Avidity, protein-protein interface area, and engineered dimers — parameter DB
Consumer: STRC Engineered Homodimer Avidity (h26), downstream STRC Mini-STRC Single-Vector Hypothesis (h03), STRC Synthetic Peptide Hydrogel HTC (h09). Written 2026-04-23 during h26 parameter-provenance audit.
1. Effective-concentration (C_eff) theory
Foundational references
- Jencks 1981 — “On the attribution and additivity of binding energies”, PNAS 78(7):4046. DOI: 10.1073/pnas.78.7.4046. Introduced the “chelate effect” decomposition for bivalent binding: ΔG_bivalent = ΔG_A + ΔG_B + ΔG_connection, where ΔG_connection (~−RT ln C_eff) captures the entropic cost of restricting the second binding event.
- Mammen, Choi, Whitesides 1998 — “Polyvalent Interactions in Biological Systems”, Angew Chem Int Ed 37:2754. PubMed 29711117. Definitive review. Formalizes C_eff and discusses the conditions under which polyvalent binding exceeds additive monovalent contributions.
- Krishnamurthy, Estroff, Whitesides 2006 — “Multivalency in Ligand Design”, Methods Principles Med Chem Ch.2. Wiley. Treatment of linker-length dependence of C_eff; formula for free energy of heterodivalent binding where −RT ln [C_eff(r)] encodes translational/rotational entropy + linker conformational entropy.
- Kramer & Karpen 1998 — “Spanning binding sites on allosteric proteins with polymer-linked ligand dimers”, Nature 395:710. Empirical measurement: polymer-linked bivalent cGMP shows up to 10³× potency improvement over monovalent cGMP for CNG channels. The key result: C_eff is in the mM range for flexible polymer linkers.
Key quantitative values
| Parameter | Value | Notes |
|---|---|---|
| Typical C_eff for flexible tethered ligands | 10⁻⁴ to 10⁻² M (0.1–10 mM) | Kramer & Karpen 1998; Krishnamurthy 2006. Depends strongly on linker length and rigidity. |
| Kd improvement (bivalent over monovalent) | Kd_mono / C_eff | For Kd_mono = 100 nM and C_eff = 1 mM: improvement = 10,000× = 4 log units. For C_eff = 0.1 mM: 1,000×. |
| ΔG_connection for protein homodimer | ~−4 to −8 kcal/mol | Jencks 1981 estimate for translational + rotational entropy restriction. The actual value for a protein–protein interface depends on linker flexibility. |
| Practical range cited in drug design | 10–10⁵× improvement | Wide range because C_eff is exquisitely sensitive to linker geometry and receptor separation. |
Critical caveat for h26
The avidity formula requires knowing Kd_monovalent. For STRC × TMEM145, no SPR, BLI, ITC, or fluorescence Kd exists in the literature (fully documented in strc-tmem145-interactions). The “100-1000× improvement” claim in STRC Engineered Homodimer Avidity is a ratio applied to an unmeasured baseline. The formula is correct; the inputs are absent.
2. Interface area → Kd empirical trends
Key reference
- Chen, Sawyer, Regan 2013 — “Protein-protein interactions: General trends in the relationship between binding affinity and interfacial buried surface area”, Protein Science 22(4):510. PMC 3610057.
Data
| Metric | Value |
|---|---|
| Dataset | 113 heterodimeric complexes |
| Correlation (BSA vs log Kd) | Spearman ρ = −0.53, P = 2.5×10⁻⁹, R² = 0.25 |
| Smallest interface | 381 Ų → Kd = 1 mM |
| Largest interface | 3,393 Ų → Kd = 3 pM |
| Scatter at fixed BSA | Kd varies 4 orders of magnitude for a given BSA |
| Energy density (small interfaces, <2000 Ų) | ~4–13 cal mol⁻¹ Å⁻² |
| Energy density (large interfaces, >2000 Ų) | levels off to ~3–4 cal mol⁻¹ Å⁻² |
| Protein-protein only (no peptide) | R² = 0.058 — near-zero predictive power |
Implication for h26
The AF3 Ultra-Mini homodimer interface (stump zone aa 1077-1131 + deep ARM zone aa 1579-1590) has not been converted to BSA. Even if it were, BSA → Kd mapping has R² = 0.25 for all types, ≈ 0.06 for protein-protein. A BSA measurement from a modeled structure would have an additional structural uncertainty layer on top of this. BSA from AF3 cannot predict Kd to better than ~4 orders of magnitude.
3. AF3 ipTM → Kd calibration
What ipTM is
ipTM (interface predicted template modeling score) was introduced with AlphaFold-Multimer (Evans et al. 2021, bioRxiv 2021.10.04.463034). It is a confidence metric for the accuracy of the predicted interface structure, not a predictor of binding affinity.
Formally: ranking_confidence = 0.8 × ipTM + 0.2 × pTM.
What ipTM is NOT
ipTM has no calibrated mapping to Kd. Multiple independent analyses confirm this:
- Dunbrack ipSAE 2025 (PMC 11844409): ipTM is systematically depressed by disordered regions and accessory domains unrelated to the interaction interface. KRAS + RAF1-RBD shows ipTM drop from 0.90 → 0.59 when 120 disordered residues per chain are added, despite the interaction being unchanged. ipTM is a geometric accuracy score, not a thermodynamic affinity score.
- Chen et al. 2013 and the BSA literature confirm that even a correct structure with known BSA predicts Kd only to R² ≈ 0.06 for protein-protein pairs. ipTM assesses how correctly the structure is predicted, not the thermodynamic stability of the interface.
- No published paper demonstrates an empirical calibration curve of AF3 ipTM vs experimentally measured Kd across a matched benchmark set as of 2026-04-23.
