Luminal UOX Conditional Capacity and Measurement Identifiability¶
The exploitable weakness is intestinal urate disposal: a luminal UOX system could increase elimination if it consumes urate that would otherwise return to circulation. The current evidence does not establish the relevant human operating regime. COMP-050 instead defines what can be calculated conditionally and what must be measured before a dynamic model can answer that biological question.
Result: METHOD_MAP_DERIVED; biological regime NOT_EVALUATED. Evidence level: deterministic computational method, not biological validation.
What the capacity boundary means¶
For a declared window, fixed substrate occupancy, and a calibrated reaction-site active-capacity time course:
J_total_mean is mean total local urate influx from systemic and other sources. q = 1 is the conditional point at which integrated UOX capacity equals total local influx. It is not a closed dynamic mass balance, a dose, a production target, or a serum-urate prediction. Actual removal also depends on changing substrate, initial and terminal inventory, reabsorption, outflow, unattributed loss, oxygen, and retained activity.
A_time = ∫Vmax_active(t)dt / (Vmax_initial × T). It is the dimensionless active-capacity time-area retained across the declared window T, not an enzyme-abundance or oxygen proxy.
The exact response surface spans the declared dimensionless scenarios; its extrema are 101/400 and 1,010 for required initial capacity relative to mean total local influx. Those are grid boundaries, not physiological estimates or planning values.
Why urate concentration is insufficient¶
Three constructed constant-volume steady states use the same concentration, Km, and total influx. Their UOX-attributed fluxes are 1/10, ½, and 9/10 in dimensionless units, while non-UOX loss changes so that dC/dt = 0 in every case.
The same concentration trajectory can therefore conceal a nine-fold difference in UOX removal within the declared rate law. A terminal urate value—and even an ideal concentration time course without the missing flux observations—cannot identify local UOX activity.
What each measurement combination can identify¶
The structural audit uses an exact rational coefficient matrix. A target is identifiable only when its coefficient vector lies in the row space of the governing and observation equations.
| Measurement combination | Local UOX removal | Calibrated active capacity | Declared local ledger | Systemic-origin UOX removal |
|---|---|---|---|---|
| Terminal urate amount only | Not identifiable | Not identifiable | Not identifiable | Not identifiable |
| Initial/terminal urate + qualified product equivalent | Conditionally identifiable | Not identifiable | Not identifiable | Not identifiable |
| Add calibrated reaction-site capacity | Conditionally identifiable | Identifiable | Not identifiable | Not identifiable |
| Add both source influxes, reabsorption, outflow, and source-resolved product fate | Conditionally identifiable | Identifiable | Structurally identifiable | Conditionally identifiable |
“Conditionally identifiable” means only under ideal, noiseless observations. It does not mean that an assay has been validated or that the variables are practically estimable with useful precision.
Product qualification is load-bearing¶
Calling a signal “UOX product” is not enough. The product-equivalent observation requires:
- analyte identity and UOX specificity;
- validated stoichiometry and matrix recovery;
- initial product, non-UOX formation, sampling, outflow, degradation, and scavenging fate;
- no-UOX or inactive-UOX, no-urate, and matrix controls;
- prespecified recovery, mass-balance, and interference criteria; and
- source-resolved product fate for systemic-origin attribution.
When COMP-050 removes the qualified total and source-resolved product observations, local UOX removal becomes non-identifiable in every measurement combination. The complete declared ledger also fails because UOX removal cannot be separated from the explicit unattributed-loss term.
Decision boundary¶
COMP-050 supplies a measurement contract, not a replacement physiological model. It does not:
- determine whether oral UOX works;
- identify a human substrate, oxygen, residence, or reabsorption regime;
- select a sequence, topology, host, formulation, or dose;
- establish production sufficiency or serum-urate effect;
- validate a product assay or prove practical identifiability; or
- address peroxide, barrier, or clinical safety.
H08 therefore remains open. The next useful evidence is an exact-configuration experiment that measures qualified product formation and calibrated reaction-site capacity under defined substrate and oxygen conditions, followed by source and boundary-fate measurements sufficient to reconstruct every declared ledger term. Practical closure additionally requires the algebraically reconstructed unattributed residual to pass a prespecified mass-balance tolerance. See validation §1.33 and the H08 falsification card.