(317c) Substrate-Induced Oscillatory Activity of An Enzyme Regulated by Multisite Phosphorylation

Despite the fact that the MAPK signaling cascade has been well studied before due to its fundamental importance in life science, studies of oscillatory behavior associated with it are relatively few.

One of these studies [1] shows that oscillatory activity can arise proactively from the backward coupling between a bistable double phosphorylation stage and a previous upstream stage in the cascade.

Recent studies [2] demonstrated that substrates can control the level of MAPK phosphorylation retroactively by competing with phosphatases.

In this work, we demonstrate that oscillatory activity can also be induced retroactively in a double phosphorylation  stage by a downstream substrate,  whose degradation is catalyzed by the end product of the stage (the double phosphorylated enzyme form);  this constitutes a forward coupling between the double phosphorylation stage and a downstream stage in the cascade.

We propose a simple form of such a system, and present parameter values for which oscillatory activity arises.

We then reduce the full model (using time-scale separation) to a simplified one, which qualitatively agrees with the full model at the appropriate limit.

We quantify the behavior in the form of a two-parameter diagram: one parameter is related to the level of input to the cascade, while the other is related to the load (the amount of downstream substrate).

The resulting monostable, bistable and oscillatory regimes are marked on this diagram. Based on our observations we hypothesize the existence of two necessary (even if not sufficient) conditions for the oscillatory activity to arise in this system: (1) an associated subsystem – keeping the substrate level fixed – is bistable;  and (2) a separation exists between the time scale of substrate degradation (slow) and those associated with the double phosphorylation stage (fast).

References

1. Qiao, L., R. B. Nachbar, I.G. Kevrekidis, S. Y. Shvartsman. 2007. Bistability and oscillations in the Huang-Ferrell model of MAPK signaling. PLOS Comput. Biol. 3:1819-1826.
2. Kim, Y., Z. Paroush, K. Nairz, E. Hafen, G. Jimenez, and S. Y. Shvartsman. 2011. Substrate-dependent control of MAPK phosphorylation in vivo. Mol. Syst. Biol. 7:467.