Coordinate-independent model reductions of chemical reaction networks based on geometric singular perturbation theory

Timothy Earl Figueroa Lapuz, Martin Wechselberger

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:57 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s tQSSA reduction for the irreversible Michaelis–Menten case (ε := γ, δ = 0) computes the same fast eigenvalue λ(s), uses the same oblique projection Π^S_0, and derives the same leading-order reduced slow flow ds/dt = -ε β s(α + s)/(α β + (α + s)^2) (eq. 3.17), as well as the product rate identity on the slow manifold. The candidate solution reproduces these steps and formulas. A small notational hiccup around dp/dt in one equation is clarified by the paper’s own remark, and matches the candidate’s result. Hence both are correct and essentially the same proof.

Referee report (LaTeX)

\textbf{Recommendation:} no revision

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper’s ci-GSPT treatment and parameterization-method framing are carefully executed and reproduce the classical tQSSA reduction in a coordinate-independent way. The candidate solution replicates the same derivation accurately. Minor notational friction around one displayed formula for dp/dt is self-corrected by the paper’s remark and tables, and does not undermine correctness. The contribution is solid within the applied singular perturbation/model-reduction literature for enzyme kinetics.