#!/usr/bin/env python3 """ comp-019 — Gut-Lumen Uricase x ABCG2 Genotype Flux Model ======================================================== Phase B in-silico flux model. Predicts steady-state delta-SUA in: - WT/WT (100% functional ABCG2) - Q141K heterozygous (75% functional) - Q141K homozygous (50% functional) - Severe ABCG2 dysfunction (25% functional) under three uricase-dose scenarios (low / mid / high). Model logic ----------- 1. Daily mass balance: total urate production = renal + intestinal + (any uricase) 2. Intestinal compartment: ABCG2-mediated secretion follows Michaelis-Menten v = Vmax * [S] / (Km + [S]) In vivo, [S] (lumen urate) is ~0.6 uM at baseline, far below Km (8240 uM). So secretion rate ~ (Vmax / Km) * [S] — i.e., LINEAR in substrate. 3. Adding luminal uricase pulls lumen [S] toward zero (uricase is fast: kcat/Km for A. flavus uricase >> ABCG2 transport rate). This effectively doubles the basolateral->apical urate gradient (since the apical "back-pressure" from accumulated lumen urate is cleared). 4. Genotype scaling: secretion capacity = baseline * functional_class. Anchored against Miyazaki 2025 direct measurement. 5. Renal partial compensation: when gut excretion changes by dF, kidney compensates by (1 - r) * dF where r is the compensation fraction (central estimate 0.30, i.e. kidney offsets 30% of the gut delta). 6. Steady-state SUA: assume ~1-month timescale equilibration. Delta-SUA per day at new steady state = delta-flux (mg/day) / clearance (L/day). We instead use the algebraic shortcut: delta-SUA/SUA-baseline = -delta-flux / total-baseline-flux (1st-order kinetic approximation). Sensitivity: Monte Carlo over parameter uncertainty bounds in flux_model_parameters.json. Outputs central estimate + 90% CI. Usage: python3 flux_model.py Outputs land in ../outputs/. """ import json import math import random from pathlib import Path from collections import defaultdict # ---------------------------------------------------------------------- # I/O paths # ---------------------------------------------------------------------- HERE = Path(__file__).resolve().parent INPUTS_DIR = HERE.parent / "inputs" OUTPUTS_DIR = HERE.parent / "outputs" OUTPUTS_DIR.mkdir(parents=True, exist_ok=True) # ---------------------------------------------------------------------- # Load parameters # ---------------------------------------------------------------------- def load_params() -> dict: with open(INPUTS_DIR / "flux_model_parameters.json", "r") as f: return json.load(f) # ---------------------------------------------------------------------- # Core flux model — single deterministic evaluation # ---------------------------------------------------------------------- def evaluate_scenario( *, functional_class: float, uricase_dose_mg_per_day: float, uricase_specific_activity_U_per_mg: float, intestinal_baseline_fraction: float, total_daily_production_mg: float, renal_compensation_fraction: float, sua_baseline_mg_dL: float, ) -> dict: """ Compute predicted delta-SUA (mg/dL) and supporting fluxes. Returns a dict with: baseline_intestinal_mg : intestinal urate excretion at baseline (no uricase) baseline_renal_mg : renal urate excretion at baseline baseline_intestinal_genotype_adjusted_mg : intestinal flux at this genotype delta_intestinal_with_uricase_mg : added flux from uricase x ABCG2 gradient net_delta_flux_mg : after renal compensation delta_sua_mg_dL : predicted serum urate change uricase_capacity_mg_per_day : raw enzyme capacity (substrate-saturating bound) """ # 1. Baseline mass balance (WT, healthy kidney) baseline_renal = total_daily_production_mg * (1 - intestinal_baseline_fraction) baseline_intestinal_wt = total_daily_production_mg * intestinal_baseline_fraction # 2. Genotype-adjusted baseline intestinal capacity # (functional_class = 1.0 for WT; 0.5 for Q141K hom; etc.) baseline_intestinal_geno = baseline_intestinal_wt * functional_class # The remainder shifts to kidney (Matsuo 2014 directional finding) under # baseline conditions — but kidney capacity is already at-or-near ceiling # in gout patients, so the SUA equilibrates upward. Without uricase, # delta_SUA from genotype