Detecting parameter regions for bistability in reaction networks

Angelica Torres; Elisenda Feliu

Detecting parameter regions for bistability in reaction networks

Department of Mathematical Sciences

1 Downloads (Pure)

Abstract

Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling.

Original language	English
Journal	arXiv.org
Publication status	Published - 30 Sept 2019

Access to Document

1909.13608v1

Cite this

@article{f99154860af04851b91b7b5bdc7a2511,

title = "Detecting parameter regions for bistability in reaction networks",

abstract = " Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling. ",

keywords = "q-bio.MN, math.DS",

author = "Angelica Torres and Elisenda Feliu",

year = "2019",

month = sep,

day = "30",

language = "English",

journal = "arXiv.org",

}

TY - JOUR

T1 - Detecting parameter regions for bistability in reaction networks

AU - Torres, Angelica

AU - Feliu, Elisenda

PY - 2019/9/30

Y1 - 2019/9/30

N2 - Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling.

AB - Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling.

KW - q-bio.MN

KW - math.DS

M3 - Journal article

JO - arXiv.org

JF - arXiv.org

ER -