The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent channel fluctuations or the stochastic nature of neurotransmitter release. Here we propose an alternative approach using a simple leaky integrate-and-fire model with a noisy threshold. Initially, we develop a mathematical treatment of the neuronal response to periodic forcing using tools from linear response theory and use this to highlight how a noisy threshold can enhance downstream signal reconstruction. We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times. This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure. An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

多年来，神经元放电的可变性一直是研究的热点。从建模的角度来看，它经常在基于电导的尖峰模型中进行研究，使用加性或乘性噪声项来表示通道波动或神经递质释放的随机性质。在这里，我们提出了一种替代方法，使用具有噪声阈值的简单泄漏集成和发射模型。最初，我们使用线性响应理论中的工具开发了对周期性强迫的神经元响应的数学处理，并使用它来强调噪声阈值如何增强下游信号重建。我们进一步开发了一个更通用的框架，以基于对首次通过时间的计算来理解对大振幅强迫的响应。这非常适合理解随机锁模，为此我们在数值上确定了 Arnol'd 舌结构。对来自腹侧耳蜗核内定期发射的星状神经元的数据进行检查，对正弦振幅调制的纯音作出反应，显示了与这些预测一致的舌头结构，并强调在单个星状细胞忠实地编码周期性刺激。