Determining the key biochemical species to forewarn sudden transitions in Cdc2-cyclin B/Wee1 system

The Cdc2-cyclin B/Wee1 kinase system exhibits bistability between alternative steady states,which emerges due to the mutual inhibition between Cdc2-cyclin B and Wee1 kinases. Al-ternative steady states are M phase-like state and G2 arrest state, which have implicationsin the cell cycle progression at the G2 phase in eukaryotic cells. A slight alteration in thefeedback strength can drive sudden transitions between these contrasting alternative statesupon crossing a critical threshold or a tipping point. The phenomenon of critical slowingdown (CSD) has been widely used to identify the proximity to a tipping point. However,determining the key variable or species that best signals CSD is a challenging task and holdssignificance in complex biological processes. Here, we determine the leading variable or ob-servation direction (OD) from the direction of CSD to best detect an upcoming transitionin the Cdc2-cyclin B/Wee1 model system. We find that with increasing feedback strength,the Cdc2-cyclin B is the OD, as it produces a stronger signal than that of Wee1. Withdecreasing feedback strength, both Cdc2-cyclin B and Wee1 produce similar signals and canbe used as OD. Further, the noise-sensitive direction highlights the effect of stochasticity inCdc2-cyclin B and Wee1 for increasing and decreasing feedback strength, respectively. Wealso perform sensitivity analyses that reveal the robustness of the OD. Finally, we comparethe efficacy of OD with principal component analysis (PCA) while detecting a tipping point.