TY - JOUR

T1 - Multistationarity and Bistability for Fewnomial Chemical Reaction Networks

AU - Feliu, Elisenda

AU - Helmer, Martin

PY - 2019

Y1 - 2019

N2 - Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open mathematical problem. One successful strategy consists of analyzing small networks and deducing that some of the properties are preserved upon passage to the full network. Motivated by this, we study chemical reaction networks with few chemical complexes. Under mass action kinetics, the steady states of these networks are described by fewnomial systems, that is polynomial systems having few distinct monomials. Such systems of polynomials are often studied in real algebraic geometry by the use of Gale dual systems. Using this Gale duality, we give precise conditions in terms of the reaction rate constants for the number and stability of the steady states of families of reaction networks with one non-flow reaction.

AB - Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open mathematical problem. One successful strategy consists of analyzing small networks and deducing that some of the properties are preserved upon passage to the full network. Motivated by this, we study chemical reaction networks with few chemical complexes. Under mass action kinetics, the steady states of these networks are described by fewnomial systems, that is polynomial systems having few distinct monomials. Such systems of polynomials are often studied in real algebraic geometry by the use of Gale dual systems. Using this Gale duality, we give precise conditions in terms of the reaction rate constants for the number and stability of the steady states of families of reaction networks with one non-flow reaction.

KW - Chemical reaction networks

KW - Fewnomial systems

KW - Gale duality

KW - Multistationarity and bistability

KW - Real algebraic geometry

KW - Steady states of dynamical systems

UR - http://www.scopus.com/inward/record.url?scp=85058847056&partnerID=8YFLogxK

U2 - 10.1007/s11538-018-00555-z

DO - 10.1007/s11538-018-00555-z

M3 - Journal article

C2 - 30564990

AN - SCOPUS:85058847056

VL - 81

SP - 1089

EP - 1121

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 4

ER -