Modeling noise propagation in time-delayed auto-inhibitory genetic circuits

Abstract

The abundance of specific protein molecules in genetically identical cell populations exposed to the same external environment can show remarkable cell-to-cell variations as biochemical reactions are inherently stochastic and occur with low numbers of molecular copies. Such variations in gene products are commonly known as gene expression noise. One of the mechanisms for cells to reduce such noise is auto-regulatory negative feedback (auto-inhibition), commonly found across organisms. This auto-inhibition is subjected to unavoidable time-delays associated with transcriptional and translational processes. Sufficient time-delays and strong auto-inhibition can generate sustained oscillations in gene products, which is a common mechanism for precise timekeeping in many biomolecular clocks. While the importance of time-delays in the generation of oscillations is well appreciated, its role in stochastic dynamics is not well understood in the absence of sustained oscillations. Here, we investigate the interplay between the feedback strength and the time-delay to study the noise propagation in the non-oscillatory regime using linear stability analysis, the linear noise approximation, and stochastic simulations. From a simple auto-regulatory model with one protein species (no delay), we systematically introduce one-step and two-step time-delays by incorporating intermediate dynamics with additional second and third species, respectively. Interestingly, the negative feedback in the presence of time-delay can show counterintuitive noise behavior to our common perception about its role as a noise buffer.