The study of biochemical pathways usually focuses on a small section of the protein interaction network. Fluctuations in such a system are not only generated intrinsically by molecular dynamics, but also extrinsically, by interactions of the system with the rest of the network and its environment. Concentration fluctuations of a substance outside the studied system can enter it through a nonlinear uptake reaction which acts as a nonlinear filter. Varying the intensity of the input noise varies the mean of the output noise after the passage through the filter, which causes a change of stability properties of the system. 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. I demonstrate this by an example of two different models of lac operon . The bistable switch responds to fluctuations in extracellular TMG/lactose concentration  in an asymmetric manner because of the displacement of its bistability region to the right: As noise intensity increases, uninduction becomes easier and induction becomes more difficult . The steady-state displacement due to weak and rapid extrinsic noise passing through a nonlinear filter is a universal phenomenon: It is independent of the kinetics of the system but it only depends on the filtering function. The calculation method presented enables even qualitative predictions of this effect, only by inspection of the experimental data .
The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system : intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. 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 Michaelis-Menten reaction , then the graph of the system's steady states vs. the mean of the input signal always shifts to the right as noise intensity increases. We test the predictions on two models of lac operon , where TMG/lactose uptake is driven by a Michaelis-Menten enzymatic process. We show that as a consequence of the steady state displacement due to fluctuations in extracellular TMG/lactose concentration the lac switch responds in an asymmetric manner : as noise intensity increases, switching off lactose metabolism becomes easier and switching it on becomes more difficult .
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the protein interaction network. Fluctuations
a protein interactions network. Two distinct sources contribute to the noise
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are not only generated intrinsically by molecular dynamics, but also extrinsically, by interactions of the system with the rest of the network and its environment. Concentration fluctuations of a substance outside the studied system can enter it
: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system
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the intensity of the input noise
input noise intensity
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output
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causes a change of
changes the
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Using an analytical method of small noise expansion, I prove that
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:
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reaction of
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type (reactionrate function monotonically increasing and concave)
reaction
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steady states of the system always shift
graph of the system's steady states vs. the mean of the input signal always shifts
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I demonstrate this by an example of two different
We test the predictions on two
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. The bistable switch responds
, where TMG/lactose uptake is driven by a Michaelis-Menten enzymatic process. We show that as a consequence of the steady state displacement due
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the lac switch responds
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because of the displacement of its bistability region to the right: As
: as
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uninduction
switching off lactose metabolism
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induction
switching it on
D
. The steady-state displacement due to weak and rapid extrinsic noise passing through a nonlinear filter is a universal phenomenon: It is independent of the kinetics of the system but it only depends on the filtering function. The calculation method presented enables even qualitative predictions of this effect, only by inspection of the experimental data