Anomalous fluctuation scaling laws in stochastic enzyme kinetics: Increase of noise strength with the mean concentration

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It is commonly thought that if a rate constant is perturbed such that the intracellular concentration of a certain species increases, then the fluctuations in the concentration will correspondingly decrease in strength. We here test whether this conventional wisdom generally holds true. We study the dependence of the noise strength (the coefficient of variation) in protein concentrations as a function of the mean protein concentration for a system in which protein is transported in and out of an intracellular compartment and it is catalyzed into a product by a multisubunit enzyme inside the compartment. The mean protein concentration is varied through perturbation of one of the rate constants. For low protein concentrations, the noise strength scales as [P]-1/2, where [P] is the mean concentration; this is the conventional fluctuation scaling law. However, we show that over a wide range of physiological concentrations, there are manifest anomalous fluctuation scaling laws proportional to [P]0 and [P](N-1)/2, where N is the number of binding sites of the multisubunit enzyme. These laws are particularly conspicuous when the rate of protein import into the compartment is much larger than its export rate out of the compartment and when the enzyme exhibits positive cooperativity. The results imply that over a certain range of physiological concentrations, noise strength remains the same or increases with the mean protein concentration. This contradicts the popularly held notion that noise strength decreases with increasing concentration and suggests that noise can be important even when the number of molecules is large.

Original languageEnglish
Article number012710
JournalPhysical Review E - Statistical, Nonlinear and Soft Matter Physics
Issue number1
Publication statusPublished - 16 Jan 2014


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