Friedl, Andrew
Abstract
**Background:** POLG disease-biology interpretation can conflate catalytic-subunit import, total POLGA abundance, POLGB association, active DNA engagement and synthesis readouts. A finite accessory-capacity model creates a narrower question: whether exact total-POLGA and synthesis trajectories can identify assembly, loss and capacity parameters, and which gain calibration remains unresolved.
**Objective:** This working paper retains the selected question: In a declared POLG catalytic-subunit turnover model with finite POLGB, known imported input and absolute total POLGA, which assembly, loss and capacity parameters are conditionally recoverable from a constant-gain synthesis signal, which activity quantity still needs gain calibration, and how does the matched pseudo-first-order buffered limit erase the nonlinear coefficient information?
**Methods:** Current primary-literature verification and archived primary texts were used only to bound claims. A deterministic synthetic ODE analysis replayed the declared finite-POLGB model with seven capacity values, two constant synthesis gains, three matched-family settings, two derivative-perturbation magnitudes and 99 automated checks. No patient data, fitted biological rates, pooled effect size, treatment ranking, rescue efficacy claim or clinical inference was generated.
**Results:** The replayed analysis passed 99 of 99 deterministic checks. In full-rank finite-capacity trajectories, the coefficient inverse recovered assembly, dissociation, free loss, associated loss, capacity and the effective synthesis coefficient κ with maximum reported exact-recovery error below 1e-5. Constant detector-gain changes left recovered assembly, loss and capacity parameters unchanged while scaling recovered κ. Equal gain-activity products produced identical total and synthesis outputs, so effective per-associated-pool activity k was not separated from detector gain g. As capacity increased from 4 to 1,000,000 at fixed pseudo-first-order assembly a, nonlinear coefficients r and s decreased from 0.2 and 0.1667 to 8e-7 and 6.667e-7, and the relative coefficient condition increased from 218.9 to 31,014,096.9.
**Conclusions:** The result is a conditional mathematical discriminator, not biological validation. Under the declared POLG model, absolute total POLGA, known imported input and a constant-gain synthesis signal can be sufficient for assembly, loss and capacity recovery, while effective per-associated-pool activity remains gain-confounded unless detector gain is known. Knowing detector gain would separate g from the effective coefficient k in this model, but would not by itself establish intrinsic kcat or the active enzyme fraction. Application to purified assays, cells, organoids, animals or patients requires separate proof of input calibration, total-protein calibration, active-pool meaning, POLGB capacity, free-enzyme activity and gain stability.
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DOI: 10.5281/zenodo.23300190