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SUMMARY:A deficiency zero theorem for a class of power law kinetic systems
with independent decompositions
DTSTART;VALUE=DATE-TIME:20180711T050000Z
DTEND;VALUE=DATE-TIME:20180711T053000Z
DTSTAMP;VALUE=DATE-TIME:20241104T105303Z
UID:indico-contribution-10@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Angelyn Lao (De La Salle University)\nIn this paper\
, we study power law kinetics on chemical reaction networks with Independe
nt decompositions\, i.e. the network is the union of subnetworks whose rea
ction sets form a partition of the network's reaction set and the network'
s stoichiometric subspace is the direct sum of the stoichiometric subspace
s of the subnetworks. Our main result is a Deficiency Zero Theorem when th
e subnetworks are weakly reversible and have linear independent reactant c
omplexes (we denote the latter property as “zero reactant deficiency”)
and have kinetics with linear Independent kinetic order vectors (we denot
e this set of kinetics with “PL-RLK”). We elaborate the context of our
result by presenting an overview of previous results on network decomposi
tion (which we propose to call “Decomposition Theory”) and a discussio
n of existing Deficiency Zero Theorems. To our knowledge\, our result is t
he first Deficiency Zero Theorem which is valid for a class of kinetics wh
ich display non-reactant determined kinetic orders\, i.e. there are reacta
nt complexes whose branching reactions have differing kinetic order vector
s (we call this set of kinetics “PL-NDK”). In previous work\, we showe
d the occurrence of PL-NDK kinetics in numerous models of complex biochemi
cal systems. We apply our results to characterize the positive equilibria
of a power law approximation of R. Schmitz's model of the earth's carbon c
ycle in its pre-industrial state\, which provided the original motivation
for our study.\n\nhttps://conferences.maths.unsw.edu.au/event/2/contributi
ons/10/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/10/
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