Determination of Temporal Order among the Components of an Oscillatory System

Abstract

Oscillatory systems in biology are tightly regulated process where the individual components (e.g. genes) express in an orderly manner by virtue of their functions. The temporal order among the components of an oscillatory system may potentially be disrupted for various reasons (e.g. environmental factors). As a result some components of the system may go out of order or even cease to participate in the oscillatory process. In this article, we develop a novel framework to evaluate whether the temporal order is unchanged in different populations (or experimental conditions). We also develop methodology to estimate the order among the components with a suitable notion of "confidence." Using publicly available data on S. pombe, S. cerevisiae and Homo sapiens we discover that the temporal order among the genes cdc18; mik1; hhf1; hta2; fkh2 and klp5 is evolutionarily conserved from yeast to humans.

Fig 1. An illustration of the temporal order among genes g ₁, g ₂, …, g ₈ whose phase angles are in order along a circle (in counterclock-wise direction).