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What do we mean by biological complexity?

Jacques Ricard¹

¹Institut Jacques-Monod, CNRS, université Paris-7, 2, place Jussieu, 75251 Paris cedex 05, France. meunier@ijm.jussieu.fr

Comptes Rendus Biologies

|May 21, 2003

Summary

Biological networks exhibit integration, emergence, and complexity by analyzing information theory. Network properties determine if joint entropy equals, exceeds, or falls below individual entropies, indicating information content and complexity.

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Area of Science:

Systems biology
Information theory
Biophysics

Background:

Biological networks, such as enzyme and metabolic networks, often involve nodes not associated with all network properties.
Classical information theory principles, like subadditivity, may not apply in these complex scenarios.

Purpose of the Study:

To precisely define integration, emergence, and complexity in biological networks using information theory.
To explore how joint entropy relates to individual entropies in network analysis.

Main Methods:

Application of Shannon's information theory to biological networks.
Analysis of subadditivity principles in relation to network properties and node associations.
Investigation of joint entropy versus the sum of individual entropies for network components.

Main Results:

If joint entropy equals the sum of individual entropies, network properties reduce to component properties, indicating no information.
If joint entropy is less than the sum of individual entropies, the network displays integration and positive information.
If joint entropy is smaller than the sum of individual entropies, the network exhibits emergent properties, complexity, and negative information.

Conclusions:

The relationship between joint and individual entropies quantifies network integration, emergence, and complexity.
Negative information, indicative of complexity, is enhanced in systems far from equilibrium.
Information theory provides a framework for understanding the information processing capabilities of biological systems.

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