Dynamic effects of extrinsic noise in a simple oscillatory gene network with delayed negative-feedback regulation: an electronic modeling approach

Gene expression is intrinsically stochastic due to the small number of molecules involved in some of the underlying biochemical reactions. The resulting molecule-count random fluctuations are known as biochemical noise. The dynamic effects of intrinsic noise (that originated within the system) have been widely studied. However, the effects of the noise coming from other sources the system is in contact with, or extrinsic noise, is not so well understood. In this work we introduce an electronic model for a simple gene oscillatory network, with delayed negative-feedback regulation. Notably, this model accounts for the intrinsic biochemical noise due to the slow promoter switching between the active and inactive states; but dismisses biochemical noise due to mRNA and protein production and degradation. We characterize the oscillatory behavior of this gene network by varying all the relevant parameter values within biologically meaningful ranges. Finally, we investigate how different sources of extrinsic noise affect the system dynamic behavior. To simulate extrinsic noise we consider stochastic time series coming from another circuit simulating a gene network. Our results indicate that, depending on the parameter affected by extrinsic noise and the power spectra of the stochastic time series, the system quasi-periodic behavior is affected in different ways.