Neural Comput. 2011 Jan;23(1):124-59. doi: 10.1162/NECO_a_00061. Epub 2010 Oct 21.
Stochastic models of synaptic plasticity propose that single synapses perform a directed random walk of fixed step sizes in synaptic strength, thereby embracing the view that the mechanisms of synaptic plasticity constitute a stochastic dynamical system. However, fluctuations in synaptic strength present a formidable challenge to such an approach. We have previously proposed that single synapses must interpose an integration and filtering mechanism between the induction of synaptic plasticity and the expression of synaptic plasticity in order to control fluctuations. We analyze a class of three such mechanisms in the presence of possibly non-Markovian plasticity induction processes, deriving expressions for the mean expression time in these models. One of these filtering mechanisms constitutes a discrete low-pass filter that could be implemented on a small collection of molecules at single synapses, such as CaMKII, and we analyze this discrete filter in some detail. After considering Markov induction processes, we examine our own stochastic model of spike-timing-dependent plasticity, for which the probability density functions of the induction of plasticity steps have previously been derived. We determine the dependence of the mean time to express a plasticity step on pre- and postsynaptic firing rates in this model, and we also consider, numerically, the long-term stability against fluctuations of patterns of neuronal connectivity that typically emerge during neuronal development.
突触可塑性的随机模型提出，单个突触在突触强度上进行固定步长的定向随机游走，从而接受突触可塑性机制构成随机动力系统的观点。然而，突触强度的波动对这种方法提出了巨大的挑战。我们之前曾提出，为了控制波动，单个突触必须在突触可塑性的诱导和突触可塑性的表达之间插入一个整合和滤波机制。我们在可能存在非马尔可夫可塑性诱导过程的情况下分析了三类这样的机制，推导出了这些模型中平均表达时间的表达式。这些滤波机制之一是一种离散的低通滤波器，可以在单个突触上的一小部分分子上实现，例如 CaMKII，我们对这个离散滤波器进行了一些详细的分析。在考虑了马尔可夫诱导过程之后，我们研究了我们自己的基于尖峰时间依赖可塑性的随机模型，之前已经推导出了该模型中可塑性诱导步骤的概率密度函数。我们确定了在该模型中表达一个可塑性步骤的平均时间与前后神经元放电率之间的依赖关系，并且还考虑了在神经元发育过程中通常出现的神经元连接模式的长期稳定性对波动的影响。
