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

Abstract

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.

Molecular Engineering of Robustness and Resilience in Enzymatic Reaction Networks

“…19,20 Figure 3a illustrates how we use flow (with flow rate constant k f ) 37 to maintain the network out-of-equilibrium. In flow, our system exhibits sustained oscillations only in a limited parameter space.…”

Design of a multicellular feedback control strategy in a synthetic bacterial consortium

“…Orthogonal quorum sensing systems are being exploited to implement communication across the two populations within the consortium [27]. Moreover, in a realistic scenario the interaction between the inducer molecule acting as the external control reference and the parts within the controller population could be mediated by an intermediate species which in turn affects the production of the regulator forming the complex with the signaling molecule coming from the target cells [28].…”

Interaction sign patterns in biological networks: From qualitative to quantitative criteria

“…An inhibited module and an activated module are suitably interconnected in the synthetic biomolecular circuits proposed in [8], so as to induce by design oscillatory and bistable behaviours in minimal network models with monomeric regulators.…”

“…where (consistently with the reasonable parameter values for the system that are given in [8]) we can choose as nominal valuesā = 4 · 10 −3 ,b = 3 · 10 −3 ,c = 2 · 10 −3 ,d = 3 · 10 −2 , e = 6 · 10 −3 ,f = 1 · 10 −3 ,k = 4 · 10 −3 andh = 3 · 10 −3 . Parameters h and k represent the effect of titration reactions.…”

“…The system describing the activated module, after a sign change in the second variable, has a Jacobian J (A) of the same form (12), where now reasonable nominal values [8] areā = 3 · 10 −3 ,b = 80 · 10 −3 ,c = 2 · 10 −3 ,d = 3 · 10 −2 , e = 6 · 10 −3 ,f = 1 · 10 −3 ,k = 4 · 10 −3 andh = 3 · 10 −3 . Also in this case, h and k represent the effect of titration.…”