Parametric modeling of mechanical effects on circadian oscillators
Circadian rhythms are archetypical examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are also affected by the cells mechanical environment. Here we extend a standard biochemical model of circadian rhythmicity to include mechanical effects in a parametric manner. Using experimental observations to constrain the model, we suggest specific ways in which the mechanical signal might affect the clock. Additionally, a bifurcation analysis of the system predicts that these mechanical signals need to be within an optimal range for circadian oscillations to occur. Cells are nonlinear dynamical elements, which in multicellular tissues are commonly coupled to one another. Much work has been done, both theoretically and experimentally, to understand this coupling and to identify its dynamical consequences from a biochemical viewpoint. In contrast, much less is known about how the mechanical interactions between cells affect these dynamics. Recent work has shown, for instance, that circadian oscillations degrade substantially in populations of cells in vitro when cell density decreases sufficiently. Here we use this fact to constrain a standard model of circadian oscillations, and propose a way through which external mechanical signals and internal biochemical interactions could combine in clock cells.