2013/12/17 by Dietrich Flockerzi, Flockerzi, Dietrich, Katharina Holstein +3
Biochemistry, Genetics and Molecular Biology · #37N25 #92C42 #92C45 #FOS: Biological sciences #Molecular Networks (q-bio.MN) #msc:37N25 #msc:92C42 #msc:92C45 #q-bio.MN
paper · pdf · doi:10.48550/arxiv.1312.4774
arxiv created 2014/04/23 · arxiv updated 2014/04/24
Multisite protein phosphorylation plays a prominent role in intracellular processes like signal transduction, cell-cycle control and nuclear signal integration. Many proteins are phosphorylated in a sequential and distributive way at more than one phosphorylation site. Mathematical models of n-site sequential distributive phosphorylation are therefore studied frequently. In particular, in \em Wang and Sontag, 2008, it is shown that models of n-site sequential distributive phosphorylation admit at most 2n-1 steady states. Wang and Sontag furthermore conjecture that for odd n, there are at most n and that, for even n, there are at most n+1 steady states. This, however, is not true: building on earlier work in \em Holstein et.al., 2013, we present a scalar determining equation for multistationarity which will lead to parameter values where a 3-site system has 5 steady states and parameter values where a 4-site system has 7 steady states. Our results therefore are counterexamples to the conjecture of Wang and Sontag. We furthermore study the inherent geometric properties of multistationarity in n-site sequential distributive phosphorylation: the complete vector of steady state ratios is determined by the steady state ratios of free enzymes and unphosphorylated protein and there exists a linear relationship between steady state ratios of phosphorylated protein.