alone is captured implicitly in the patient's # baseline SUA. We're computing delta-SUA from uricase intervention, # so this term is the reference. # 3. Uricase capacity in raw enzyme terms. # 1 U = 1 umol/min at pH 8.5, 37C. # Per day: 1 U sustained = 1 umol/min * 1440 min/day = 1440 umol/day. # Convert to mg uric acid: 1440 umol * 168.11 ug/umol / 1000 = 242 mg/day per U. # Adjust for in-vivo specific-activity attenuation (~75% at colon pH). in_vivo_activity_factor = 0.75 enzyme_capacity_umol_per_day = ( uricase_dose_mg_per_day * uricase_specific_activity_U_per_mg * in_vivo_activity_factor * 1440 # min/day ) enzyme_capacity_mg_per_day = enzyme_capacity_umol_per_day * 168.11 / 1000 # 4. The KEY question: does uricase capacity exceed the intestinal urate # flux from blood->gut at this genotype? If yes, uricase clamps lumen # [urate] near zero (substrate-limited regime). If no, uricase saturates # (capacity-limited regime). delivered_intestinal_flux_mg_per_day = baseline_intestinal_geno capacity_ratio = enzyme_capacity_mg_per_day / max(delivered_intestinal_flux_mg_per_day, 1.0) # 5. Effect of uricase on net intestinal urate elimination. # Substrate-limited regime (capacity_ratio >= 1.0): uricase drains # everything that comes through, so delta_intestinal scales with the # gradient improvement. With baseline lumen urate near zero (it's # already low, ~0.6 uM), the gradient improvement is bounded by # the reabsorption fraction of the ~30% urate that normally cycles # back. Per Yu 2015 / Bhatnagar 2016 review, ~30-50% of secreted # intestinal urate is reabsorbed in the colon. So the maximum # additional flux uricase can extract is ~30-50% of the delivered # flux — this is the "sink amplification factor." # Capacity-limited regime (capacity_ratio < 1.0): max additional # flux is the enzyme capacity itself. sink_amplification_factor = 0.40 # central; uricase prevents reabsorption of # ~40% of secreted urate if capacity_ratio >= 1.0: # Substrate-limited: uricase clamps lumen, gradient improvement # = sink_amplification * delivered_flux delta_intestinal = sink_amplification_factor * delivered_intestinal_flux_mg_per_day else: # Capacity-limited: bounded by enzyme throughput delta_intestinal = min( enzyme_capacity_mg_per_day, sink_amplification_factor * delivered_intestinal_flux_mg_per_day, ) # 6. Renal partial compensation. When gut excretion increases by # delta_intestinal, the kidney down-regulates excretion by # renal_compensation_fraction * delta_intestinal. net_delta_flux = delta_intestinal * (1 - renal_compensation_fraction) # 7. Delta-SUA via 1st-order steady-state approximation. # Baseline mass balance: total production = total elimination (steady). # SUA_new / SUA_baseline = (production - delta_elimination) / production # delta_SUA = -SUA_baseline * (delta_elimination / production) delta_sua_mg_dL = -sua_baseline_mg_dL * (net_delta_flux / total_daily_production_mg) return { "baseline_renal_mg": baseline_renal, "baseline_intestinal_wt_mg": baseline_intestinal_wt, "baseline_intestinal_genotype_adjusted_mg": baseline_intestinal_geno, "uricase_capacity_mg_per_day": enzyme_capacity_mg_per_day, "capacity_ratio": capacity_ratio, "delta_intestinal_with_uricase_mg": delta_intestinal, "net_delta_flux_mg": net_delta_flux, "delta_sua_mg_dL": delta_sua_mg_dL, } # ---------------------------------------------------------------------- # Sensitivity analysis via Monte Carlo # ---------------------------------------------------------------------- def sample_uniform(low: float, high: float) -> float: return random.uniform(low, high) def monte_carlo_delta_sua( params: dict, *, functional_class: float, uricase_dose_mg_per_day: float, sua_baseline_mg_dL: float, n_samples: int = 5000, ) -> dict: """Monte Carlo sensitivity over parameter ranges in flux_model_parameters.json.""" samples = [] for _ in range(n_samples): prod_mg = sample_uniform( params["daily_mass_balance"]["total_daily_urate_production_mg_per_day"]["low"], params["daily_mass_balance"]["total_daily_urate_production_mg_per_day"]["high"], ) gut_frac = sample_uniform( params["daily_mass_balance"]["intestinal_excretion_fraction_normal_kidney"]["low"], params["daily_mass_balance"]["intestinal_excretion_fraction_normal_kidney"]["high"], ) spec_act = params["uricase_kinetic_priors"]["specific_activity_U_per_mg"]["central"] renal_comp = sample_uniform( params["renal_compensation_fraction"]["low"], params["renal_compensation_fraction"]["high"], ) result = evaluate_scenario( functional_class=functional_class, uricase_dose_mg_per_day=uricase_dose_mg_per_day, uricase_specific_activity_U_per_mg=spec_act, intestinal_baseline_fraction=gut_frac, total_daily_production_mg=prod_mg, renal_compensation_fraction=renal_comp, sua_baseline_mg_dL=sua_baseline_mg_dL, ) samples.append(result["delta_sua_mg_dL"]) samples.sort() return { "median": samples[n_samples // 2], "p05": samples[int(0.05 * n_samples)], "p95": samples[int(0.95 * n_samples)], "mean": sum(samples) / n_samples, "stdev": math.sqrt( sum((s - sum(samples) / n_samples) ** 2 for s in samples) / (n_samples - 1) ), } # ---------------------------------------------------------------------- # Main scenario sweep # ---------------------------------------------------------------------- def main(): random.seed(42) params = load_params() # Genotype scenarios + sex baseline-SUA scenarios genotypes = { "WT_male": {"functional_class": 1.00, "sua_baseline_mg_dL": 8.0, "label": "WT/WT, male gout patient"}, "Q141K_het_male": {"functional_class": 0.75, "sua_baseline_mg_dL": 8.5, "label": "Q141K heterozygous, male gout patient"}, "Q141K_hom_male": {"functional_class": 0.50, "sua_baseline_mg_dL": 9.5, "label": "Q141K homozygous, male gout patient"}, "WT_female": {"functional_class": 1.00, "sua_baseline_mg_dL": 7.0, "label": "WT/WT, female gout patient"}, "Q141K_het_female": {"functional_class": 0.75, "sua_baseline_mg_dL": 7.5, "label": "Q141K heterozygous, female gout patient"}, "Q141K_hom_female": {"functional_class": 0.50, "sua_baseline_mg_dL": 8.0, "label": "Q141K homozygous, female gout patient"}, "Severe_dysfunction_male": {"functional_class": 0.25, "sua_baseline_mg_dL": 10.5, "label": "Severe ABCG2 dysfunction (Q126*+Q141K compound), male"}, } uricase_doses = { "low_5mg": params["uricase_dose_scenarios"]["low_dose_mg_per_day"], "mid_25mg": params["uricase_dose_scenarios"]["mid_dose_mg_per_day"], "high_50mg": params["uricase_dose_scenarios"]["high_dose_mg_per_day"], } results = { "_metadata": { "model_version": "comp-019 v1.0", "model_assumptions": [ "ABCG2 operates in linear regime in vivo (lumen urate ~0.6 uM << Km 8240 uM)", "Uricase clamps lumen urate to ~0; sink amplification factor 0.40 (40% of secreted urate would have been reabsorbed without uricase)", "Genotype scales secretion capacity linearly per Matsuo 2014 + Miyazaki 2025 framework", "Renal compensation offsets 30% of gut delta-flux (sensitivity: 0-50%)", "1st-order steady-state approximation for delta-SUA", ], "monte_carlo_n": 5000, "random_seed": 42, }, "central_estimates": {}, "monte_carlo": {}, } # Central estimates (deterministic) + MC sensitivity (90% CI) for geno_key, geno in genotypes.items(): results["central_estimates"][geno_key] = {} results["monte_carlo"][geno_key] = {} for dose_key, dose_mg in uricase_doses.items(): central = evaluate_scenario( functional_class=geno["functional_class"], uricase_dose_mg_per_day=dose_mg, uricase_specific_activity_U_per_mg=params["uricase_kinetic_priors"]["specific_activity_U_per_mg"]["central"], intestinal_baseline_fraction=params["daily_mass_balance"]["intestinal_excretion_fraction_normal_kidney"]["central"], total_daily_production_mg=params["daily_mass_balance"]["total_daily_urate_production_mg_per_day"]["central"], renal_compensation_fraction=params["renal_compensation_fraction"]["central"], sua_baseline_mg_dL=geno["sua_baseline_mg_dL"], ) results["central_estimates"][geno_key][dose_key] = central mc = monte_carlo_delta_sua( params, functional_class=geno["functional_class"], uricase_dose_mg_per_day=dose_mg, sua_baseline_mg_dL=geno["sua_baseline_mg_dL"], n_samples=5000, ) results["monte_carlo"][geno_key][dose_key] = mc # Write JSON results with open(OUTPUTS_DIR / "flux_model_results.json", "w") as f: json.dump(results, f, indent=2) # Write human-readable summary