TY - JOUR

T1 - Intermediates, Catalysts, Persistence, and Boundary Steady States

AU - Marcondes de Freitas, Michael

AU - Feliu, Elisenda

AU - Wiuf, Carsten

PY - 2017

Y1 - 2017

N2 - For dynamical systems arising from chemical reaction networks, persistenceis the property that each species concentration remains positively bounded awayfrom zero, as long as species concentrations were all positive in the beginning. Wedescribe two graphical procedures for simplifying reaction networks without breakingknown necessary or sufficient conditions for persistence, by iteratively removing socalledintermediates and catalysts from the network. The procedures are easy to applyand, in many cases, lead to highly simplified network structures, such as monomolecularnetworks. For specific classes of reaction networks, we show that these conditionsfor persistence are equivalent to one another. Furthermore, they can also be characterizedby easily checkable strong connectivity properties of a related graph. In particular,this is the case for (conservative) monomolecular networks, as well as cascades of alarge class of post-translational modification systems (of which the MAPK cascadeand the n-site futile cycle are prominent examples). Since one of the aforementionedsufficient conditions for persistence precludes the existence of boundary steady states,our method also provides a graphical tool to check for that.

AB - For dynamical systems arising from chemical reaction networks, persistenceis the property that each species concentration remains positively bounded awayfrom zero, as long as species concentrations were all positive in the beginning. Wedescribe two graphical procedures for simplifying reaction networks without breakingknown necessary or sufficient conditions for persistence, by iteratively removing socalledintermediates and catalysts from the network. The procedures are easy to applyand, in many cases, lead to highly simplified network structures, such as monomolecularnetworks. For specific classes of reaction networks, we show that these conditionsfor persistence are equivalent to one another. Furthermore, they can also be characterizedby easily checkable strong connectivity properties of a related graph. In particular,this is the case for (conservative) monomolecular networks, as well as cascades of alarge class of post-translational modification systems (of which the MAPK cascadeand the n-site futile cycle are prominent examples). Since one of the aforementionedsufficient conditions for persistence precludes the existence of boundary steady states,our method also provides a graphical tool to check for that.

KW - math.DS

KW - q-bio.MN

U2 - 10.1007/s00285-016-1046-9

DO - 10.1007/s00285-016-1046-9

M3 - Journal article

C2 - 27480320

VL - 74

SP - 887

EP - 932

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 4

ER -