Mechanistic models of α-synuclein homeostasis for Parkinson’s disease: A blueprint for therapeutic intervention

Elena Righetti, Alice Antonello, Luca Marchetti, Enrico Domenici, Federico Reali

incompletemedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The uploaded PDF is a broad review of mechanistic models for α-synuclein aggregation and clearance; it discusses two-moment reductions (aggregate number and mass) and first-order (pseudo–first-order) clearance approximations but does not state or prove the specific linear 2×2 ODE result or the threshold D = δ_M δ_N − (2k_+ m)(k_2 m^{n_s}) > 0 for existence/stability of a unique positive equilibrium. The candidate model solves that concrete ODE correctly, with sound positivity, stability, global convergence, and sensitivity analyses. Hence, relative to the posed SOLVER_QUESTION, the paper is incomplete while the model is correct. This is consistent with the review’s high-level guidance that such reductions are common and that clearance has been approximated to enable tractable analysis, without providing the explicit proof required here .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

As a review, the paper is clear and useful. Relative to the SOLVER\_QUESTION, it does not provide the explicit theorem or proof for the linear two-moment ODE with first-order clearance; instead it motivates such reductions and approximations at a high level. Including a short, worked linear example with the D>0 threshold would bridge the gap between guidance and concrete analysis without altering the paper’s scope.