The Gain Stability and Output Signal-to-noise Ratio Analysis of the Negative Feedback Control in Genetic Circuits

S. Liu and C. Chen

Abstract
Negative feedback genetic circuits (NFGC) are key regulatory motif of cellular robustness with the capability of reducing noise in genetic interaction network. NFGC have the same control theory frame as negative feedback amplifier circuits (NFAC). NFAC can enhance gain stability and output signal-to-noise ratio (OSNR) of output signal (voltage). Whether NFGC possess these two advantages or not is still unclear. We have investigated the advantages of NFGC through using feedback depth analysis to explore the gain stability, and analyzed OSNR of some typical negative feedback genetic circuits by modeling the corresponding electrical systems. The two methods are both based on the similarity of electrical and biological systems within the control theory framework. We found that NFGC can achieve high gain stability compared with linear cascade. Meanwhile, negative feedback can enhance gain stability by adjusting effective input, thereby making genetic circuits more robust to noise. Moreover, OSNR in NFGC have no enhancement, compared with the respective linear cascades. These findings suggest novel implications in how cellular systems with negative feedback can control signal and noise, and supply some guidance for controlling and synthesizing genetic circuits.

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Keywords
noise control, effective input, synthetic biology, modelling