Specific numbers in h26 that treat ipTM as Kd proxy
| Constant | Claimed value | Problem |
|---|---|---|
| STRC × TMEM145 monomer “Kd” | ~100 nM (derived from ipTM 0.43) | ipTM 0.43 has no mapped Kd. The 100 nM value appears in strc-tmem145-interactions as the red-flag constant; it is uncalibrated. |
| GOLD-pruned ipTM 0.68 → “stronger binding” | implied ≫ 100 nM | Pruning changes which residues contribute to the score; it does not transform ipTM into Kd. |
Conclusion: any Kd number derived from AF3 ipTM for STRC × TMEM145 is speculative. This includes all avidity math in h26 that uses a monomer Kd input.
Disclaimer to include in any downstream analysis: “AF3 ipTM values are confidence scores for structural accuracy, not binding affinity measurements. Mapping ipTM to Kd is not supported by published calibration data. All Kd estimates derived from ipTM should be treated as placeholder values spanning at least 3–4 orders of magnitude until experimental measurement is available.”
4. Disulfide engineering Kd benchmarks
Key references
- Wetzel, Perry, Baase, Becktel 1988 — “Disulfide bonds and thermal stability in T4 lysozyme”, PNAS 85:401. Engineered disulfide in monomeric protein; ΔΔG_stability ~1–3 kcal/mol per well-placed S–S. This is a monomeric folding example, not a dimer interface example.
- Sauer lab / lambda repressor — engineered intersubunit disulfide at dimer interface increases DNA binding activity and thermal stability. Confirmed dimer formation (SEC + CD). No quantitative Kd for the homodimerization itself reported.
- Matsumura, Becktel, Levitt, Matthews 1989 — PNAS 86:6562. Cumulative stabilization from multiple disulfides: ~1 kcal/mol ΔΔG each, additive up to ~3.
Typical Kd improvement from a single engineered intermolecular disulfide
| Modification | Typical ΔΔG | Kd improvement | Caveat |
|---|---|---|---|
| Single S–S at dimer interface (geometric match) | −1 to −3 kcal/mol | 6–150× (e1–3 / RT) | Only valid if geometry is optimal; mismatched geometry gives 0 or destabilizes |
| Single aromatic-aromatic replacement (Tyr→Trp across C2) | −0.5 to −2 kcal/mol | 2–30× | Depends on packing geometry; steric penalty is common for Trp |
| Single charge → neutral (Arg→Phe) | −0.5 to +0.5 kcal/mol | 0.4–2× | Removing a buried charged residue has unpredictable outcome if solvation changes |
Note: these ranges apply to cases with a confirmed dimer and a measured ΔΔG. For h26, there is no wet-lab Kd for the WT homodimer, so ΔΔG cannot be computed relative to a baseline.
The L-zipper precedent (Alber 1992 Curr Opin Struct Biol) for Trp substitution at a leucine-zipper position gives −0.5 to −1.5 kcal/mol per position — this is what underpinned the S1579W/R1581Y design in h26. AF3 Phase 1 results suggest the approach fails for this specific interface, likely because the 1579-1581 triplet is more deeply embedded in the ARM repeat than a surface-exposed leucine-zipper position.
5. Red flags — h26 Kd inheritance from unmeasured baseline
All quantitative claims in h26 that involve Kd are downstream of the following unmeasured input:
STRC × TMEM145 Kd (not measured in any paper as of 2026-04-23)
Tracing the dependency:
| h26 claim | Dependency on unmeasured Kd | Can be rescued without Kd? |
|---|---|---|
| ”Avidity drops effective Kd 100-1000ד | Requires Kd_monomer as input to ratio | No — ratio is dimensionless but Kd_dimer = Kd_mono / (C_eff × N_factor) |
| “1 nM dimer Kd” | Direct: assumes 100 nM monomer | No |
| ”100 nM → 1 nM improvement sufficient for OHC engagement” | Requires knowing the minimum effective Kd for OHC TMEM145 engagement | No — requires cellular occupancy data |
| Avidity principle validity | Independent — principle is textbook-valid | YES — the avidity framework is correct regardless of the Kd baseline |
| AF3 gate ipTM ≥ 0.50 for dimer | Does NOT depend on Kd; it is a structural confidence score | YES — this gate is internally meaningful even without Kd |
| Phase 1 results (ALL 4 mutants fail) | Does NOT depend on Kd | YES — homodimer engineering failed on structural grounds, independent of Kd |
How many h26 numbers are downstream of the unmeasured Kd: 3 out of 4 quantitative claims (Kd_dimer value, improvement factor magnitude, clinical sufficiency assessment). Only the phase-pass/fail determination is independent of the unmeasured baseline.
h26 is fundamentally unverifiable at the quantitative level until:
- An experimental STRC × TMEM145 Kd is measured (SPR/BLI), OR
- A cellular occupancy assay (HEK293 co-IP titration) establishes the minimum STRC expression needed for TMEM145 engagement, providing an implicit Kd floor.
The Phase 1 failure adds a separate blocking condition: no current engineered variant exists to apply the avidity math to. Both blockers would need to be resolved before h26 can make quantitative claims.
Connections
[part-of]_hub (literature-params)[applies]STRC Engineered Homodimer Avidity (h26)[applies]STRC Mini-STRC Single-Vector Hypothesis (h03) — avidity math cross-applies if dimer ever confirmed[applies]STRC Synthetic Peptide Hydrogel HTC (h09) — Kd baseline gap is shared[see-also]strc-tmem145-interactions — the upstream Kd-gap documentation[see-also]STRC Engineered Homodimer Phase 1 Results[see-also]STRC Homodimer Interface From CIF