Rhythmic activity which underlies motor output is often initiated and controlled by descending modulatory projection pathways onto central pattern generator (CPG) networks. In turn, these descending pathways receive synaptic feedback from their target CPG network, which can influence the CPG output. However, the mechanisms underlying such bi-directional synaptic interactions are mostly unexplored. We develop a reduced mathematical model, including both feed-forward and feedback circuitry, to examine how the synaptic interactions involving two projection neurons, MCN1 and CPN2, can produce and shape the activity of the gastric mill CPG in the crab stomatogastric nervous system. We use simplifying assumptions that are based on the behavior of the biological system to reduce this model down to 2 dimensions, which allows for phase plane analysis of the model output. The model shows a distinct activity for the gastric mill rhythm that is elicited when MCN1 and CPN2 are co-active compared to the rhythm elicited by MCN1 activity alone. Furthermore, the presence of feedback to the projection neuron CPN2 provides a distinct locus of pattern generation in the model which does not require reciprocally inhibitory interactions between the gastric mill CPG neurons, but is instead based on a half-center oscillator that occurs through a tri-synaptic pathway that includes CPN2. Our modeling results show that feedback to projection pathways may provide additional mechanisms for the generation of motor activity. These mechanisms can have distinct dependence on network parameters and may therefore provide additional flexibility for the rhythmic motor output.

中文翻译：

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对下降的投射神经元的突触反馈如何影响振荡网络活动的建模探索。

通常通过降低调制投影路径到中央模式发生器（CPG）网络上来启动和控制构成电机输出基础的节律活动。反过来，这些下降路径从其目标CPG网络接收突触反馈，这会影响CPG输出。但是，这种双向突触相互作用的基础机制大多尚未被探索。我们开发了一个简化的数学模型，包括前馈电路和反馈电路，以检查涉及两个投射神经元MCN1和CPN2的突触相互作用如何产生并影响蟹胃胃神经系统中胃磨CPG的活动。我们使用基于生物系统行为的简化假设将这个模型缩小到2维，允许对模型输出进行相平面分析。该模型显示了与MCN1活动单独引起的节奏相比，当MCN1和CPN2共同活动时引起的针对胃磨节奏的独特活动。此外，对投射神经元CPN2的反馈的存在提供了模型中模式生成的独特位点，该位点不需要在胃磨CPG神经元之间进行相互抑制性相互作用，而是基于通过三位点发生的半中心振荡器-CPN2的突触途径。我们的建模结果表明，对投影路径的反馈可能会为运动活动的产生提供其他机制。这些机制可能对网络参数有明显的依赖性，因此可以为有节奏的电机输出提供额外的灵活性。