Role of intercellular coupling and delay on the synchronization of genetic oscillators

Abstract

Living cells encode diverse biological clocks for circadian timekeeping and formation of rhythmic structures during embryonic development. A key open question is how these clocks synchronize across cells through intercellular coupling mechanisms. To address this question, we leverage the classical motif for genetic clocks the Goodwin oscillator where a gene product inhibits its own synthesis via time-delayed negative feedback. More specifically, we consider an interconnected system of two identical Goodwin oscillators (each operating in a single cell), where state information is conveyed between cells via a signaling pathway whose dynamics is modeled as a first-order system. In essence, the interaction between oscillators is characterized by an intercellular coupling strength and an intercellular time delay that represents the signaling response time. Systematic stability analysis characterizes the parameter regimes that lead to oscillatory dynamics, with high coupling strength found to destroy sustained oscillations. Within the oscillatory parameter regime we find both in-phase and anti-phase oscillations with the former more likely to occur for small intercellular time delays. Finally, we consider the stochastic formulation of the model with low-copy number fluctuations in biomolecular components. Interestingly, stochasticity leads to qualitatively different behaviors where in-phase oscillations are susceptible to the inherent fluctuations but not the anti-phase oscillations. In the context of the segmentation clock, such synchronized in-phase oscillations between cells are critical for the proper generation of repetitive segments during embryo development that eventually leads to the formation of the vertebral column.