Entropy as a Robustness Marker in Genetic Regulatory Networks

Area of Science:

• Systems Biology
• Computational Biology
• Genetics

Background:

• Genetic regulatory networks (GRNs) evolve complex control systems with inhibitors and activators.
• MicroRNAs (miRNAs) and circular RNAs (circRNAs) act as ubiquitous double brakes, reducing attractors in GRNs.
• Network complexity is defined by nodes, connectivity, strong components, and interaction graph size.

Purpose of the Study:

• To quantify GRN dynamics complexity using attractor entropy.
• To characterize stability and robustness by return rates after perturbations.
• To establish mathematical relationships between complexity, stability, and robustness indices.

Main Methods:

• Utilizing Markov chains for threshold Boolean random regulatory networks.
• Applying a Hopfield-like update rule for network dynamics.
• Defining complexity and stability using attractor entropy and Kolmogorov-Sinai entropy.

Main Results:

• Attractor entropy quantifies dynamical complexity by measuring invariant measure spread.
• Stability and robustness are characterized by recovery rates from dynamical and structural perturbations.
• Entropy measures of invariant measure and Markov transition matrix serve as complexity, stability, and robustness indices.

Conclusions:

• Links between complexity, stability, and robustness indices can characterize biological system resilience.
• This approach provides practical insights into the physiological and pathological dynamics of GRNs.
• The kinin-kallikrein system in angioedema serves as a case study for assessing GRN resilience.