Noise reduction for enzymatic reactions: A case study for stochastic product clearance

A basic (though rather general) enzymatic reaction scheme is investigated here, with a substrate that transforms into a product by means of the catalytic action of an enzyme. The aim is of quantifying the effects of feedback in noise propagation. Noise sources are twofold: one affects the enzyme production, assuming to happen according to finite bursts of molecules; the other concerns the product clearance, with the classical linear elimination rate affected by a Bernoulli random variable that can switch 'on' or 'off' the clearance. Two distinct feedback control schemes on enzyme production are considered here: one from the final product of the pathway activity, the other from the enzyme accumulation (negative autoregulation). Metabolic noise is defined in terms of the square of the coefficient of variation of the product, and computations are carried out by means of moment equations. Results show that, according to the type of the feedback parameter chosen to tune the feedback action, one of the two feedback schemes is preferable to the other with respect to noise reduction.