Metabolic noise reduction for enzymatic reactions: the role of a negative feedback

This note deals with a basic (though rather general) enzymatic reaction scheme, and investigates the role of a negative feedback with respect to the noise reduction. To this end, three distinct cases are considered: one with the enzyme produced without feedback regulation, another with the enzyme regulated in feedback by the product of the enzymatic reaction, and a third one where the enzyme is self-regulated. Metabolic noise is evaluated in terms of the coefficient of variation of the product of the enzymatic reaction, aiming at measuring its fluctuations around the average steady-state value. Due to the high dimensionality and to the double time-scale of the considered reaction network, which makes unfeasible the classical theoretical/statistical computations of the equilibrium distribution, the system is investigated by means of the Linear Noise Approximation (LNA) approach and numerical results are reported. Furthermore, the assumption of Quasi-Steady- State Approximation (QSSA) is employed to obtain approximate analytical expressions of the noise. The results show the unmistakable role of the negative feedback, which always manages to reduce the metabolic noise with respect to the unregulated case.