Mathematical Analysis of Electrical Oscillations in Anterior Pituitary Cells

这个项目是一种数学和实验相结合的方法来分析荷尔蒙分泌的脑下垂体细胞的行为。我们记录细胞的电活动，并利用它的特征来校准数学模型。这种校准是在图形处理单元(GPU)的帮助下完成的，该图形处理单元用于快速优化适应度函数，该适应度函数将模型电压轨迹的特征与实验记录的特征进行比较。一旦校准，该模型就被用来预测生物参数变化的影响，例如各种类型离子电流的电导。然后在用于校准模型的同一个电池上测试这些预测，使用动态钳位技术向真实电池注入基于模型的离子电流。为了帮助我们理解模型，从而做出更有用的预测，我们使用几何奇异摄动方法来理解电活动尖峰和爆发模式的基础，以及不同类型活动发生的参数范围。生物系统数学模型的最终目标是生成可以在实验室进行测试的假设。如果模型校准得很好，那么测试模型做出的预测是确定我们对模型中反映的生物学的理解是否正确的最佳方式。特别是，如果对模型预测的测试失败，那么这意味着我们对作为模型基础的生物学的理解有问题。然而，这只有在模型校准良好的情况下才是正确的，因为一个模型在其公式上是正确的，但在其参数化方面是不正确的，可能会导致错误的预测。考虑到许多生物系统中存在的细胞到细胞的高度异质性，这一警告尤其重要。例如，一个细胞可能表现出一种类型的活动模式，而相同类型的相邻细胞可能表现出非常不同的活动模式，反映了生物参数值的差异。在这个项目中，我们将快速模型校准与动态钳位技术相结合，基于单个细胞的活动来校准模型，然后在同一细胞上测试该模型所做的预测，从而克服了与细胞异质性相关的问题。

This project is a hybrid mathematical/experimental approach to the analysis of the behavior of hormone-secreting pituitary cells. We record a cell's electrical activity and use features of this to calibrate a mathematical model. This calibration is done with the aid of a graphics processing unit (GPU) for fast optimization of a fitness function that compares features of the model voltage trace to those of the experimental recording. Once calibrated, the model is used to make predictions about the effects of changes in biological parameters, such as the conductances of various types of ionic currents. These predictions are then tested on the same cell that was used to calibrate the model, using the dynamic clamp technique to inject a model-based ionic current into a real cell. To help with our understanding of the model, and thus to make more useful predictions, we use geometric singular perturbation methods to understand the basis for spiking and bursting patterns of electrical activity, and the parameter ranges where different types of activity occur.The ultimate goal of mathematical models for biological systems is to generate hypotheses that can be tested in the lab. If the model is well calibrated, then testing a prediction made by the model is the best way to determine if our understanding of the biology that is reflected in the model is correct. In particular, if a test of a model prediction fails, then it means that something is wrong with our understanding of the biology that was the basis for the model. However, this is only true if the model is well calibrated, since a model that is correct in its formulation, but incorrect in its parameterization, can lead to incorrect predictions. This caveat is particularly important given the great degree of cell-to-cell heterogeneity that exists in many biological systems. For example, a cell may exhibit one type of pattern of activity, while a neighboring cell of the same type may exhibit a very different pattern of activity, reflecting differences in biological parameter values. In this project, we combine fast model calibration with the dynamic clamp technique to calibrate a model based on a single cell's activity, and then test predictions made by the model on the same cell, overcoming problems associated with cellular heterogeneity.