Homeostatic processes that provide negative feedback to regulate neuronal firing rates are essential for normal brain function. Indeed, multiple parameters of individual neurons, including the scale of afferent synapse strengths and the densities of specific ion channels, have been observed to change on homeostatic time scales to oppose the effects of chronic changes in synaptic input. This raises the question of whether these processes are controlled by a single slow feedback variable or multiple slow variables. A single homeostatic process providing negative feedback to a neuron’s firing rate naturally maintains a stable homeostatic equilibrium with a characteristic mean firing rate; but the conditions under which multiple slow feedbacks produce a stable homeostatic equilibrium have not yet been explored. Here we study a highly general model of homeostatic firing rate control in which two slow variables provide negative feedback to drive a firing rate toward two different target rates. Using dynamical systems techniques, we show that such a control system can be used to stably maintain a neuron’s characteristic firing rate mean and variance in the face of perturbations, and we derive conditions under which this happens. We also derive expressions that clarify the relationship between the homeostatic firing rate targets and the resulting stable firing rate mean and variance. We provide specific examples of neuronal systems that can be effectively regulated by dual homeostasis. One of these examples is a recurrent excitatory network, which a dual feedback system can robustly tune to serve as an integrator.

中文翻译：

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通过双重稳态机制稳定控制点火速率平均值和方差。

提供负反馈以调节神经元放电速率的体内平衡过程对于正常的大脑功能至关重要。实际上，已经观察到单个神经元的多个参数，包括传入突触强度的大小和特定离子通道的密度，会在稳态时标上发生变化，从而抵制突触输入的慢性变化。这就提出了这些过程是由单个慢反馈变量还是由多个慢变量控制的问题。为神经元的放电速率提供负反馈的单个稳态过程自然会保持稳定的稳态平衡，并具有特征性的平均放电速率。但是尚未探究多个缓慢反馈产生稳定的稳态平衡的条件。在这里，我们研究了一个高度通用的稳态点火速率控制模型，其中两个慢变量提供负反馈，以将点火速率推向两个不同的目标速率。通过使用动力学系统技术，我们证明了这种控制系统可以用来稳定地维持神经元的特征发动速率平均值和面对扰动的方差，并得出发生这种情况的条件。我们还导出了一些表达式，这些表达式阐明了稳态触发率目标与所产生的稳定触发率均值和方差之间的关系。我们提供了可以通过双重稳态有效调节的神经元系统的特定示例。这些示例之一是循环激励网络，双反馈系统可以对其进行鲁棒的调整以用作积分器。