Connectivity, Sensitivity, and Attractor Dynamics in Boolean Networks (Spring 2027)

Boolean networks are widely used to model complex biological systems, particularly gene regulatory networks, and to understand how interactions among individual components give rise to collective behavior. How do network connectivity and dynamical sensitivity influence the long-term behavior of Boolean networks? Previous studies have suggested that Boolean networks with lower sensitivity tend to exhibit more ordered dynamics, including fewer and shorter attractors. However, the extent to which these relationships hold across different network structures and modeling assumptions remains an important question.

In this project, students will work on this question using both theoretical and computational approaches. For the latter, they will use BoolForge, our recently developed Python package for the controlled generation and analysis of Boolean networks, to investigate two related questions: (1) Does effective connectivity provide a better predictor of attractor dynamics than traditional connectivity? (2) How does average sensitivity relate to the number and lengths of attractors?

Students will revisit selected findings from previous studies by generating random Boolean networks, analyzing their attractor structures, and systematically comparing results under different network properties and sampling assumptions. The project will combine computational experiments, data analysis, and mathematical reasoning, contributing to a broader research effort to better understand the relationship between network structure and dynamics.

For more information contact Ruodan Liu (rliu8@iastate.edu)

People:

Pre-requisites:

References:

[1] Kadelka, C., & Coberly, B. (2026). BoolForge: Controlled Generation and Analysis of Boolean Functions and Networks. Bioinformatics, 42(8), btag576. https://doi.org/10.1093/bioinformatics/btag576

[2] Shmulevich, I., & Kauffman, S. A. (2004). Activities and Sensitivities in Boolean Network Models. Physical Review Letters, 93, 048701. https://doi.org/10.1103/PhysRevLett.93.048701

[3] Gates, A. J., Correia, R. B., Wang, X., & Rocha, L. M. (2021). The Effective Graph Reveals Redundancy, Canalization, and Control Pathways in Biochemical Regulation and Signaling. Proceedings of the National Academy of Sciences, 118(12), e2022598118. https://doi.org/10.1073/pnas.2022598118