Molecular structure has been measured thousands of times and the numbers agree. So why does our work keep saying “not measured by us”? The answer is specific, not general: most of it transfers, and exactly two things don't.
Physics and geometry. Avogadro, kT, diffusion limits, Collins–Kimball and Berg–Purcell transport. Bilayer 4 nm. An Ig domain 4 nm; a Fab 4×5×7 nm from thousands of crystal structures. Ectodomain heights from SAXS and crystallography, agreeing to within an ångström across labs.
Our 14 nm reach, the 11.4–18.9 nm epitope spans, the Ceff footprint, the L₂/L₁ bound — all of this. No hedging needed, and this is the biggest tier.
Solution kinetics for a named pair, by SPR or BLI. Inter-lab agreement of roughly 2–3× is normal, and the ranking within a mutant ladder is more reliable than any absolute value. Every kon and koff we use comes from here.
Absolute receptor copy number and surface density. Quantitative-flow-cytometry methodology states plainly that antibody-based methods cannot deliver objective, reproducible, absolute quantification. Calibration depends on bead standards, lot-specific fluorophore ratios, compensation settings that differ by instrument, nonspecific binding that alone reads as ~500 receptors per cell, passage number, and the enzyme used to lift the cells.
This is specifically our problem, because our central claim is that density is the governing variable. The input we lean on hardest has the worst calibration.
Rate constants at a live cell–cell interface are not the same numbers as in solution. For TCR–pMHC: 2D off-rates run orders of magnitude faster than 3D, with a FRET assay giving 4–12×. 2D affinities span three logs where solution spans one, so SPR compresses dynamic range. 2D binding is cytoskeleton-dependent — perturbing actin changes it. And the worst of it: 3D off-rate correlates inversely with T-cell responsiveness while 2D off-rate correlates positively. That is a sign disagreement, not a scale factor.
The molecules are in the same environment. The measurements are not. An SPR chip is a protein on glass in flowing buffer; a synapse is two live membranes under cytoskeletal tension. The field has known this for fifteen years without resolving the conversion.
Our criterion says the two cell populations sit on opposite sides of the assay clock. Here is where they actually sit, and what a 2D correction does to them.
1/λ; faster on-rates speed it too, so there is no compensating term. The tolerance is about 3.2× on the best variant, and two of six variants are already past it at λ = 1 — which Section 6.2 states in print.| variant | τ single-arm | τ relaxation | t / τ | breaks at |
|---|---|---|---|---|
| parental | 3,846 s | 19.4 h | 0.31 | 3.24× |
| VkY92A | 526 s | 16.6 h | 0.36 | 2.77× |
| VkY91A | 213 s | 13.8 h | 0.43 | 2.31× |
| VkR95A | 43 s | 7.3 h | 0.83 | 1.21× |
| VkR95A+VhD97A | 29 s | 5.5 h | 1.09 | past |
| VkY94A+VhY99A | 28 s | 5.3 h | 1.14 | past |
The split is not between measured and unmeasured. It is between ratios and absolutes — the same rule we already found for mechanism, showing up again in measurement error.
+1.068 under a 3×, 10× or 5× systematic error on either axis.N₂₀ = 40.16/µm² is linear in the density calibration. A 10× error gives 432.10.04 × A and not a number.The field is not starting over every study. It has a structural and physical foundation that transfers exactly, a kinetic layer good to a few fold, and two soft places: how many receptors are really on a cell, and what a rate constant becomes when you put both molecules in live apposed membranes instead of on a chip. Our work inherits both and no others.
The 2D discrepancy is measured for TCR–pMHC — a receptor under active cytoskeletal load, which is proposed as the cause of its high apparent off-rate. An IgG-format antibody arm binding a surface antigen is not obviously under that load. Whether the 2D correction transfers to an engager arm has never been measured, and that is a narrower, more answerable question than the one we started from.
It is also the single most valuable measurement anyone could make for this framework — ahead of the contact-area image, because it decides whether the criterion stands at all rather than which of two readings of a threshold is right.
Distances to scale at 8 px/nm. Rate constants and densities from the primary tables of the two published affinity series; relaxation times from our conserved three-species model. Nothing here was measured by us.