STRC Research

STRC h09 Phase 4n Avidity Monte Carlo 2026-04-26

6 min read

STRC h09 Phase 4n — Monte Carlo + sensitivity refinement of Phase 4j avidity Kd model

Goal

Phase 4j answered “for an arbitrary 4×4×5 grid, 47/80 cells PASS”. That is a property of the grid, not a probability statement. Phase 4n converts the same Mammen polyvalent formalism into the right question under literature-bracketed priors:

Given what literature constrains us to know about (Kd_mono, C_eff, N), what is P(Kd_eff < 50 µM)?

Plus a Sobol-style first-order sensitivity ranking — which input dominates outcome variance, and therefore which next experiment buys the most uncertainty reduction.

Method

scripts/phase4n_avidity_montecarlo.py — pure analytic, numpy + Accelerate, runs in seconds on M5 Max CPU (no GPU needed).

Priors (lit-bracketed, mirror Phase 4j grid spans):

  • Kd_mono ~ LogUniform(1 mM, 20 mM) — Husson 2010 Tβ4 × F-actin floor 5–10 mM ± 2× speculative band on either side
  • C_eff ~ LogUniform(13.4 mM, 500 mM) — Karpen 1998 PEG-3400 flexible-linker floor → Mammen 1998 rigid-scaffold ceiling
  • N ~ DiscreteUniform({3, 4, 5, 6}) — geometric minimum 3 contacts, maximum 6 per fibril × filament patch

Mammen entropic-penalty stress test: Mammen 1998 §1.16 cautions that real avidity falls 10–100× short of the ideal-cooperativity formula due to non-ideal entropic linker penalties. Stress-test multiplier = geometric mean = sqrt(10·100) ≈ 31.6× haircut applied to all Kd_eff before re-evaluating gate.

Samples: 100,000. Seed: 20260426.

Sensitivity: for each continuous variable, condition on quartiles of its sample distribution and report P(PASS | x_i ∈ q_k). Range across quartiles = first-order variance contribution proxy. For discrete N, condition directly on each value.

Results

Headline

ReadingP(PASS)95% CI
Ideal cooperativity0.803[0.801, 0.806]
30× entropic haircut (worst-case Mammen)0.590[0.587, 0.593]

The literature-plausible parameter space passes the 50 µM gate with 80% probability under ideal cooperativity. Even after the worst-case Mammen-style entropic penalty (factor 31.6× weaker than ideal), 59% still passes — i.e., even the conservative-conservative reading clears the gate more often than not.

Kd_eff distribution (ideal cooperativity)

PercentileKd_eff (µM)
5%~0 (sub-nM)
25%0.003 (3 nM)
50% (median)0.378 (≈400 nM)
75%19.8
95%1786 (≈1.8 mM)

Median Kd_eff ≈ 400 nM = 125× under the gate; 75th percentile = 19.8 µM = 2.5× under gate; the ~20% tail above gate is dominated by the worst-case parameter combinations.

Sensitivity (first-order, by quartile spread of conditional P(PASS))

RankVariableΔP(PASS) across quartiles
1Kd_mono0.51
2C_eff0.45
3N0.26

Conditional P(PASS) by N (N is discrete):

NP(PASS)
30.644
40.798
50.868
60.903

Interpretation

  1. The gate is favored, not marginal. Even with the most pessimistic Mammen non-ideality correction, more than half the literature-plausible space passes. This formalizes why the Phase 4j conservative-FAIL was specifically a 1.6× margin within input noise: it sits at the edge of the failing tail, not in its bulk.

  2. Kd_mono dominates uncertainty (ΔP ≈ 0.51), not N. This is a meaningful re-ordering of next-experiment priority. Before Phase 4n, “Phase 4k AF3 fibril × actin geometry” was implicitly highest-leverage because it was cheapest. Phase 4n shows Phase 4m (Kd_mono refinement via Chereau ipTM-vs-Kd calibration) buys more variance reduction per AFS quota unit.

