A Bayesian Solution to Inverse Problem for Circadian Cycles

Most organisms exhibit various endogenous oscillating behaviors which provide crucial information as to how the internal biochemical processes are connected and regulated. Understanding the molecular mechanisms behind these oscillators requires interdisciplinary efforts combining both biological and computer experiments, as the latter can complement the former by simulating perturbed conditions with higher resolution. Harmonizing the two types of experiment, however, poses significant statistical challenges due to identifiability issues, numerical instability, and ill behavior in high dimension. This article devises a new Bayesian calibration framework for oscillating biochemical models. The proposed Bayesian model is estimated using an advanced MCMC which can efficiently infer the parameter values that match the simulated and observed oscillatory processes. Also proposed is an approach to sensitivity analysis approach based on the intervention posterior. This approach measures the influence of individual parameters on the target process by utilizing the obtained MCMC samples as a computational tool. The proposed framework is illustrated with circadian oscillations observed in a filamentous fungus, Neurospora crassa.