Suvak Onder, Demir Alper
Department of Electrical and Electronics Engineering, College of Engineering, Koç University Rumeli Feneri Yolu 34450 Sariyer Istanbul, Turkey.
EURASIP J Bioinform Syst Biol. 2012 Jun 11;2012(1):6. doi: 10.1186/1687-4153-2012-6.
Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise.
In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses.
The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations.
生化振荡器在细胞中执行关键功能，例如，它们建立生物钟。振荡器的动力学行为最好用标量相位来描述和分析。相位的一个严格且有用的定义基于振荡器的所谓等时线。基于等时线的连续振荡器的相位计算技术已被用于表征各种类型的振荡器在噪声等扰动影响下的行为。
在本文中，根据从这种振荡器的连续状态近似获得的信息，我们将这些相位计算方法的适用性扩展到作为离散分子系统的生化振荡器。特别是，我们描述了用于计算由随机模拟算法生成的样本路径的离散分子振荡器的瞬时相位的技术。我们对准确性进行了评论，并推导了某些用于评估所提出的相位计算方法可行性的度量。对著名生物振荡器样本路径的相位计算实验验证了我们的分析。
基于本文提出的相位计算技术，可以表征由构成分子振荡器的机制的离散和随机性质产生的噪声的影响。等时线的概念是建立振荡器相位概念的自然选择。我们提出的等时线理论相位计算方法可以应用于任何维度的离散分子振荡器，前提是在离散状态下观察到的振荡行为在连续状态近似中不会消失。如果不借助这种近似开发适当的相位模型理论，就有可能对分子振荡器中的相位噪声现象的全通用性进行分析。
