[Emergence and biological complexity]

Biological networks possess an organization that expresses their potential information. A function, I(X:Y)N, called mutual information of integration, define, on a quantitative basis, three types of organization. If I(X:Y)N=0, the properties of the global system XY can be reduced to the properties of its component sub-systems X and Y. Hence, XY is not a real system displaying collective properties but the mere collection of X and Y. Its properties are the properties of the sub-systems X and Y. If I(X:Y)N>0, the system is integrated. Although it behaves as a coherent whole, it does not possess many collective properties. Last, if I(X:Y)N<0, the system possesses emergent collective properties and can be considered complex for it possesses many collective properties that cannot be predicted from the independent study of component sub-systems X and Y. In a biological system, the emergence of information usually means the emergence of a novel function. This is probably what is occurring with enzymes. If a protein binds two ligands able to interact, and if the condition above is fulfilled, then the protein behaves as an enzyme able to allow a catalytic reaction between the two reagents.