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Abstract: We present a simple analytical tool which gives an approximate insight intothe stationary behavior of nonlinear systems undergoing the influence of a weakand rapid noise from one dominating source, e.g. the kinetic equationsdescribing a genetic switch with the concentration of one substrate fluctuatingaround a constant mean. The proposed method allows for predicting theasymmetric response of the genetic switch to noise, arising from thenoise-induced shift of stationary states. The method has been tested on anexample model of the lac operon regulatory network: a reduced Yildirim-Mackeymodel with fluctuating extracellular lactose concentration. We calculateanalytically the shift of the system-s stationary states in the presence ofnoise. The results of the analytical calculation are in excellent agreementwith the results of numerical simulation of the noisy system. The simulationresults suggest that the structure of the kinetics of the underlyingbiochemical reactions protects the bistability of the lactose utilizationmechanism from environmental fluctuations. We also show that, in theconsequence of the noise-induced shift of stationary states, the presence offluctuations stabilizes the behavior of the system in a selective way: althoughthe extrinsic noise facilitates, to some extent, switching off the lactosemetabolism, the same noise prevents it from switching on.



Autor: Anna Ochab-Marcinek

Fuente: https://arxiv.org/







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