Before revision:  Using an analytical method of small noise expansion, I prove that when weak and rapid noise enters the system through a reaction of Michaelis-Menten type (reactionrate function monotonically increasing and concave) , then the steady states of the system always shift to the right as noise intensity increases.
After revision:  The steady-state displacement due to small noise is independent on the kinetics of the system but it only depends on the nonlinearity of the input function. For monotonically increasing and concave input functions such as the Michaelis-Menten uptake rate, we give a simple argument based on the small-noise expansion, which enables qualitative predictions of the steady-state displacement only by inspection of experimental data: when weak and rapid noise enters the system through a reaction of Michaelis-Menten type (reactionrate function monotonically increasing and concave) , then the steady states of the system always shift to the right as noise intensity increases.