Stochastic fluctuations in protein interaction networks are nearly Poissonian

Abstract

Gene regulatory networks are comprised of biochemical reactions, which are inherently stochastic.Each reaction channel contributes to this stochasticity in different measure. In this paper we study the stochastic dynamics of protein interaction networks (PIN) that are made up of monomers and dimers. The network is defined by the dimers, which are formed by hybridizing two monomers.The size of a PIN was defined as the number of monomers that interacts with at least one other monomer (including itself). We generated 4200 random PIN of sizes between 2 and 8 (600 per size) and simulated via the Gillespie algorithm the stochastic evolution of copy numbers of all monomers and dimers until they reached a steady state. The simulations revealed that the Fano factors of both monomers and dimers in all networks and for all time points were close to one, either from below or above. Only 10% of Fano factors for monomers were above 1.3 and 10% of Fano factors for dimers were above 1.17, with 5.54 and 3.47 as the maximum value recorded for monomers and dimers, respectively. These findings suggests that PIN in real biological setting contribute to the overall stochastic noise that is close to Poisson. Our results also show a correlation between stochastic noise, network size and network connectivity: for monomers, the Fano factors tend towards 1 from above, while the Fano factors for dimers tend towards 1 from below. For monomers, this tendency is amplified with increased network connectivity.