Parameter regions that give rise to 2[n/2]+1 positive steady states in the n-site phosphorylation system
The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and Sontag (2008) it is shown that for certain choices of the reaction rate constants and total conservation constants, the system can have 2[n/2]+1 positive steady states (that is, n+1 positive steady states for n even and n positive steady states for n odd). In this paper we give open parameter regions in the space of reaction rate constants and total conservation constants that ensure these number of positive steady states, while assuming in the modeling that roughly only 1/4 of the intermediates occur in the reaction mechanism. This result is based on the general framework developed by Bihan, Dickenstein, and Giaroli (2018), which can be applied to other networks. We also describe how to implement these tools to search for multistationarity regions in a computer algebra system and present some computer aided results.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
On the reaction rate constants that enable multistationarity in the two-site phosphorylation cycle
Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualit…
Phenomenology of an in-host model of hepatitis C
This paper carries out an analysis of the global properties of solutions of an in-host model of hepatitis C for general values of its parameters. A previously unknown stable steady state on the boundary of the positive o…
Some bounds on positive equilibria in mass action networks
We present some results helpful for parameterising positive equilibria, and bounding the number of positive nondegenerate equilibria, in mass action networks. Any mass action network naturally gives rise to a set of poly…
Parameter region for multistationarity in $n-$site phosphorylation networks
Multisite phosphorylation is a signaling mechanism well known to give rise to multiple steady states, a property termed multistationarity. When phosphorylation occurs in a sequential and distributive manner, we obtain a …
A necessary condition for non-monotonic dose response, with an application to a kinetic proofreading model -- Extended version
Steady state nonmonotonic ("biphasic") dose responses are often observed in experimental biology, which raises the control-theoretic question of identifying which possible mechanisms might underlie such behaviors. It is …