Calcium spiking with cumulative refractoriness - statistics of the fluctuations and implications for Calcium signaling

钙离子是一种重要的信号分子，在所有真核细胞中都有应用。钙信号由随机的局部过程（喷流）组成，其相互作用产生全局浓度变化（尖峰，波）。我们可以在一次实验中同时观察到局部事件和全局波。这种观察宏观事件从微观过程中出现的机会使该系统对物理学来说很有趣。钙信号传导在许多特征中表现出大的细胞间变异性，但也显示出在细胞群中保守的性质。我们想了解微观和宏观现象之间的关系-泡芙和尖峰，以及信号是如何在面对细胞的变异性和随机性。钙峰被描述为一系列事件（点过程），后续事件（更新过程）之间具有统计学独立的间隔。然而，尖峰的产生受到适应过程的影响，这不能基于独立的事件间间隔来捕获。在这个项目中，我们将开发理论模型的钙喷和尖峰，包括累积的适应过程，这是描述了一个难治变量。在分析我们的一个模型（多维积分激发模型）时，我们将使用理论神经科学中为具有明显间隔相关性的神经尖峰而开发的方法。在一个平行的方法，我们将使用离散随机模型的基础上等待时间分布，并开发新的分析方法进行分析。除了解决钙信号的可变性的作用，我们希望了解细胞的可变性和保守的细胞特性之间的关系。

Calcium is an important signalling molecule which is used in all eukaryotic cells. Calcium signals consist of random local processes (puffs), whose interaction generates global concentration changes (spikes, waves). We can observe both the local events and the global waves in a single experiment. This opportunity to watch the emergence of macroscopic events from microscopic processes renders the system interesting for Physics in general. Calcium signalling exhibits large cell-to-cell variability in many features but also shows properties conserved across the cell population. We would like to understand the relation between microscopic and macroscopic phenomena – puffs and spikes, and how signalling is possible in the face of cell variability and randomness. Calcium spikes have been described as a sequence of events (a point process) with statistically independent intervals between subsequent events (a renewal process). However, the spike generation is subject to an adaptation process, which cannot be captured on the basis of independent inter-event intervals. In this project, we will develop theoretical models for calcium puffs and spikes including cumulative adaptation processes, which are described by a refractory variable. In the analysis of one of our models (multidimensional integrate-and-fire model), we will use methods from theoretical neuroscience developed for neural spiking with pronounced interval correlations. In a parallel approach, we will use discrete stochastic models based on waiting time distributions and develop new analytical methods for their analysis. In addition to addressing the role of variability in calcium signalling, we hope to understand the relation between cell variability and the conserved properties of the cells.