STRC Research

STRC h09 Phase 4j Avidity Kd Model 2026-04-26

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STRC h09 Phase 4j — Closed-form avidity Kd model (RADA16-tail91 fibril × F-actin)

Goal. Computationally substitute the wet-lab Phase 2c gate (WH2 × F-actin Kd ≤ 50 µM) under the project’s no-wet-lab rule. Propagate the literature-validated single-WH2 × F-actin floor (Husson 2010 Tβ4 = 5–10 mM) through the polyvalent avidity formalism to predict effective Kd of the assembled RADA16-tail91 fibril × F-actin filament.

Inputs (primary literature, all in vault)

ParameterValueSource
Kd_mono (WH2 × F-actin)5–10 mM (Tβ4 floor; WH2 × F-actin itself NEVER measured)2026-04-23-husson-wh2-multifunctionality
Avidity formalismKd_eff = Kd_mono · (Kd_mono / C_eff)^(N−1)1998-mammen-polyvalent-interactions-angew eqn 1.16
C_eff formula1000 / (N_A · (2/3) · π · r³)1998-kramer-karpen-polymer-ligand-dimers-nature
C_eff range (rigid scaffold)50–500 mMMammen 1998 Table 14
Additivity / ΔG_connectionΔG = −RT ln(C_eff)1981-jencks-binding-energies-additivity-pnas
Fibril span (RADA16-WH2-tail91)10.2 nm/constructSTRC Hydrogel HTC Phase 1 Self-Assembly
F-actin actin-monomer pitch5.5 nm long-pitch helixActin Polymerization Kinetics Reference Table
Gate thresholdKd_eff < 50 µMh09 hub S-promotion condition (index.md)

Method

scripts/phase4j_avidity_kd_model.py — pure analytic, no compute. Sweep grid:

  • Kd_mono ∈ {1, 5, 10, 20} mM (Husson Tβ4 floor ± speculative ±2×)
  • C_eff ∈ {13.4, 50, 100, 500} mM (Karpen flexible-floor → Mammen rigid-ceiling)
  • N ∈ {2, 3, 4, 5, 6} simultaneous geometry-coherent contacts

Pre-registered scenarios:

  • Conservative: Kd_mono = 10 mM, C_eff = 50 mM, N = 4
  • Nominal: Kd_mono = 5 mM, C_eff = 100 mM, N = 5

Pre-registered pass criterion: conservative-scenario Kd_eff < 50 µM = computational gate substitute PASS.

Results

CONSERVATIVE: Kd_mono=10 mM, C_eff=50 mM, N=4 → Kd_eff = 80 µM     FAIL (1.6× over gate)
NOMINAL:      Kd_mono=5 mM,  C_eff=100 mM, N=5 → Kd_eff = 31 nM    PASS (×1500 under gate)
GRID: 47/80 cells PASS (59% of cooperative-regime parameter space)

Artifact: artifacts/phase4j_avidity_kd_2026-04-26.json (full grid + per-row ΔG_per_contact).

What the conservative-FAIL means

The gate-substitute does NOT close at the most pessimistic literature-defensible assumptions. Conservative case misses by 1.6× — within the noise of (a) Kd_mono uncertainty (Husson Tβ4 5–10 mM is itself ±2×), (b) C_eff lower-bound conservatism (RADA16 is rigid β-sheet → upper-end Mammen range more apt), (c) N = 4 is geometric minimum (proper RADA16/F-actin alignment likely supports 5–6).

What the 47/80 PASS means

Across the literature-plausible parameter space, 59% of cells clear the 50 µM gate. The fail region is concentrated where (Kd_mono is at upper bound) AND (C_eff is at flexible-linker floor) AND (N ≤ 3). Any single concession to the favorable side closes the gate.

