Stochastic Analysis Of An Incoherent Feedforward Genetic Motif

TL;DR

This paper analyzes how incoherent feedforward genetic circuits buffer noise in protein levels and reveals that downstream noise can increase despite upstream noise being buffered, due to changes in fluctuation time-scales.

Contribution

It provides a mathematical analysis of stochastic dynamics in incoherent feedforward circuits, showing noise buffering at the protein level and downstream noise amplification.

Findings

Steady-state distribution of Y is independent of upstream regulator X.

Downstream noise in Z increases with upstream noise in X.

Fluctuation time-scales are key to noise propagation in the network.

Abstract

Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. One such mechanism is the incoherent feedforward circuit. We analyze a simplistic version of this circuit, where an upstream regulator X affects both the production and degradation of a protein Y. Thus, any random increase in X's copy numbers would increase both production and degradation, keeping Y levels unchanged. To study its stochastic dynamics, we formulate this network into a mathematical model using the Chemical Master Equation formulation. We prove that if the functional dependence of Y's production and degradation on X is similar, then the steady-distribution of Y's copy numbers is independent of X. To investigate how fluctuations in Y propagate downstream, a protein Z whose production rate only depend on Y is introduced. Intriguingly, results show that the extent of noise in Z increases with noise in X, in spite of the fact that the magnitude of noise in Y is invariant of X. Such counter intuitive results arise because X enhances the time-scale of fluctuations in Y, which amplifies fluctuations in downstream processes. In summary, while feedforward systems can buffer a protein from noise in its upstream regulators, noise can propagate downstream due to changes in the time-scale of fluctuations.