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

钙是一种重要的信号分子，在所有真核细胞中都有使用。钙信号由随机的局部过程(喷雾)组成，它们的相互作用会产生全局浓度变化(尖峰、波动)。我们可以在一次实验中同时观测到局地事件和全球海浪。这种从微观过程中观察宏观事件出现的机会使该系统对整个物理学来说都很有趣。钙信号在许多特征上表现出很大的细胞间变异性，但也显示出在细胞群体中保守的特性。我们想要了解微观和宏观现象之间的关系--喷雾和尖峰，以及面对细胞的变异性和随机性，信号传递是如何可能的。钙峰值被描述为一系列事件(点过程)，后续事件之间具有统计上独立的间隔(更新过程)。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捉。在这个项目中，我们将开发包括累积适应过程在内的钙泡和尖峰的理论模型，这些过程由一个难变的变量来描述。在我们的一个模型(多维积分与点火模型)的分析中，我们将使用理论神经科学中的方法，这些方法是为具有显著的区间相关性的神经放电而开发的。在并行方法中，我们将使用基于等待时间分布的离散随机模型，并开发新的分析方法来分析它们。除了阐述细胞变异性在钙信号转导中的作用外，我们还希望了解细胞变异性与细胞保守性之间的关系。

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.