Basins of Attraction, Commitment Sets, and Phenotypes of Boolean Networks

Area of Science:

• Computational Biology
• Systems Biology
• Network Science

Background:

• Boolean networks are crucial for systems biology but analyzing their attractors and basins is computationally challenging.
• Existing software lacks robust tools for computing and visualizing basins, especially for asynchronous, non-deterministic models.
• States in non-deterministic models can belong to multiple basins, complicating theoretical and computational approaches.

Purpose of the Study:

• To develop methods for partitioning the state space of Boolean networks based on attractor commitment.
• To introduce and formalize notions of markers and phenotypes for analyzing long-term behaviors of selected network nodes.
• To provide computational tools for analyzing these concepts in biological systems.

Main Methods:

• Partitioning the state space into attractor commitment sets.
• Generalizing commitment sets to define markers and phenotypes based on pre-selected node behaviors.
• Developing equivalent Computation Tree Logic (CTL) model checking queries.
• Extending the NuSMV model checker and integrating new modules into the PyBoolNet Python package.

Main Results:

• Successfully partitioned state spaces into attractor commitment sets.
• Defined and computed markers and phenotypes, illustrating their utility in a bladder cancer model.
• Provided an extended NuSMV version and new PyBoolNet modules for computing and visualizing these sets.

Conclusions:

• The developed methods and tools facilitate the analysis of complex Boolean networks, particularly in systems biology.
• Attractor commitment sets, markers, and phenotypes offer a robust framework for understanding system dynamics and long-term behaviors.
• The PyBoolNet package provides accessible tools for researchers to compute and visualize these complex network properties.