Noninvasive inference methods for interaction and noise intensities of coupled oscillators using only spike time data

Reconstruction of phase dynamics from macroscopic observations based on linear and nonlinear response theories

We propose a method to reconstruct the phase dynamics in rhythmical interacting systems from macroscopic responses to weak inputs by developing linear and nonlinear response theories, which predict the responses in a given system. By solving an inverse problem, the method infers an unknown system: the natural frequency distribution, the coupling function, and the time delay which is inevitable in real systems. In contrast to previous methods, our method requires neither strong invasiveness nor microscopic observations. We demonstrate that the method reconstructs two phase systems from observed responses accurately. The qualitative methodological advantages demonstrated by our quantitative numerical examinations suggest its broad applicability in various fields, including brain systems, which are often observed through macroscopic signals such as electroencephalograms and functional magnetic response imaging.

Enhanced precision of circadian rhythm by output system

Circadian rhythms are biological rhythms with a period of approximately 24 h that persist even under constant conditions without daily environmental cues. The molecular circadian clock machinery generates physiological rhythms, which can be transmitted into the downstream output system. Owing to the stochastic nature of the biochemical reactions and the extracellular environment, the oscillation period of circadian rhythms exhibited by individual organisms or cells is not constant on a daily basis with variations as high as 10%, as reflected by the coefficient of variation. Although the fluctuations in the circadian rhythm are measured through a reporter system such as bioluminescence or fluorescence, which is an example of output systems, experimentally confirming whether the fluctuations found in the reporter system are the same as those in the circadian clock is challenging. This study investigated a coupled system of a circadian clock and its output system numerically and analytically, and then compared the fluctuations in the oscillation period of the two systems. We found that the amount of fluctuations in the output system is smaller than that in the circadian clock, assuming the degradation rate of the molecules responsible for the output system is a typical value for protein degradation. The results indicate that the output system can improve the accuracy of the circadian rhythm without the need for any denoising processes.