Abstract
Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.
Highlights
Multistability is one of the clearest manifestations of nature’s nonlinearity
We demonstrate that in a noisy system, a dynamically changing switch confers robustness to the transition timing if the noise in the slow variable is negligible compared to the noise in the fast variable
Mitotic entry is triggered by the activation of the kinase cyclin-dependent kinase 1 (Cdk1), which sets into motion many of the changes a cell undergoes during mitosis
Summary
Multistability is one of the clearest manifestations of nature’s nonlinearity. A multistable system can, under exactly the same conditions, be in different stable steady states. When there are multiple valleys, the ball’s initial position determines where it will end up These valleys can appear and disappear as the shape of the terrain changes. Another way to look at such a changing terrain is by plotting the steady state position of the ball (labeled output) as a function of a parameter that determines the shape of the terrain (labeled input) (Fig 1B). When the input crosses a threshold value, the initial stable valley disappears and the ball is forced to move to the right valley (situation 3). This transition is discontinuous, fast and irreversible. These points are called saddle-node points in the language of bifurcation theory
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