Biological systems often oscillate to maintain their intended function. The beating of the heart is a good example. It is often the case that different oscillators interact and sometimes synchronize. The process by which synchronization happens is not well understood, but mathematical and computational models may provide some insight.
Bartocci et al. describe oscillator time automata as a class of time automata that we can use to model biological systems. They then show how synchronization of populations of oscillators can be described using biological oscillator synchronization logic (BOSL). A central focus of the paper is the introduction of a model for checking algorithms for the BOSL. This is important because it provides a framework for using BOSL to identify synchronization patterns in a population of oscillators.
The approach presented is very much driven by theoretical computer science and the mathematics and logic of oscillators. This is certainly a reasonable approach to the problem, but it is interesting to think about how the authors could extend the work using formal statistical methods such as hypothesis testing. This would require establishing a null hypothesis, an alternate hypothesis, a test statistic, and a decision rule.
Here, a null hypothesis could be “no synchrony among a population of oscillators.” We could identify a test statistic from the BOSL and determine statistical significance using permutation testing. Here, we could generate 104 or more randomly generated populations of oscillators to estimate the null distribution of the test statistic. We can estimate a p-value measuring the probability of a type I error or false positive from this null distribution. Alternatively, we could use bootstrapping to estimate the standard error of the test statistic and then to construct a confidence interval for hypothesis testing.
This type of merger of theoretical computer science and statistics will be necessary for bringing methods such as BOSL to biologists for solving real-world problems such as the development of new drugs that can target oscillating biological systems with health implications.
