Pseudo-nullclines enable the analysis and prediction of signaling model dynamics.

A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines.

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems.

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks.

Robustness in spatially driven bistability in signaling systems.

Biological systems are spatially organized. This microscopic heterogeneity has been shown to produce emergent complex behaviors such as bistability. Even though the connection between spatiality and dynamic response is essential to understand biological output, its robustness and extent has not been sufficiently explored.