Analysis of coupled genetic oscillators with delayed positive feedback interconnections

Genetic oscillators have a fundamental role in the regulation not only of intracellular, but also of intercellular functions: for instance, in the segmentation clock, the synchronised oscillation of neighbouring cells generates spatial travelling waves that induce segmentation of precursors of the vertebral column. To investigate this type of phenomena, we consider the behaviour of two genetic negative feedback oscillators, each operating in a different cell, coupled by an intercellular positive-feedback interconnection with delays. The two coupled systems are nominally identical, but can be different due to noise and cell-to-cell variability. When they can be different in general, we study the effect of positive-feedback and of delay in inducing an oscillatory behaviour. When they are identical, we study how the intercellular feedback delay affects the phase difference between the two oscillators.