Wang Yongqiang, Hori Yutaka, Hara Shinji, Doyle Francis J
Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080 USA.
Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8656 Japan.
IEEE Trans Automat Contr. 2014 Jan;59(1):211-216. doi: 10.1109/TAC.2013.2270072.
Most biological rhythms are generated by a population of cellular oscillators coupled through intercellular signaling. Recent experimental evidence shows that the collective period may differ significantly from the autonomous period in the presence of intercellular delays. The phenomenon has been investigated using delay-coupled phase oscillators, but the proposed phase model contains no direct biological mechanism, which may weaken the model's reliability in unraveling biophysical principles. Based on a published gene regulatory oscillator model, we analyze the collective period of delay-coupled biological oscillators using the multivariable harmonic balance technique. We prove that, in contradiction to the common intuition that the collective period increases linearly with the coupling delay, the collective period turns out to be a periodic function of the intercellular delay. More surprisingly, the collective period may even decrease with the intercellular delay when the delay resides in certain regions. The collective period is given in a closed-form in terms of biochemical reaction constants and thus provides biological insights as well as guidance in synthetic-biological-oscillator design. Simulation results are given based on a segmentation clock model to confirm the theoretical predictions.
大多数生物节律是由通过细胞间信号传导耦合的一群细胞振荡器产生的。最近的实验证据表明，在存在细胞间延迟的情况下，集体周期可能与自主周期有显著差异。该现象已使用延迟耦合相位振荡器进行了研究，但所提出的相位模型不包含直接的生物学机制，这可能会削弱模型在揭示生物物理原理方面的可靠性。基于一个已发表的基因调控振荡器模型，我们使用多变量谐波平衡技术分析延迟耦合生物振荡器的集体周期。我们证明，与集体周期随耦合延迟线性增加的常见直觉相反，集体周期结果是细胞间延迟的周期函数。更令人惊讶的是，当延迟位于某些区域时，集体周期甚至可能随细胞间延迟而减小。集体周期以生化反应常数的封闭形式给出，因此为合成生物振荡器设计提供了生物学见解和指导。基于一个分割时钟模型给出了模拟结果，以证实理论预测。
