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Minimum complexity drives regulatory logic in Boolean models of living systems
Ajay Subbaroyan1,2, Olivier C Martin3,4, Areejit Samal1,2
1The Institute of Mathematical Sciences (IMSc), Chennai 600113, India.
PNAS Nexus
|January 30, 2023
Summary
Biological networks utilize specific Boolean functions (BFs), not random ones. This study finds that simpler, less complex BFs like read-once functions (RoFs) and nested canalyzing functions (NCFs) are common, explaining their odd bias and regulatory importance.
Area of Science:
- Systems Biology
- Computational Biology
- Network Science
Background:
- Random Boolean networks (RBNs) are widely used to model biological regulation.
- The logical update rules (Boolean functions, BFs) in these networks are often assumed to be random, which may not reflect biological reality.
Purpose of the Study:
- To investigate the prevalence of biologically meaningful Boolean functions (BFs) in published regulatory network models.
- To explain observed properties of these BFs, such as odd bias and enrichment of specific function types, using complexity measures.
Main Methods:
- Systematic analysis of 2,687 BFs extracted from published biological network models.
- Evaluation of BFs based on two complexity measures: Boolean complexity and average sensitivity.
- Correlation of function properties (e.g., odd bias) with minimized complexity.
Main Results:
- A significant proportion of BFs from biological models exhibit an odd bias (odd number of ON outputs across input combinations).
- Read-once functions (RoFs) and nested canalyzing functions (NCFs) are enriched in biological models.
- RoFs minimize Boolean complexity and inherently possess odd bias; NCFs minimize both Boolean complexity and average sensitivity.
Conclusions:
- The non-random nature of BFs in biological networks is characterized by minimized complexity.
- Odd bias and the prevalence of RoFs and NCFs are explained by their low Boolean complexity and average sensitivity.
- Minimum complexity is a key principle underlying the regulatory logic of biological networks.
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