Mathematical Analysis of Electrical Oscillations in Anterior Pituitary Cells

这个项目是一个混合的数学/实验方法来分析分泌激素的垂体细胞的行为。我们记录下细胞的电活动，并利用其特征来校准数学模型。该校准是在图形处理单元（GPU）的帮助下完成的，用于快速优化适应度函数，该适应度函数将模型电压迹线的特征与实验记录的特征进行比较。一旦校准，该模型就可以用来预测生物参数变化的影响，比如各种类型离子电流的电导。然后在用于校准模型的相同电池上对这些预测进行测试，使用动态钳技术将基于模型的离子电流注入实际电池。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的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产生可以在实验室中验证的假设。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好方法。特别是，如果对模型预测的测试失败了，那就意味着我们对作为模型基础的生物学的理解出了问题。然而，这只有在模型校准得很好的情况下才是正确的，因为一个模型如果在公式上是正确的，但在参数化上是不正确的，就会导致不正确的预测。考虑到存在于许多生物系统中的细胞间的巨大异质性，这一警告尤为重要。例如，一个细胞可能表现出一种类型的活动模式，而邻近的相同类型的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。在本项目中，我们将快速模型校准与动态钳夹技术相结合，基于单个细胞的活性校准模型，然后在同一细胞上测试模型的预测，克服了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.