Propagation of fluctuations in interaction networks governed by the law of mass action

Abstract

Using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. We introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. Our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. We then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. An exact analytic expression for the decay constant is obtained for the case of uniform interactions on the Bethe lattice. Our general findings are illustrated using a real biological network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.

4 pages; 2 figures

References in corpus (1)

• Propagation of large concentration changes in reversible protein binding networks

Cited by in corpus (6)

• Propagation of large concentration changes in reversible protein binding networks
• Topological Determinants of Perturbation Spreading in Networks
• Fluctuations in Mass-Action Equilibrium of Protein Binding Networks
• Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity
• Stability of gene regulatory networks
• Cost and Capacity of Signaling in the Escherichia coli Protein Reaction Network