Physical Frameworks and Theories on How Autonomous Biological Oscillators Synchronize

Rhythms and oscillations are widely observed in biological systems. However, it is unclear how such noisy systems can produce robust and consistent timing, or how individual molecules or time-keeping systems couple together to produce macroscopically observable rhythms. Here, we focus on the synchronization of oscillatory processes at different scales: from the sub-cellular to the cellular and intercellular levels. Using examples from the circadian rhythms in cyanobacteria, cell cycle in eukaryotes, the firing of neurons, and from other emerging findings on the frontier of autonomous clocks, we discuss different paradigms of coupling or entrainment. We then highlight different methods of analysis from deterministic to stochastic approaches. Specifically, we discuss methods to quantify synchronization and its possible physical mechanisms, as well as prevailing mathematical models. Lastly, we close with a discussion of suggestions for new experiments or theoretical investigation.