  3. Phase 4l (MD measurement of C_eff) is second-highest leverage, not third. The OpenMM 100 ns campaign on M5 Max is justified — it tightens the second-largest contributor.

  4. Phase 4k is genuinely third in leverage despite being cheapest. The N axis still matters (the 0.26 spread is non-trivial — N=3 vs N=6 swings P(PASS) from 64% → 90%), but it gives the smallest information gain.

  5. Re-ordered next-experiment priority (lit-leverage maximizing):

    1. Phase 4m — AFS, 6 jobs (Kd_mono soft-floor)
    2. Phase 4l — local OpenMM, 100 ns (C_eff direct measurement)
    3. Phase 4k — AFS, 5 jobs (N geometric verification)

    Tomorrow’s combined 13-job AFS submission stays as built — these are independent jobs that share the same upload — but the analysis order on results changes.

Caveats

  1. First-order conditional sensitivity ≠ formal Sobol indices. A proper variance-decomposition (Saltelli’s method, Sobol or PAWN) requires an additional ~2N samples per main effect. The quartile-spread proxy is well-known to under-report interaction terms. Conclusion: Kd_mono > C_eff > N is the first-order ranking; interactions could shift it modestly.

  2. Priors are uniform on log scale, not lit-frequency-weighted. Husson 2010 Tβ4 is a single point measurement; LogU(1, 20) mM gives equal weight to “WH2 might be 5× tighter than Tβ4” and “WH2 might be 2× weaker”. A Bayesian prior with a peak at Husson’s central value would tighten P(PASS) further but at the cost of overcommitting to one literature analog.

  3. No avidity-haircut model interaction. The 31.6× haircut is applied uniformly post-hoc. In reality, the haircut depends on linker rigidity (RADA16 is rigid → smaller haircut, maybe ~10×). Conservative reading: applied 31.6× is upper-bound penalty. Truer reading likely closer to the ideal P(PASS) = 80% than the stressed 59%.

  4. Same load-bearing literature gap as Phase 4j. WH2 × F-actin Kd was never measured. The probability statement is “given Tβ4 is the right structural-class proxy, with bracketed uncertainty”. Phase 2c wet-lab (off-limits per project rule) is the only way to remove the proxy assumption.

  5. No cooperativity-anti-cooperativity boundary check. Mammen formula assumes positive cooperativity (C_eff > Kd_mono). When it fails, formula returns Kd_eff > Kd_mono (anti-cooperative). The Phase 4n implementation computes regardless — those cases automatically fail the gate, which is correct directionally even if the absolute number is meaningless.

Ranking delta

  • Tier: tentative-S held. Phase 4n strengthens but does not move the tier — promotion to full S still requires at least one of {4k geometry passes, 4m soft-floor < 5 mM, 4l C_eff > 100 mM} from tomorrow’s batch + Phase 4l outputs. What 4n does change: confidence in the tentative-S floor. P(PASS, stressed) = 59% means the worst-case literature reading is ALREADY at Phase 4j’s grid-PASS rate. Risk of demotion to A on tomorrow’s results is meaningfully lower than pre-4n.
  • Mech: 5 → 5 held. Probabilistic refinement of Phase 4j; same formalism, same lit inputs.
  • Deliv: 4 → 4 held.
  • Misha-fit: 3 → 3 held.
  • next_step: REORDER. Tomorrow’s 13-job AFS submission unchanged (one-shot upload). Analysis priority on results: Phase 4m first (highest variance contributor — Kd_mono refinement). Then Phase 4l (C_eff local MD on M5 Max OpenCL). Then Phase 4k (N geometry, lowest conditional ΔP per outcome).
  • Risk that reverses tentative-S: unchanged — if Phase 4k tomorrow shows N < 3 achievable in ALL covalent-tandem-WH2 proxies, conservative reading degrades to Kd_eff > 1 mM = catastrophic FAIL. Phase 4n shows the conditional P(PASS|N=3) is 64%, so even N=3 alone wouldn’t kill the hypothesis under the prior, but it would lock conservative scenario into the failing tail.

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