Ligand depletion
Fraction of added ligand bound
Modeled Planning tolerance
ASSAY DESIGN / FINITE-BATH BINDING
Free-Dose Check.
You know the dose you added.
Check the dose left free.
ONE QUESTION. EXPLICIT ASSUMPTIONS.
Does ligand depletion matter across your titration? Explore a conserved, equilibrium 1:1 model before changing cells or volume.
Read the modelThe browser runtime could not load. Your inputs have not been sent anywhere. Check your connection and retry, or use the offline Python CLI.
THE APPROXIMATION IS THE QUESTION
Start with a binding design.
Enter your incubation conditions, declare what the model can assume, and check every concentration. Or load an explicitly synthetic case to explore.
01Quantify depletion
Free ligand, occupancy, and approximation error.
02Preserve uncertainty
Ranges in, ranges out. No invented midpoint.
03Test a change
Cell and volume limits, with practical constraints.
A small model, not an assay verdict.
Equilibrium. One ligand per independent site. Conserved ligand and binding capacity. No avidity, internalization, or functional potency inference.
MODEL-BASED ASSESSMENT
Site occupancy
Exact binding versus free = added
Exact Naive
Points are evaluated input doses; connecting lines are visual guides. Shading shows marginal bounds, not joint trajectories or confidence intervals. Zero-dose controls are excluded from the log axis and retained in the table.
ONE VARIABLE AT A TIME
What would meet your tolerance?
Alternative condition
Every concentration, accounted for.
Full precision in exports. Display values are rounded.
| Added nM | Free nM | Bound nM | Depletion % | Occupancy % | Naive % | Error pp | Assessment |
|---|
Depletion: fraction of ligand bound. Occupancy: fraction of sites occupied. They are not the same quantity.
Assumptions & evidence record
TRANSPARENT BY DESIGN
Established equations.
Inspectable decisions.
The contribution is a small pre-experiment check, not a new binding theory. No affinity fitting. No functional potency correction. No hidden acceptance threshold.
Download Python + source ↓The model
Kd = (RT − B)(LT − B) / B
The solver uses a scaled, cancellation-resistant solution and independently evaluates free ligand. Site concentration comes from accessible sites, cell number, and incubation volume. Bounds use all four input corners.
The design rule
Rcap = εLT + εKd / (1 − ε)
The lowest positive dose sets the binding-capacity limit. Recommended volume is rounded up and cells down, then rechecked through the same model.
Scientific context: Hulme & Trevethick, 2010; Hunter & Cochran, 2016; Kamprath et al., 2023.