Signal and noise propagation in genetic circuits

Abstract

Interactions between genes in living organisms are intrinsically stochastic. This not only gives rise to phenotypic variation in clonal populations of cells, but also fundamentally limits signaling fidelity and cellular memory. Accurately predicting noise propagation in gene networks is thus crucial for reverse engineering natural networks and designing reliable synthetic genetic circuits. To determine how noise propagates through gene networks we measure, in single bacterial cells, expression variability and correlations between genes in a cascade and correlations with a constitutive gene. We find that noise in a gene is determined by its intrinsic fluctuations, transmitted noise from upstream genes and global noise affecting all genes. Our results imply that the dominant noise sources can be external to any given gene and that even for networks in which no component has significant intrinsic noise, total noise can be significant due to amplification of global fluctuations. We develop a Langevin type model that explains the complex behaviour exhibited by the noises and correlations, and reveals the dominant noise sources from the biochemical characteristics of the individual genes. The model successfully predicts the noises and correlations as the network is systematically perturbed. It also indicates that the additional information from the protein expression distributions can be used to better determine the system parameters and provides the basis for a Monte Carlo simulation method, which allows for fast, approximate simulations of the distributions.

As an extension and proof of applicability of the approach, we choose a natural network, the E. Coli lactose uptake network, to predict the dynamic behaviour of the distributions. We measure population distributions of protein numbers as a function of time, and show that prediction of dynamic distributions requires only a few noise parameters from the steady state noise measurements in addition to the rates that characterize a deterministic model. Our results show that even though noise sources are ubiquitous and network dependent, the protein distributions and even their dynamic behavior can be predicted from basic parameters, and the simplicity of the formulae brings the promise of decoding and designing the genetic networks that control the function of all living cells.