Optimization of experimental designs for biological rhythm discovery

Equally spaced temporal sampling is the standard protocol for the study of biological rhythms. These equispaced designs perform well when calibrated to an oscillator’s period, yet can introduce systematic biases when applied to rhythms of unknown periodicity. Here, we investigate how optimizing the timing of measurements can improve rhythm detection across a range of experimental settings. When the period of a rhythm is known, we prove that equispaced designs provide optimal statistical power. In studies targeting specific sets of candidate rhythms, we construct optimal alternatives to equispaced designs to simultaneously maximize power at all frequencies under consideration. For studies investigating continuous period ranges, we show numerically how blindspots near the Nyquist rate can be resolved through timing optimization. Our computational methods are available through our PowerCHORD library. Our findings across all experimental contexts suggest that timing optimization is an effective yet under-explored tool for improving biological rhythm discovery.Author summary: Biological systems often exhibit fluctuations when observed over time. Statistical tests can help to determine whether these fluctuations are evidence of an underlying biological cycle or attributable to noise. The sensitivity of these tests depends not only on the sheer number of observations, but also on when observations are taken along the cycle. We confirm that the standard practice of making observations at equal intervals along the cycle is indeed the most sensitive design for a fixed sample size, however, this approach is only tenable for cycles of known duration. When we attempted to extend standard practices to the context of discovering cycles of unknown length, we uncovered significant drawbacks that would lead to meaningful signals being overlooked. We overcame these limitations of equispaced measurements by developing a mathematical optimization framework that is applicable when cycle length is unknown or when equispaced designs are infeasible. Solving this problem numerically for a range of experimental conditions produced designs that have the potential to expedite the discovery of novel biological rhythms.