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 qualitative behavior of the solutions with respect to the parameter values gives rise to complex problems within real algebraic geometry, concerning the study of the signs of multivariate polynomials over the positive orthant. In this work we provide further insight into the number of positive steady states of a benchmark model, namely the two-site phosphorylation cycle. In particular, we provide new conditions on the reaction rate constants for the existence of one or three positive steady states, partially filling a gap left in previous works.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
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 p…
In distributive phosphorylation catalytic constants enable non-trivial dynamics
Ordered distributive double phosphorylation is a recurrent motif in intracellular signaling and control. It is either sequential (where the site phosphorylated last is dephosphorylated first) or cyclic (where the site ph…
Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an …
The multistationarity structure of networks with intermediates and a binomial core network
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous wo…
Understanding Multistationarity of Fully Open Reaction Networks
This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multi…
EpidemiologyGraph AttentionGraph Learning