Department of Statistics, University of Georgia, Athens, GA.
School of Electrical and Computer Engineering, College of Engineering, University of Georgia, Athens, GA.
Yale J Biol Med. 2019 Jun 27;92(2):169-178. eCollection 2019 Jun.
Four inter-related measures of phase are described to study the phase synchronization of cellular oscillators, and computation of these measures is described and illustrated on single cell fluorescence data from the model filamentous fungus, . One of these four measures is the phase shift in a sinusoid of the form x(t) = cos), where t is time. The other measures arise by creating a replica of the periodic process x(t) called the Hilbert transform which is 90 degrees out of phase with the original process x(t). The second phase measure is the phase angle between the replica and x(t), taking values between -π and π. At extreme values the Hilbert Phase is discontinuous, and a continuous form of the Hilbert Phase is used, measuring time on the nonnegative real axis (t). The continuous Hilbert Phase is used to define the phase for an experiment beginning at time and ending at time . In that phase differences at time are often of ancillary interest, the Hilbert Phase is subtracted from . This difference is divided by 2 to obtain the phase in cycles. Both the Hilbert Phase and the phase are functions of time and useful in studying when oscillators phase-synchronize in time in signal processing and circadian rhythms in particular. The phase of cellular clocks is fundamentally different from circadian clocks at the macroscopic scale because there is an hourly cycle superimposed on the circadian cycle.
描述了四种相互关联的相位度量方法，用于研究细胞振荡器的相位同步，并描述和说明了这些度量方法在来自模型丝状真菌的单细胞荧光数据上的计算。这四个度量中的一个是相位偏移在形式为 x(t) = cos 的正弦波中，其中 t 是时间。其他度量方法是通过创建周期性过程 x(t)的副本（称为 Hilbert 变换）来产生的，该副本与原始过程 x(t)相差 90 度。第二个相位度量是副本和 x(t)之间的相位角，取值范围在-π 到 π 之间。在极值处，Hilbert 相位是不连续的，因此使用了连续形式的 Hilbert 相位，在非负实轴上测量时间 (t)。连续 Hilbert 相位用于定义从时间开始到时间结束的实验的相位。在该相位中，时间的相位差通常是辅助性的，因此从 Hilbert 相位中减去。将该差值除以 2 以获得周期中的相位。在信号处理和生物钟节律特别是，Hilbert 相位和相位都是时间的函数，在研究振荡器何时在时间上相位同步时非常有用。细胞钟的相位与宏观尺度上的生物钟根本不同，因为在生物钟周期上叠加了一个小时周期。
