Average Measures of Phase and Synchrony in Inhomogeneous Populations of Circadian Oscillators

Abstract

Circadian misalignment between the phase of molecular circadian oscillators and the external environment has been linked to adverse health effects, including cardiovascular disease, obesity, cancer, and psychiatric disorders. Desynchrony of the circadian clock within populations of oscillators has also been linked to these conditions. For this reason, we wish to develop a control strategy to shift molecular circadian phase while also controlling for population synchrony. Previous work has demonstrated that model predictive control can effectively solve this problem when synchrony is determined directly by measuring the phase of each cell in a homogeneous population. Such cell-specific phase measurements are rarely possible in vivo, and such homogeneity is not biologically plausible. For these reasons, we wish to design an observer that can accurately determine the mean phase of the population and derive a proxy for population synchrony. We show that a model parameterized with the average parameter set of the population can be used to sense phase from mean population expression levels, despite inaccuracies when sensing the phase of a single cell. Similarly, we are able to use the average amplitude of the population in comparison to the amplitude of the average population oscillator as a measure of synchrony within the population. Taken together, these two metrics, based on the average behavior of the cell, allow us to control the phase and synchrony of the population of cellular oscillators without measuring the phase of individual cells.