Complexity and limited knowledge render it impractical to write down the equations describing a cellular system completely. Cellular biophysics uses hypotheses-based modelling instead. How can we set up models with predictive power beyond the experimental examples used to develop them? The two textbook systems of cellular biophysics, \(\hbox {Ca}^{2+}\) signalling and neuronal membrane potential dynamics, both face this question. Both systems also have a non-equilibrium feature in common: on different time scales and for different observables, they exhibit stochastic spiking, i.e., sequences of stereotypical events that are separated by statistically distributed intervals, the interspike intervals (ISI). Here we review recent progress on the description of \(\hbox {Ca}^{2+}\) spikes in terms of blips, puffs and cellular \(\hbox {Ca}^{2+}\) spikes and focus on stochastic models that can explain the statistics of the single ISIs, in particular its mean and variance and the cell-to-cell variability of these statistics. We also review models of the stochastic integrate-and-fire type and measures like the spike-train power spectrum or the serial correlation coefficient that are used to describe neuronal spike trains. These concepts from computational neuroscience might be applicable for understanding long-term memory effects in \(\hbox {Ca}^{2+}\) spiking that extend beyond a single ISI, such as cumulative refractoriness.

复杂性和有限的知识使得写下完整描述细胞系统的方程变得不切实际。细胞生物物理学改为使用基于假设的建模。我们如何建立具有超出用于开发它们的实验示例的预测能力的模型？细胞生物物理学的两个教科书系统，\(\hbox {Ca}^{2+}\)信号传导和神经元膜电位动力学，都面临这个问题。这两个系统也有一个共同的非平衡特征：在不同的时间尺度上，对于不同的可观察量，它们表现出随机尖峰，即由统计分布的间隔、尖峰间隔 (ISI) 分隔的刻板事件序列。这里我们回顾一下最近关于\(\hbox {Ca}^{2+}\)尖峰，泡芙和细胞\(\hbox {Ca}^{2+}\)尖峰，并专注于可以解释单个 ISI 统计数据的随机模型，特别是它的均值和方差以及细胞到- 这些统计数据的细胞变异性。我们还回顾了随机积分和发射类型的模型以及用于描述神经元尖峰序列的尖峰序列功率谱或序列相关系数等度量。这些来自计算神经科学的概念可能适用于理解\(\hbox {Ca}^{2+}\)尖峰中超出单个 ISI的长期记忆效应，例如累积不应期。