Probabilistic approach for predicting periodic orbits in piecewise affine differential models.

Area of Science:

• Systems Biology
• Computational Biology
• Dynamical Systems

Background:

• Piecewise affine models offer qualitative insights into system dynamics, particularly in genetic regulatory networks.
• These models partition state spaces into hyperrectangles, forming transition graphs for system trajectories.

Purpose of the Study:

• To propose and compare two novel definitions for transition probability between nodes in a piecewise affine system's graph.
• To enable parameter analysis by relating system parameters to observed transitions between hyperrectangles.

Main Methods:

• Defining transition probability based on the volume of initial conditions within a hyperrectangle leading to another.
• Representing system dynamics as trajectories on a transition graph with hyperrectangles as nodes.

Main Results:

• The proposed methods quantify transition probabilities, allowing for parameter inference and prediction.
• Demonstrated application in a gene regulatory network with two negative feedback loops.

Conclusions:

• The developed transition probability definitions facilitate parameter identification for desired system behaviors, such as high-probability periodic orbits.
• This approach aids in predicting likely periodic orbits based on system parameters, exemplified by gene regulatory network analysis.