Statistical Mechanics of Organization, Information, and Emergence in Protein Networks

Abstract

Biochemical networks usually possess information that expresses the degree of organization and integration of the system. A function, I(X : Y)_N, called mutual information of integration, allows one to define, on a quantitative basis, three dierent types of organization and integration of these systems. If I(X : Y)_N = 0, the network is devoid of any collective property and does not possess any information. If, alternatively, I(X : Y)_N > 0, the system is integrated, i.e., it behaves as a coherent whole but possesses few collective properties. Last, if I(X : Y)_N < 0, the system is emergent, or complex, and possesses many collective properties. Reduction of the properties of a network to the properties of its component subnetworks is possible only in the first case considered above. Emergence of both information and collective properties in a protein network can appear as a consequence of a competition between two ligands for the same sites of a protein, or as a consequence of conformation changes of the proteins. One can easily derive the expression of the mutual information of integration of a network in steady state provided that a condition, called generalized microscopic reversibility, applies. This condition implies that the transition states of substrate release and catalysis stabilize the same conformation of the enzyme involved in these two processes. Departure from generalized microscopic reversibility, and from thermodynamic equilibrium, results in a change of the value of the mutual information of integration of the system.