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Self-sustaining positive feedback loops in discrete and continuous systems.

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We identified conditions for self-sustaining positive feedback loops in gene regulatory and signal transduction networks. These robust feedback loops can trap system states, ensuring stability even with external control.

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Biomolecular networksBoolean modelsFeedbackNetwork controlODEs

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Area of Science:

  • Systems biology
  • Biophysics
  • Computational biology

Background:

  • Gene regulatory networks (GRNs) and signal transduction pathways are crucial for cellular functions.
  • Monotonic ordinary differential equations (ODEs) with Hill functions are common dynamic frameworks for modeling these biological systems.
  • Understanding the conditions for stable system states and feedback mechanisms is essential.

Purpose of the Study:

  • To derive conditions under which activity or inactivity in one component of a biological network induces and sustains activity or inactivity in another.
  • To characterize the properties of positive feedback loops in these dynamic systems, specifically their self-sustaining and control-robust nature.
  • To demonstrate the practical application of these findings using examples of bistability, hysteresis, and a T-cell signaling model.

Main Methods:

  • Modeling biological networks using monotonic ordinary differential equations (ODEs) composed of Hill functions.
  • Deriving mathematical conditions for sustained activity or inactivity propagation between system variables.
  • Analyzing the emergent properties of positive feedback loops, including state-space trapping.
  • Applying the derived conditions to analyze established models of gene regulation and signal transduction.

Main Results:

  • Identified specific conditions that lead to self-sustaining positive feedback loops in biological networks.
  • Demonstrated that these feedback loops can "trap" the system in a particular state, making it robust to external perturbations.
  • Showcased the utility of the framework by analyzing bistability and hysteresis in gene regulatory networks.
  • Successfully applied the analysis to a T-cell signal transduction model from existing literature.

Conclusions:

  • The derived conditions provide a theoretical foundation for understanding robust feedback mechanisms in biological networks.
  • The concept of state-space trapping explains the stability and resilience observed in systems with positive feedback.
  • This framework offers valuable insights for the design and analysis of synthetic biological circuits and understanding cellular decision-making.