Molecular Titration Promotes Oscillations and Bistability in Minimal Network Models with Monomeric Regulators

Molecular titration is emerging as an important biochemical interaction mechanism within synthetic devices built with nucleic acids and the CRISPR/Cas system. We show that molecular titration in the context of feedback circuits is a suitable mechanism to enhance the emergence of oscillations and bistable behaviors. We consider biomolecular modules that can be inhibited or activated by input monomeric regulators; the regulators compete with constitutive titrating species to determine the activity of their target. By tuning the titration rate and the concentration of titrating species, it is possible to modulate the delay and convergence speed of the transient response, and the steepness and dead zone of the stationary response of the modules. These phenomena favor the occurrence of oscillations when modules are interconnected to create a negative feedback loop; bistability is favored in a positive feedback interconnection. Numerical simulations are supported by mathematical analysis showing that the capacity of the closed loop systems to exhibit oscillations or bistability is structural.