MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract

Flockerzi, Dietrich

N-site phosphorylation systems with 2N-1 steady states

with Carsten Conradi (also MPI Magdeburg, em e-mail: conradi@mpi-magdeburg.mpg.de) and
Katharina Holstein (Fraunhofer IFF VDTC, Joseph-von-Fraunhofer-Strasse 1, 39106 Magdeburg, Germany, em e-mail: katharina.holstein@iff.fraunhofer.de)

Multisite phosphorylation networks are encountered in many intracellular processes like signal transduction, cell-cycle control or nuclear signal integration. In em Wang and Sontag, 2008, the authors study the number of steady states in general $N$-site sequential distributive phosphorylation and show that there are at most $2N-1$ steady states. They furthermore conjecture that, for odd $N$, there are at most $N$ and that, for even $N$, there are at most $N+1$ steady states. Building on earlier work in em Holstein et.al., 2013, we present a scalar determining equation for multistationarity which will lead to $5$ steady states for a $3$-site and to $7$ steady states for a $4$-site phosphorylation system and hence to conterexamples to the conjecture of Wang and Sontag. We conclude with a brief biological interpretation of the inherent geometric properties of multistationarity.

em Keywords: Sequential distributed phosphorylation; mass-action kinetics; multistationarity; determining equation -- MR 37N25, 92C42, 92C45

small em References
(1) K. Holstein, D. Flockerzi, and C. Conradi: Multistationarity in sequential distributed multisite phosphorylation networks. em Bulletin of Mathematical Biology, 75: 2028-2058, 2013.
(2) L. Wang and E. Sontag: On the number of steady states in a multiple futile cycle. em Journal of Mathematical Biology, 57:29--52, 2008.