High Cooperativity In Negative Feedback Can Amplify Noisy Gene Expression

Abstract

Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protein. Increasing the strength of the feedback may lead to dramatically different outcomes depending on a key parameter, the noise load, which is defined as the squared coefficient of variation the protein exhibits in the absence of feedback. Combining stochastic simulation with asymptotic analysis, we identify a critical value of noise load: for noise loads smaller than critical, the coefficient of variation remains bounded with increasing feedback strength; contrastingly, if the noise load is larger than critical, the coefficient of variation diverges to infinity in the limit of ever greater feedback strengths. Interestingly, high-cooperativity feedbacks have lower critical noise loads, implying that low-cooperativity feedbacks in burst size can be preferable for noisy proteins. Finally, we discuss our findings in the context of previous results on the impact of negative feedback in burst size and burst frequency on gene-expression noise.