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Reduction, integration and emergence in biochemical networks
Author(s) -
Ricard Jacques
Publication year - 2004
Publication title -
biology of the cell
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.543
H-Index - 85
eISSN - 1768-322X
pISSN - 0248-4900
DOI - 10.1016/j.biolcel.2004.07.003
Subject(s) - reduction (mathematics) , basis (linear algebra) , biology , molecule , process (computing) , upper and lower bounds , node (physics) , combinatorics , physics , mathematics , computer science , quantum mechanics , mathematical analysis , geometry , operating system
Most studies of molecular cell biology are based upon a process of decomposition of complex biological systems into their components, followed by the study of these components. The aim of the present paper is to discuss, on a physical basis, the internal logic of this process of reduction. The analysis is performed on simple biological systems, namely protein and metabolic networks. A multi‐sited protein that binds two ligands x and y can be considered the simplest possible biochemical network. The organization of this network can be described through a comparison of three systems, i.e. XY , X and Y . X and Y are component sub‐systems that collect states x i and y j , respectively, i.e. protein states that have bound either i molecules of x (whether or not these states have also bound y ), or j molecules of y (whether or not these states have bound x ). XY is a system made up of the specific association of X and Y that collects states x i y j . One can define mean self‐informations per node of the network, < H(X) >, < H(Y) > and < H(X,Y) >. Reduction of the system XY into its components is possible if, and only if, < H(X,Y) >,is equal to the sum of < H(X) > and < H(Y) >. If < H(X,Y) > is smaller than the sum of< H(X) > and < H(Y) >, the system is integrated , for it has less self‐information than the set of its components X and Y . It can also occur that < H(X,Y) >, be larger than the sum of < H(X) > and < H(Y) >. Hence, the system XY displays negative integration and emergence of self‐information relative to its components X and Y . Such a system is defined as complex . Positive or negative integration of the system implies it cannot be reduced to its components. The degree of integration can be measured by a function < I ( X : Y )>, called mutual information of integration. In the case of enzyme networks, emergence of self‐information is associated with emergence of catalytic activity. Moreover, if the enzyme reaction is part of a metabolic sequence, its mutual information of integration can be increased by an effect of context of this sequence.