Measuring synchronization of stochastic oscillators in biology

Abstract

A fundamental problem in physics is measuring and modeling the synchronization of coupled stochastic oscillators. The problem is relatively recent in biology, where it has become possible to measure stochastic oscillators in single cells. A variety of synchronization measures have been proposed to describe a field of coupled stochastic oscillators. We introduce a synchronization measure new to this problem (but old to Genetics) called the intraclass correlation (ICC). The ICC is simple to interpret and has a statistical framework for inference. We illustrate ICC behaviour in the Kuramoto phase-locking model and on a field of over 25,000 oscillators in single cells measured every half-hour over a ten day interval.