The superchiasmatic nucleus (SCN) serves as the primary circadian (24hr) clock in mammals and is known to control important physiological functions such as the sleep-wake cycle, hormonal rhythms, and neurotransmitter regulation. Experimental results suggest that some of these functions reciprocally influence circadian rhythms, creating a highly complex network. Among the clock’s downstream products, orphan nuclear receptors REV-ERB and ROR are particularly interesting because they coordinately modulate the core clock circuitry. Recent experimental evidence shows that REV-ERB and ROR are not only crucial for lipid metabolism but are also involved in dopamine (DA) synthesis and degradation, which could have meaningful clinical implications for conditions such as Parkinson’s disease and mood disorders. We create a mathematical model consisting of differential equations that express how the circadian variables are influenced by light, how REV-ERB and ROR feedback to the clock, and how REV-ERB, ROR, and BMAL1-CLOCK affect the dopaminergic system. The structure of the model is based on the findings of experimentalists. We compare our model predictions to experimental data on clock components in different light-dark conditions and in the presence of genetic perturbations. Our model results are consistent with experimental results on REV-ERB and ROR and allow us to predict the circadian variations in tyrosine hydroxylase and monoamine oxidase seen in experiments. By connecting our model to an extant model of dopamine synthesis, release, and reuptake, we are able to predict circadian oscillations in extracellular DA and homovanillic acid that correspond well with experimental observations. The predictions of the mathematical model are consistent with a wide variety of experimental observations. Our calculations show that the mechanisms proposed by experimentalists by which REV-ERB, ROR, and BMAL1-CLOCK influence the DA system are sufficient to explain the circadian oscillations observed in dopaminergic variables. Our mathematical model can be used for further investigations of the effects of the mammalian circadian clock on the dopaminergic system. The model can also be used to predict how perturbations in the circadian clock disrupt the dopaminergic system and could potentially be used to find drug targets that ameliorate these disruptions.

中文翻译：

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昼夜节律和多巴胺的数学模型

超级嵌合神经核（SCN）在哺乳动物中是主要的生物钟（24小时），并且已知能控制重要的生理功能，例如睡眠-觉醒周期，荷尔蒙节律和神经递质调节。实验结果表明，其中一些功能会相互影响昼夜节律，从而形成高度复杂的网络。在时钟的下游产品中，孤核受体REV-ERB和ROR特别有趣，因为它们可以协调核心时钟电路。最近的实验证据表明，REV-ERB和ROR不仅对脂质代谢至关重要，而且还参与了多巴胺（DA）的合成和降解，这对于帕金森氏病和情绪障碍等疾病可能具有有意义的临床意义。我们创建了一个由微分方程组成的数学模型，这些微分方程表示昼夜节律变量如何受到光的影响，REV-ERB和ROR如何反馈到时钟以及REV-ERB，ROR和BMAL1-CLOCK如何影响多巴胺能系统。该模型的结构基于实验者的发现。我们将模型的预测结果与时钟数据在不同的明暗条件下以及存在基因扰动的情况下的实验数据进行比较。我们的模型结果与REV-ERB和ROR的实验结果一致，并允许我们预测实验中看到的酪氨酸羟化酶和单胺氧化酶的昼夜节律变化。通过将我们的模型与现有的多巴胺合成，释放和再摄取模型联系起来，我们能够预测细胞外DA和高香草酸中的昼夜节律振荡，这与实验观察非常吻合。数学模型的预测与各种各样的实验观察结果一致。我们的计算表明，实验者提出的REV-ERB，ROR和BMAL1-CLOCK影响DA系统的机制足以解释在多巴胺能变量中观察到的昼夜节律振荡。我们的数学模型可用于进一步研究哺乳动物生物钟对多巴胺能系统的影响。该模型还可以用于预测生物钟中的扰动如何破坏多巴胺能系统，并且可以潜在地用于发现缓解这些破坏的药物靶标。数学模型的预测与各种各样的实验观察结果一致。我们的计算表明，实验者提出的REV-ERB，ROR和BMAL1-CLOCK影响DA系统的机制足以解释在多巴胺能变量中观察到的昼夜节律振荡。我们的数学模型可用于进一步研究哺乳动物生物钟对多巴胺能系统的影响。该模型还可以用于预测生物钟中的扰动如何破坏多巴胺能系统，并且可以潜在地用于发现缓解这些破坏的药物靶标。数学模型的预测与各种各样的实验观察结果一致。我们的计算表明，实验者提出的REV-ERB，ROR和BMAL1-CLOCK影响DA系统的机制足以解释在多巴胺能变量中观察到的昼夜节律振荡。我们的数学模型可用于进一步研究哺乳动物生物钟对多巴胺能系统的影响。该模型还可以用于预测生物钟中的扰动如何破坏多巴胺能系统，并且可以潜在地用于发现改善这些破坏的药物靶标。BMAL1-CLOCK和BMAL1-CLOCK对DA系统的影响足以解释在多巴胺能变量中观察到的昼夜节律振荡。我们的数学模型可用于进一步研究哺乳动物生物钟对多巴胺能系统的影响。该模型还可以用于预测生物钟中的扰动如何破坏多巴胺能系统，并且可以潜在地用于发现缓解这些破坏的药物靶标。BMAL1-CLOCK和BMAL1-CLOCK对DA系统的影响足以解释在多巴胺能变量中观察到的昼夜节律振荡。我们的数学模型可用于进一步研究哺乳动物生物钟对多巴胺能系统的影响。该模型还可以用于预测生物钟中的扰动如何破坏多巴胺能系统，并且可以潜在地用于发现缓解这些破坏的药物靶标。