Intermediates, Catalysts, Persistence, and Boundary Steady States
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Intermediates, Catalysts, Persistence, and Boundary Steady States. / Marcondes de Freitas, Michael; Feliu, Elisenda; Wiuf, Carsten.
In: Journal of Mathematical Biology, Vol. 74, No. 4, 2017, p. 887–932.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 160402408