Computational analysis reveals the coupling between bistability and the sign of a feedback loop in a TGF-β1 activation model

Abstract

Background Bistable behaviors are prevalent in cell signaling and can be modeled by ordinary differential equations (ODEs) with kinetic parameters. A bistable switch has recently been found to regulate the activation of transforming growth factor-β1 (TGF-β1) in the context of liver fibrosis, and an ordinary differential equation (ODE) model was published showing that the net activation of TGF-β1 depends on the balance between two antagonistic sub-pathways. Results Through modeling the effects of perturbations that affect both sub-pathways, we revealed that bistability is coupled with the signs of feedback loops in the model. We extended the model to include calcium and Krüppel-like factor 2 (KLF2), both regulators of Thrombospondin-1 (TSP1) and Plasmin (PLS). Increased levels of extracellular calcium, which alters the TSP1-PLS balance, would cause high levels of TGF-β1, resembling a fibrotic state. KLF2, which suppresses production of TSP1 and plasminogen activator inhibitor-1 (PAI1), would eradicate bistability and preclude the fibrotic steady-state. Finally, the loop PLS − TGF-β1 − PAI1 had previously been reported as negative feedback, but the model suggested a stronger indirect effect of PLS down-regulating PAI1 to produce positive (double-negative) feedback in a fibrotic state. Further simulations showed that activation of KLF2 was able to restore negative feedback in the PLS − TGF-β1 − PAI1 loop. Conclusions Using the TGF-β1 activation model as a case study, we showed that external factors such as calcium or KLF2 can induce or eradicate bistability, accompanied by a switch in the sign of a feedback loop (PLS − TGF-β1 − PAI1) in the model. The coupling between bistability and positive/negative feedback suggests an alternative way of characterizing a dynamical system and its biological implications. Keywords: Bistability; Positive feedback; Computational modelling; ODEs; Dynamical systems; Biochemical network; TGF-β1; Bifurcation analysis