Disclaimer: All datasets in this repository are simulated or pseudodata generated solely for methodological demonstration purposes. No proprietary, confidential, patient-derived, or employer-affiliated data is included. This work represents independent research and educational development conducted outside of any employment context and does not reflect the proprietary methods, data, or intellectual property of any employer or collaborator.
This repository is released under the MIT License. © 2026 Bo Ma (tjmb03). Reuse with attribution.
A mechanistic first-in-human (FIH) dosability screen for tumor-targeted bispecific antibodies. Given a candidate's binding parameters, it answers a question you can ask before any dose exists: does this molecule even have a dosable window — a concentration that is both efficacious and safe — and if several candidates do, which has the most margin?
The worked example is an anti-MUC1 × CD40 T-cell–engaging / APC-agonist bispecific, but the model is general to any bridging bispecific whose efficacy runs through a ternary complex and whose safety runs through systemic agonist-receptor occupancy.
This is a companion to ocular-tmdd-format-selection:
same theme — use mechanism to select molecules — a different modality and a different disposition problem.
For a bridging bispecific, efficacy is not monotonic in dose. Signaling requires a productive ternary complex — tumor antigen · drug · receptor. Too little drug and there is no bridging; too much drug and each arm is saturated by its own drug molecule (the prozone / hook effect), so the trimer collapses. Efficacy is therefore bell-shaped, and you dose toward a window, not toward the maximum.
The sharper point: whether a usable window exists at all is a computable property of the molecule. Efficacy peaks at the tumor, where avidity stabilizes the trimer; the dose-limiting hazard (cytokine release) is driven by systemic, monovalent receptor occupancy, which has no avidity benefit. If the molecule's productive window sits to the right of the occupancy ceiling, no dose is both efficacious and safe — and that verdict falls out of the binding parameters alone, before a single animal or patient.
At rapid-binding equilibrium with no inter-arm cooperativity (α = 1), the trimer is
[A·drug·B] = [drug] · [A_free] · [B_free] / (KA · KB)
with the free targets depleting as drug binds (solved by fixed-point iteration in
ternary.py). Two results carry the whole model — and are pinned in the
test-suite:
- The trimer peaks at the geometric mean of the two arm KDs,
√(KA·KB)— exact in the target-excess limit and independent of how asymmetrically affinity is split between the arms. Only the product of the arm KDs sets the peak location: arms split 0.3 / 30 peak at the same concentration as 3 / 3.
- The peak height is capped by the limiting (scarcer) target. With the arm KDs fixed (peak pinned at
√(KA·KB)), sweeping one target's density moves the peak height but never its position; height climbs toward a ceiling set by the scarcer target with diminishing returns. So target density sets efficacy magnitude, separately from where the window sits.
Put together, these give the bell — narrow, with its position fixed by the KDs and its height by the targets:
Efficacy is the tumor trimer, avidity-stabilized. Safety is systemic CD40 occupancy, a plain
monovalent one-site curve (corridor.py) that defines a dosable corridor
between a MABEL floor (default 10% occupancy — the minimal-pharmacology start dose) and an occupancy
ceiling (default 25% — the CRS-risk limit). Crucially, both bounds move with the monovalent CD40 KD,
not the avidity-enhanced tumor KD.
A candidate is dosable exactly when a concentration exists that is at once productive
(tumor trimer ≥ 50% of its max, i.e. drug above the rising-shoulder onset shoulder_lo) and safe
(at or below the occupancy ceiling). That reduces to a single inequality
(screen.py):
dosable ⇔ shoulder_lo ≤ occupancy_ceiling
margin = log10( occupancy_ceiling / shoulder_lo )
Positive margin = dosable with headroom; negative = the productive window has slid right of the ceiling and no safe dose is efficacious.
Ternary-complex avidity (the slowed apparent off-rate of the assembled trimer) is modeled as a
fold-tightening of the effective tumor-arm KDs, so the tumor optimum sits at √(KA·KB) / avidity —
higher avidity pulls the bell left, into the corridor. The systemic corridor gets no avidity benefit.
Weaken avidity and the same molecule slides its productive window right, out of the corridor:
This is why avidity, not the monomer affinities, is often the load-bearing design parameter — and why the screen is worth running on a bivalent-vs-monovalent format decision.
