Qualitative and quantitative nature of mutual interactions dictate chemical noise in a democratic reaction network

The functions of a living cell rely on a complex network of biochemical reactions that allow it to respond against various internal and external cues. The outcomes of these chemical reactions are often stochastic due to intrinsic and extrinsic noise leading to population heterogeneity. The majority of calculations of stochasticity in reaction networks have focused on small regulatory networks addressing the role of timescales, feedback regulations, and network topology in propagation of noise. Here we computationally investigated chemical noise in a network with democratic architecture where each node is regulated by all other nodes in the network. We studied the effects of the qualitative and quantitative nature of mutual interactions on the propagation of both intrinsic and extrinsic noise in the network. We show that an increased number of inhibitory signals lead to ultrasensitive switching of average and that leads to sharp transition of intrinsic noise. The intrinsic noise exhibits a biphasic power-law scaling with the average, and the scaling coefficients strongly correlate with the strength of inhibitory signal. The noise strength critically depends on the strength of the interactions, where negative interactions attenuate both intrinsic and extrinsic noise.