Graphical reduction of reaction networks by linear elimination of species

TY - JOUR

T1 - Graphical reduction of reaction networks by linear elimination of species

AU - Saez Cornellana, Meritxell

AU - Wiuf, Carsten

AU - Feliu, Elisenda

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the “fast” species are assumed effectively to be at steady state with respect to the “slow” species. Under this assumption the steady state equations can be used to eliminate the “fast” variables and a new ODE system with only the slow species can be obtained. We interpret a reduced system obtained by time-scale separation as the ODE system arising from a unique reaction network, by identification of a set of reactions and the corresponding rate functions. The procedure is graphically based and can easily be worked out by hand for small networks. For larger networks, we provide a pseudo-algorithm. We study properties of the reduced network, its kinetics and conservation laws, and show that the kinetics of the reduced network fulfil realistic assumptions, provided the original network does. We illustrate our results using biological examples such as substrate mechanisms, post-translational modification systems and networks with intermediates (transient) steps.

AB - The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the “fast” species are assumed effectively to be at steady state with respect to the “slow” species. Under this assumption the steady state equations can be used to eliminate the “fast” variables and a new ODE system with only the slow species can be obtained. We interpret a reduced system obtained by time-scale separation as the ODE system arising from a unique reaction network, by identification of a set of reactions and the corresponding rate functions. The procedure is graphically based and can easily be worked out by hand for small networks. For larger networks, we provide a pseudo-algorithm. We study properties of the reduced network, its kinetics and conservation laws, and show that the kinetics of the reduced network fulfil realistic assumptions, provided the original network does. We illustrate our results using biological examples such as substrate mechanisms, post-translational modification systems and networks with intermediates (transient) steps.

KW - math.DS

KW - q-bio.MN

KW - 92C42, 80A30

U2 - 10.1007/s00285-016-1028-y

DO - 10.1007/s00285-016-1028-y

M3 - Journal article

C2 - 27221101

SN - 0303-6812

VL - 74

SP - 195

EP - 237

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 1

ER -