们能够识别一种脱敏的两种不同的机制，一种依赖性钙依赖性和一种独立于钙的脱敏机制。这些中的每一个都在马尔可夫模型中增加了4个状态，总共16个状态。该模型表明，依赖钙的脱敏必须由表现出滞后的效应分子介导，以说明观察到的动力学。尽管动力学模型本身无法识别分子，但预测的动力学应有助于指导搜索。 P2X2R模型包括P2X7R作为子模型，尽管具有修改的速率常数。相似性将通过在P2X7R模型中添加无钙脱敏的脱敏来提高相似性，该功能已知存在，但在第一次迭代中被忽略了，以便将重点放在扩张和记忆的关键特征上。这些联系应有助于阐明P2X家族的进化和发展统一。在接下来的时期，我们计划通过对P2X家族的其他成员进行建模来进一步推动这种方法。爆发振荡的分类在神经元和内分泌细胞中广泛发现的爆发振荡由静音和活性（尖峰）时期组成，这些时期通常在时间尺度上交替，通常为几秒钟至数十秒钟。这些通常是由细胞内钙的上升和下降介导的，这通过钙激活的钾通道调节了尖峰活性，但是许多其他通道机制是可能的。从数学上讲，我们从所涉及的渠道中抽象出峰值和沉默之间的过渡（称为分叉）。除了对特定细胞类型的爆发电气振荡进行建模外，我们对基于这些过渡的类型对各种爆发机制进行了长期兴趣。这使得可以建立最简单的模型，以说明每个已知模式，其中简单性是由定义过渡集所需的最小参数数量索引的。通常，单元格使用冗余参数化，因为它们必须通过处置的机制探索参数空间，例如离子通道和泵，但是最小的数学描述对于我们的理解仍然很重要。现在，我们可以与布里斯托尔大学的Krasimira Tsaneva-Atanosova合作报告重大进展，奥克兰大学的欣克·奥森（Hinke Osoingsa）在很大程度上完成了前酋长约翰·林泽尔（John Rinzel）25年前在该实验室开始的分析计划。参见参考。＃2。在2012年工业和应用数学学会的2012年生命科学会议上，这项工作也被作为邀请的全体演讲。分类方案的一种应用是了解不同单元类型表现出的爆发模式之间的连接。一个关键的激励示例是垂体间营养嗜血杆菌与乳营养素与胰腺β细胞之间的比较。两类细胞都表现出来自去极化平稳的动作电位爆发，这有效地将钙进入细胞以分泌各自的激素。我们在先前的工作中表明，在垂体模型中，尖峰是瞬态的，这是由于对高原的上部稳态的吸引力缓慢，而在β细胞中，尖峰是持续的振荡，如果钙是固定而不是缓慢变化的，则将持续存在。两种类型的细胞是发育和进化的表亲，因此可以预期，不同的爆发机制将是相关的。但是，尽管已经知道只有三个参数就可以生成Beta细胞类型的爆发模式，但我们发现垂体模式需要四个参数，进一步强调了两者之间的基本差异。尽管如此，两种类型都出现在扩展的四参数方案中，作为邻居，每种方案都可以转换为另一个参数之一。我们和其他人之前曾发现，几个可识别的参数（包括激活钙通道的阈值）都可以介导这种转化率。因此，抽象数学对生物物理学具有令人满意的证实，但这引发了其他问题。如果活动模式位于参数空间附近，那么细胞如何能够维持其身份而不是从一个角度漂移？我们认为这是一个深刻的问题，我们希望将来能够解决它。除了此处描述的特定项目外，我们还参与了法国旅游中的神经内分泌学建模的非常成功的研讨会。这是有关该主题的第三次半年度会议，涉及理论家和实验家，也是从会议中逐渐发展出来的新生跨学科社区，现在似乎已经建立了良好的自我维持。