Studying organisational closure in biological systems with process-enablement graphs

Area of Science:

• Systems Biology
• Theoretical Biology
• Graph Theory

Background:

• Biological self-organization is central to theories of life, requiring organisms to maintain their existence.
• Varying definitions of self-organization complicate identifying and comparing these features in biological systems.

Purpose of the Study:

• To develop a formal graph-theoretic framework, process-enablement graphs, for studying the organizational structure of living systems.
• To provide a precise method for comparing different models of biological self-organization.

Main Methods:

• Developed process-enablement graphs, where vertices are processes and edges represent enablements.
• Defined graph homomorphisms to enable comparison of biological models represented as graphs.
• Applied the formalism to analyze classical theories like autopoiesis, (F,A)-systems, and autocatalytic sets.

Main Results:

• A cycle in a process-enablement graph abstractly captures self-organizing components.
• The formalism provides a graph-theoretic definition of organizational closure.
• The study precisely illustrates similarities and differences in the organizational structures of various life theories.

Conclusions:

• Process-enablement graphs offer a consistent and precise way to compare descriptions of self-organization.
• The framework aids in studying systems with ambiguous life-like properties.
• While not demarcating living from non-living, it enhances the study of complex biological organization.