Binding & Affinity

Two binding workflows: saturation binding to characterize a ligand-target pair from scratch, and competition binding to derive Ki for an unlabeled compound using a labeled tracer with known Kd.

Saturation Binding (Kd, Bmax)

The model (one-site total binding)

Total = (Bmax * [L]) / (Kd + [L]) + NS * [L]

Where [L] is the free ligand concentration. Specific binding (the part that matters) is the first term:

Specific = (Bmax * [L]) / (Kd + [L])

• Kd - equilibrium dissociation constant. Lower means tighter binding.
• Bmax - maximum specific binding. Reflects receptor density.
• NS - non-specific binding component, usually linear in [L].

Specific vs optional nonspecific component

Upload one non-negative concentration column and onebinding response column. Choose the model that matches the response already represented in that table:

• One site - fit the saturable hyperbola to a prepared specific-binding response.
• One site plus nonspecific - fit the hyperbola plus a linear nonspecific term to a total-binding response.
• Model choice - set one_site orone_site_nonspecific explicitly. Separate total and nonspecific series are not jointly fitted by this workflow.

The result reports Kd and Bmax with confidence intervals when the fit can estimate them, plus the nonspecific slope for the second model.

Coverage

Gradiance estimates Kd from the nonlinear fit to the original concentration-response values. At least four observations are required. If the concentrations do not approach a plateau, Kd and Bmax may remain weakly constrained and the result carries that limitation.

What you need

• Labeled ligand titration spanning at least 0.1× Kd to 10× Kd (wider if possible). 8 concentrations, in triplicate.
• For one_site_nonspecific, a total-binding response whose residual linear component is scientifically justified.
• A single equilibrium time per concentration (kinetic association is a different workflow - see Kinetics).

Competition Binding (Ki)

The idea

Hold a labeled tracer (with known Kd) at a fixed concentration, titrate an unlabeled competitor, and measure how much labeled binding is displaced. The IC₅₀ of the displacement curve converts to Ki via Cheng-Prusoff:

Ki = IC50 / (1 + [L] / Kd)

where [L] is the tracer concentration and Kd is the tracer's previously-determined dissociation constant. The conversion handles the fact that the observed IC₅₀ depends on tracer concentration, while Ki does not.

What you need

• A previously-validated Kd of the tracer in your system. Without it, you can't derive Ki - the fit will return only the apparent IC₅₀.
• The tracer concentration used in the competition assay.
• A competitor titration covering the expected IC₅₀, ideally spanning 4 orders of magnitude.
• Vehicle (no competitor) and full-displacement (high competitor dose) controls. The agent uses these to define the binding window.

One-site competition

This workflow fits one-site displacement and reports top, bottom, IC₅₀, and Hill slope. It does not select or fit a two-site competition model. Systematic residuals or incomplete displacement are reasons to revise the experiment or choose a separately supported model with an explicit design.

QC specific to binding

See Quality Control for the full list. The ones that bite hardest in binding:

• Bmax unbounded. Highest concentration didn't saturate. Add higher-concentration points or accept that Bmax is a lower bound, not an estimate.
• Kd extrapolated. Half-saturation falls outside the tested range. Same fix as IC₅₀ extrapolation in dose-response: bracket the inflection.
• Linear non-specific dominates. When NS binding is comparable to specific at high tracer concentrations, Bmax CIs balloon. Use a higher-affinity tracer, or pre-block before measurement.
• Hill slope deviates from −1 (competition). A one-site competition has Hill = −1.0. Real values 0.85-1.15 are normal; outside that, consider two-site behavior or non-equilibrium artifacts.

What the result looks like

Saturation runs return Kd and Bmax, an optional nonspecific slope, fit diagnostics, and parameter intervals when estimable. Competition runs return IC₅₀ and return Ki only when tracer Kd and tracer concentration are both explicit. Free accounts include 20 free runs per calendar month (UTC) and can export a PNG figure and basic CSV results. Entitled accounts may also export other figure formats and a Python saved-fit replay. See Understanding your results for reading the result panel.