write_summary_md(results, genotypes, uricase_doses, params) # Print compact console table print("=" * 80) print("comp-019 — Gut-Lumen Uricase x ABCG2 Genotype Flux Model") print("=" * 80) print(f"\n{'Scenario':<35} {'Low 5mg':<14} {'Mid 25mg':<14} {'High 50mg':<14}") print("-" * 80) for geno_key, geno in genotypes.items(): line = f"{geno['label'][:34]:<35}" for dose_key in ("low_5mg", "mid_25mg", "high_50mg"): mc = results["monte_carlo"][geno_key][dose_key] line += f" {mc['median']:+.2f} mg/dL " print(line) print() print("All values are predicted delta-SUA at steady state (Monte Carlo medians).") print("Negative = serum urate reduction. See outputs/flux_model_summary.md for 90% CI.") def write_summary_md(results, genotypes, uricase_doses, params): lines = [] lines.append("# comp-019 — Flux Model Results Summary\n") lines.append("Predicted delta-SUA (mg/dL) at steady state by ABCG2 genotype and uricase dose.\n") lines.append("Negative values = serum urate reduction.\n") lines.append("\n## Central estimates (deterministic)\n") lines.append("| Scenario | Low 5 mg/d | Mid 25 mg/d | High 50 mg/d |") lines.append("|---|---|---|---|") for geno_key, geno in genotypes.items(): row = f"| {geno['label']} |" for dose_key in ("low_5mg", "mid_25mg", "high_50mg"): d = results["central_estimates"][geno_key][dose_key]["delta_sua_mg_dL"] row += f" {d:+.2f} |" lines.append(row) lines.append("") lines.append("\n## Monte Carlo 90% CI (n=5000)\n") lines.append("| Scenario | Low 5 mg/d (median, 90% CI) | Mid 25 mg/d (median, 90% CI) | High 50 mg/d (median, 90% CI) |") lines.append("|---|---|---|---|") for geno_key, geno in genotypes.items(): row = f"| {geno['label']} |" for dose_key in ("low_5mg", "mid_25mg", "high_50mg"): mc = results["monte_carlo"][geno_key][dose_key] row += f" {mc['median']:+.2f} ({mc['p05']:+.2f} to {mc['p95']:+.2f}) |" lines.append(row) lines.append("") lines.append("\n## Capacity-vs-substrate diagnostic\n") lines.append("Whether enzyme capacity exceeds delivered intestinal urate flux at this genotype + dose.") lines.append("Ratio >= 1.0 means substrate-limited (uricase clamps lumen, sink amplification factor 0.40 applies).") lines.append("Ratio < 1.0 means capacity-limited (delta-intestinal bounded by enzyme dose).\n") lines.append("| Scenario | Low 5 mg/d ratio | Mid 25 mg/d ratio | High 50 mg/d ratio |") lines.append("|---|---|---|---|") for geno_key, geno in genotypes.items(): row = f"| {geno['label']} |" for dose_key in ("low_5mg", "mid_25mg", "high_50mg"): r = results["central_estimates"][geno_key][dose_key]["capacity_ratio"] row += f" {r:.2f} |" lines.append(row) lines.append("") lines.append("\n## Model assumptions\n") for a in results["_metadata"]["model_assumptions"]: lines.append(f"- {a}") lines.append("") lines.append("\n## Headline interpretation\n") lines.append("- **WT/WT non-Q141K males DO show meaningful delta-SUA** in the flux model. The mechanism is not Q141K-dependent.") lines.append("- **Q141K-positive carriers show LESS absolute reduction** because the gut compartment they're losing access to is already partially compromised — the substrate flux that uricase can amplify is smaller.") lines.append("- **Severe ABCG2 dysfunction (~25% functional) shows the smallest absolute response** despite having the highest baseline SUA — the gut compartment is so impaired that even a perfect uricase has little substrate to work with. This is the platform's structural ceiling for the worst-impaired patients.") lines.append("- The flux model contradicts the binary 'mechanism only works in Q141K' framing. The mechanism works ACROSS genotypes; the magnitude scales with the residual ABCG2 capacity at any given genotype.") lines.append("- **Most platform-relevant conclusion:** the gut-lumen uricase target demographic should NOT be narrowed to Q141K-positive patients. The opposite — non-Q141K patients have the LARGEST per-patient response. Q141K-positive patients are still candidates but for a different reason (high unmet ULT need, allopurinol resistance).") lines.append("") with open(OUTPUTS_DIR / "flux_model_summary.md", "w") as f: f.write("\n".join(lines)) if __name__ == "__main__": main()