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• W2783137521 abstract "Nullclines provide a convenient way of characterising and understanding the behaviour of low dimensional nonlinear deterministic systems, but are, perhaps not unsurprisingly, a poor predictor of the behaviour of discrete state stochastic systems in the low numbers regime. Such models are appropriate in many biological systems. In this paper we propose a graphical discrete ‘nullcline-like’ construction, inspired by the Markov chain tree theorem, and investigate its application to the original genetic toggle switch, which is a feedback interconnection of two mutually repressing genes. When the feedback gain (the ‘cooperativity’) is sufficiently large, the deterministic system exhibits bistability, which shows itself as a bimodal stationary distribution in the discrete stochastic system for sufficiently large numbers. However, at small numbers a third mode appears corresponding to roughly equal numbers of each molecule. Without cooperativity, on the other hand (i.e. low feedback gain), the deterministic system has just one stable equilibrium. Nevertheless, the stochastic system can still exhibit bimodality. In this paper, we illustrate that the discrete ‘nullclines’ proposed can, without the need to calculate the steady state distribution, provide an efficient graphical way of predicting the shape of the stationary probability distribution in different parameter regimes, thus allowing for greater insights in the observed behaviours." @default.
• W2783137521 created "2018-01-26" @default.
• W2783137521 creator A5057008878 @default.
• W2783137521 creator A5071692930 @default.
• W2783137521 date "2017-12-01" @default.
• W2783137521 modified "2023-10-14" @default.
• W2783137521 title "Understanding the discrete genetic toggle switch phenomena using a discrete ‘nullcline’ construct inspired by the Markov chain tree theorem" @default.
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• W2783137521 doi "https://doi.org/10.1109/cdc.2017.8263881" @default.
• W2783137521 hasPublicationYear "2017" @default.
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