Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610, Japan.
J Theor Biol. 2012 Mar 21;297:61-72. doi: 10.1016/j.jtbi.2011.12.007. Epub 2011 Dec 16.
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously oscillatory cells. Such biological rhythms have notable periodicity despite the internal and external noise present in each cell. Previous experimental studies indicate that the regularity of oscillatory dynamics is enhanced when noisy oscillators interact and become synchronized. This effect, called the collective enhancement of temporal precision, has been studied theoretically using particular assumptions. In this study, we propose a general theoretical framework that enables us to understand the dependence of temporal precision on network parameters including size, connectivity, and coupling intensity; this effect has been poorly understood to date. Our framework is based on a phase oscillator model that is applicable to general oscillator networks with any coupling mechanism if coupling and noise are sufficiently weak. In particular, we can manage general directed and weighted networks. We quantify the precision of the activity of a single cell and the mean activity of an arbitrary subset of cells. We find that, in general undirected networks, the standard deviation of cycle-to-cycle periods scales with the system size N as 1/N, but only up to a certain system size N(⁎) that depends on network parameters. Enhancement of temporal precision is ineffective when N>N(⁎). We provide an example in which temporal precision considerably improves with increasing N while the level of synchrony remains almost constant; temporal precision and synchrony are independent dynamical properties. We also reveal the advantage of long-range interactions among cells to temporal precision.
生物节律是由起搏器器官产生的，如心脏起搏器器官（窦房结）和昼夜节律的主时钟（视交叉上核），它们由自主振荡细胞的网络组成。尽管每个细胞内部和外部都存在噪声，但这种生物节律具有显著的周期性。以前的实验研究表明，当噪声振荡器相互作用并实现同步时，振荡动力学的规律性会增强。这种效应称为时间精度的集体增强，已经使用特定的假设在理论上进行了研究。在这项研究中，我们提出了一个通用的理论框架，使我们能够理解时间精度对包括大小、连接性和耦合强度在内的网络参数的依赖性；迄今为止，这种效应尚未得到很好的理解。我们的框架基于一个相振荡器模型，如果耦合和噪声足够弱，该模型适用于具有任何耦合机制的一般振荡器网络。特别是，我们可以管理一般的有向和加权网络。我们量化了单个细胞的活动精度和任意细胞子集的平均活动精度。我们发现，在一般的无向网络中，周期到周期的标准偏差与系统大小 N 呈 1/N 的比例关系，但仅在一定的系统大小 N(⁎)范围内，N(⁎)取决于网络参数。当 N>N(⁎)时，时间精度的增强效果无效。我们提供了一个例子，其中时间精度随着 N 的增加而显著提高，而同步水平几乎保持不变；时间精度和同步是独立的动力学性质。我们还揭示了细胞之间长程相互作用对时间精度的优势。
