Abstract
It is well-known that noises are inevitable in gene regulatory networks due to the low-copy numbers of molecules and environmental fluctuations. In this paper, we investigate the stationary probability distribution (SPD) between both low (OFF state) and high (ON state) protein levels and mean first passage time (MFPT) in an abstract model of the Myc/E2F/miR-17-92 network presented by Aguda et al., PNAS 105, 19678 (2008), where the gene expression is assumed to be disturbed simultaneously by intrinsic and extrinsic noises that were correlated. Our results show that (i) the OFF state is enhanced by the extrinsic noise (D), while the ON state is enhanced by the intrinsic noise (Q) or cross-correlation between two noises (λ); (ii) for the cases of negative or no cross-correlation (λ⩽0.0), the increase of the noise intensity (D or Q) leads to a decline of the MFPT and enhances the probability of toggle switch to the OFF state; (iii) but for the case of positive cross-correlation (λ>0.0), the MFPT as a function of the noise intensity (D or Q) exhibits a maximum, this maximum for MFPT identifies the characteristic of noise enhanced stability of the ON state and (iv) the cross-correlation between two noises can enhance stability of the ON state.
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