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| Concentration (µM) | Response (a.u.) | Comment |
|---|---|---|
| 0.5 | 0.12 | Low signal near baseline |
| 2 | 0.33 | Transition region |
| 10 | 0.70 | Approaching saturation |
| 50 | 0.92 | Near Bmax plateau |
Equilibrium datasets often span sub‑nanomolar to millimolar concentrations, and the curve shape guides model choice. A single saturating plateau typically supports one‑site behavior, while a steeper transition can indicate cooperativity captured by a Hill slope. Mixed plateaus or shoulder regions may reflect two apparent affinity populations. For robust estimation, plan concentrations from about 0.1× to 10× the expected Kd, and include two points above the plateau to constrain Bmax. Replicates help quantify variance and reduce overfitting substantially.
Kd is the concentration producing half‑maximal response, so smaller Kd implies tighter binding. Bmax approximates the signal ceiling, which can drift with sensor capacity, immobilization level, or assay gain. When Bmax changes between runs, normalize responses or compare ratios rather than absolute amplitudes. If Hill n is greater than 1, binding appears cooperative; if below 1, heterogeneity is plausible.
R² summarizes explained variance, but residuals reveal systematic mismatch. Random residual scatter around zero suggests the model captures the trend. Curvature in residuals can imply mass‑transport limitation, baseline offset, or an unmodeled binding state. RMSE in response units helps compare fits across experiments of similar scaling. As a practical rule, an RMSE below 5% of the response range is often acceptable for screening. AIC penalizes extra parameters, so lower AIC favors simpler models when comparing fits on the same dataset.
Association traces are fit with a saturating exponential to estimate kobs and Req, where kobs governs approach speed and half‑life equals ln(2)/kobs. Dissociation traces are fit with an exponential decay to estimate koff, and the dissociation half‑life equals ln(2)/koff. Ensure responses remain positive for log‑linear stability. Use dense early timepoints, then widen spacing after the curve approaches equilibrium.
Across a concentration series, kobs typically increases linearly with analyte concentration when a simple interaction dominates. Fitting kobs = kon·[C] + koff yields kon as the slope and koff as the intercept, enabling an affinity estimate Kd ≈ koff/kon. Use consistent concentration units and avoid points affected by rebinding. If the kobs plot bends, consider transport limits or multi‑step binding.
Aim for at least 8–12 concentrations spanning below and above the expected Kd. Include multiple points near the inflection region to stabilize Kd and Hill estimates, and repeat key concentrations to assess noise.
Two-site models introduce more parameters and can fit noise. Small datasets or narrow concentration ranges produce multiple similar solutions. Use broader concentration coverage, replicate measurements, and treat two-site outputs as exploratory unless strongly supported.
A baseline offset can come from bulk signal or incomplete reference subtraction. Subtract the initial value from all points before fitting, or include early timepoints for a better baseline estimate. Keep the same processing for comparisons.
A single trace gives kobs at one concentration, which cannot uniquely separate kon and koff. Use multiple concentrations to fit the kobs line, or combine association and dissociation fits with appropriate experimental assumptions.
Low R² can reflect high noise, too few points, or a model that misses key behavior. Check residual patterns, confirm concentration accuracy, and verify that responses are within the dynamic range without saturation or clipping.
Negative values usually indicate mismatched units, data entry errors, or a poor model choice. Recheck column order, confirm positive concentrations and times, and prefer models that reflect the known mechanism and experimental setup.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.