Six hypothetical candidates (data/candidates.csv), each perturbing one lever,
run through screen_candidate and ranked by margin (examples/candidate_panel.py):
| candidate | KA / KB / avidity | tumor optimum | occupancy ceiling | margin (log₁₀) | verdict |
|---|---|---|---|---|---|
| BSP-04 | 0.2 / 5 / 8 | 0.125 nM | 1.67 nM | +2.81 | GO — loose CD40 arm ⇒ widest corridor |
| BSP-05 | 16 / 1 / 21 | 0.190 nM | 0.33 nM | +1.78 | GO — but low CD40 density ⇒ weak efficacy magnitude |
| BSP-01 | 16 / 1 / 21 | 0.190 nM | 0.33 nM | +1.77 | GO — avidity-engineered lead, optimum in corridor |
| BSP-06 | 1 / 1 / 6 | 0.167 nM | 0.33 nM | +1.66 | GO — balanced, highest efficacy magnitude |
| BSP-03 | 5 / 0.2 / 8 | 0.125 nM | 0.067 nM | +1.41 | GO* — tight CD40 arm drops the ceiling; dose to shoulder only |
| BSP-02 | 16 / 1 / 1 | 3.996 nM | 0.33 nM | −0.10 | NO-GO — avidity lost, window right of ceiling |
Three mechanistic reads the screen makes explicit:
- BSP-01 vs BSP-02 — identical arms, avidity 21 → 1. Losing avidity moves the tumor optimum from 0.19 nM (inside the corridor) to 4.0 nM (its productive shoulder now sits right of the 0.33 nM ceiling). The bivalent format is a GO; the monovalent format of the same arms is a NO-GO.
- BSP-03 vs BSP-04 — mirror-image arm asymmetry with the same tumor potency, but the CD40 arm affinity sets the systemic corridor: a tight CD40 arm (BSP-03) collapses the ceiling to 0.067 nM and leaves only shoulder-dosing; a loose CD40 arm (BSP-04) opens the widest window of the panel.
- BSP-05 vs BSP-01 — same scaffold, 10× lower tumor CD40 density. Still dosable, same optimum dose, but ~10× lower peak trimer: density sets efficacy magnitude, not dosability. Dosable ≠ efficacious.
pip install -e . # or: pip install -e ".[dev]" for the tests
python -m pytest -q # 15 tests: the two model results + the decision rule
python -m bsdose.figures # regenerate every figure in figures/ from the model
python examples/candidate_panel.py # print the ranked table + rebuild the panelProgrammatic use:
from bsdose import screen_candidate
r = screen_candidate("my-bsp", KA=16, KB=1, avidity=21, MUC1=5, CD40=0.5)
print(r.dosable, round(r.margin_log10, 2), r.verdict)
# True 1.77 GO: optimum reachable, comfortable margin- Rapid-binding equilibrium, no cooperativity (α = 1). A full kinetic dual-target TMDD would add on/off rates, internalization, and turnover; the equilibrium form is deliberately the minimal object that makes the go/no-go computable.
- Avidity is a lumped surrogate — a fold-reduction in the effective tumor-arm KDs standing in for the ternary-complex apparent off-rate; it is not resolved into geometry or reach.
- Systemic occupancy is a CRS surrogate. The 10% / 25% thresholds are placeholders for a program-specific MABEL/safety analysis, not regulatory values.
- Parameters are representative, not measured. The candidate panel is synthetic and exists to exercise the levers (avidity, arm asymmetry, target density), not to describe any real molecule.
src/bsdose/
ternary.py # trimer equilibrium; peak = √(KA·KB); height capped by limiting target
corridor.py # monovalent occupancy → MABEL floor / occupancy ceiling
screen.py # shoulder ∈ corridor → go/no-go + dosability margin
figures.py # regenerates all figures from the model
data/candidates.csv # the candidate parameter table
examples/candidate_panel.py
figures/ # generated figures + the binding schematic
tests/ # the model results and the decision rule, as assertions
Three repos on one theme — model-informed molecule selection, using mechanistic PK/PD to choose between molecular designs before any clinical data exists:
- adc-therapeutic-index — the first-in-human question for a cytotoxic ADC, where the governing logic is the mirror image of this repo: efficacy from conjugate, dose-limiting toxicity from free payload, so dose selection is toxicology/NOAEL, not MABEL.
- ocular-tmdd-format-selection — format selection for a posterior-segment target: which of naked peptide, Fab, or Fc-fusion delivers the most integrated target coverage, via a four-compartment intravitreal TMDD model with FcRn recycling.
MIT © 2026 Bo Ma