Pre-registered tightening paths (no wet-lab)

  1. Phase 4k — AF3 RADA16 fibril × F-actin patch. Test N geometry: build a single RADA16-WH2 trimer fibril (3 stacked monomers), submit vs F-actin trimer, measure how many simultaneous WH2 × actin interfaces score ipTM ≥ 0.45. AFS budget: 5 jobs (3 fibril compositions × 1–2 actin trimer orientations). Closes “Is N ≥ 4 geometrically achievable?” question.
  2. Phase 4l — MD of free RADA16-WH2 fibril. Apply Apple-Silicon-first principle: M5 Max MPS-accelerated MD (OpenMM with Metal backend OR coarse-grained MARTINI). 100 ns of explicit-solvent RADA16-WH2-tail91 self-assembled trimer, measure WH2 angular distribution + scaffold rigidity → refines C_eff from Mammen-bracketed 50–500 mM to a directly-measured number for THIS scaffold.
  3. Phase 4m — Effective Kd_mono refinement. WH2 × F-actin Kd_mono is currently the Tβ4 analog floor. Family Kd ranges 50 nM (WAVE2 × G-actin) to 5 mM (Tβ4 × F-actin) — 5 orders of magnitude. AF3 Phase 4 already showed WH2-on-F-actin scores ipTM 0.51 (Phase 4b actin axis baseline) which is in the “weak but real” regime per Dunbrack ipSAE 2025. AF3 → Kd is unmappable (avidity-and-dimers.md §3), but a comparative ratio (h09 WH2 × F-actin ipTM 0.51 / WAVE2 × G-actin ipTM 0.6+ Kd 52 nM) can put a soft floor on Kd_mono ≥ ~10 µM × G-actin Kd structural-class. Crude but better than Tβ4 floor.

Caveats

  1. WH2 × F-actin Kd_mono is unmeasured. Tβ4 is the structural-class proxy, not WH2 itself. True WH2 × F-actin could be tighter (LR-RT salt-bridge analogs in WAVE2 give 52 nM × G-actin) or weaker (mM if F-actin presents no exposed cleft). The full-formal answer requires Phase 2c wet-lab, which is off-limits.
  2. C_eff range 13.4–500 mM is broad (factor 37). Phase 4l would tighten to factor ≤2.
  3. Effective N depends on fibril–filament alignment. RADA16 (~0.5–2 nm WH2 surface periodicity) vs F-actin (5.5 nm actin pitch) — geometric sub-sampling likely. Phase 4k probes this.
  4. Mammen 1998 cautions that Kd_eff = Kd_mono · (Kd_mono / C_eff)^(N−1) is the ideal-cooperativity case; real avidity often falls 10–100× short due to entropic linker penalties even in rigid scaffolds. Conservative reading: divide all Kd_eff by 10–100.
  5. No single-molecule MD validation. Order-of-magnitude propagation only. Not a substitute for wet-lab rigor; a substitute under no-wet-lab constraint.

Ranking delta

  • Tier: tentative-S held. Cannot promote on conservative-FAIL alone (gate misses by 1.6×). Promotion requires (a) Phase 4k confirms N ≥ 4 geometrically achievable, OR (b) Phase 4l measures C_eff > 100 mM for THIS scaffold, OR (c) Phase 4m softens Kd_mono floor to <5 mM via AF3-comparative-ratio argument. Any one of three closes conservative.
  • Mech: 5 → 5 held. Avidity formalism is textbook, formula is correct, inputs are literature-backed. Mech score not improved (gate-substitute didn’t conservatively close); not lowered (math is structurally sound).
  • Deliv: 4 → 4 held.
  • Misha-fit: 3 → 3 held.
  • next_step: Phase 4k (AF3 fibril × F-actin patch) is the highest-leverage cheapest test (5 AFS jobs, ~1 quota cycle). Phase 4l (MD on M5 Max) is more rigorous but requires OpenMM-Metal install + 100 ns runtime. Order: 4k first, then 4l only if 4k confirms N ≥ 4.
  • Risk that reverses: if Phase 4k shows N < 3 achievable (RADA16/F-actin geometric mismatch fundamental), conservative scenario degrades to Kd_eff = 12 mM = catastrophic FAIL. Would demote h09 tentative-S → A.

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