Predicting flux-partitioning error in quasi-steady-state reductions of branched biochemical networks
Abstract
The quasi-steady-state approximation (QSSA) simplifies biochemical reaction networks by replacing fast intermediates with their local steady states. The accuracy of this reduction, however, depends on what the model is used to predict. In a branched network, the same branch fluxes determine both the total processing rate and the fractions directed toward competing fates. These two observables need not have the same reduction error. A first-order expansion shows that errors shared by all branches cancel when fluxes are normalized, whereas differences between branch corrections remain. The weighted dispersion of these branch-specific corrections therefore predicts the leading error in flux partitioning. This quantity can be calculated from the reduced trajectory and local derivatives, without integrating the eliminated fast subsystem. Simulations of competitive binding, enzyme saturation, shared processing, ribosome competition and a coupled slow-fast system agree with the prediction across distinct mechanisms. When branches share the same first-order lag, their fractions can remain accurate to second order even though the individual fluxes are only first-order accurate. The result provides a simple way to assess whether a QSSA reduction is accurate enough for questions about pathway allocation rather than absolute rates.
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BibTeX
@misc{thommen2026predicting,
title = {{Predicting flux-partitioning error in quasi-steady-state reductions of branched biochemical networks}},
author = {Quentin Thommen},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05735250v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Predicting flux-partitioning error in quasi-steady-state reductions of branched biochemical networks
AU - Quentin Thommen
PY - 2026
DA - 2026/09/02
PB - HAL
UR - https://hal.science/hal-05735250v1
AB - The quasi-steady-state approximation (QSSA) simplifies biochemical reaction networks by replacing fast intermediates with their local steady states. The accuracy of this reduction, however, depends on what the model is used to predict. In a branched network, the same branch fluxes determine both the total processing rate and the fractions directed toward competing fates. These two observables need not have the same reduction error. A first-order expansion shows that errors shared by all branches cancel when fluxes are normalized, whereas differences between branch corrections remain. The weighted dispersion of these branch-specific corrections therefore predicts the leading error in flux partitioning. This quantity can be calculated from the reduced trajectory and local derivatives, without integrating the eliminated fast subsystem. Simulations of competitive binding, enzyme saturation, shared processing, ribosome competition and a coupled slow-fast system agree with the prediction across distinct mechanisms. When branches share the same first-order lag, their fractions can remain accurate to second order even though the individual fluxes are only first-order accurate. The result provides a simple way to assess whether a QSSA reduction is accurate enough for questions about pathway allocation rather than absolute rates.
ER -