Fluctuations in Mass-Action Equilibrium of Protein Binding Networks

We consider two types of fluctuations in the mass-action equilibrium in protein binding networks. The first type is driven by slow changes in total concentrations of interacting proteins. The second type (spontaneous) is caused by quickly decaying thermodynamic deviations away from equilibrium. We investigate the effects of network connectivity on fluctuations by comparing them to scenarios in which the interacting pair is isolated from the network and analytically derives bounds on fluctuations. Collective effects are shown to sometimes lead to large amplification of spontaneous fluctuations. The strength of both types of fluctuations is positively correlated with the complex connectivity and negatively correlated with complex concentration. Our general findings are illustrated using a curated network of protein interactions and multiprotein complexes in baker’s yeast, with empirical protein concentrations.

Figure 1

Cumulative histogram of amplification factors for spontaneous (thermal) noise of equilibrium dimer concentrations $D_{ij}$ in the PPI network of yeast. Collective effects lead to amplification relative to the isolated dimer null model.

Figure 2

A comparison of the noise in a network dimer to two isolated dimer models defined in the text. The real noise is bound below and above by the isolated models ${\eta }^{\mathrm{isol}\mathrm{\text{−}}F}\le \eta \le {\eta }^{\mathrm{isol}\mathrm{\text{−}}C}$.