Calculator
Formula used
This tool estimates cooperativity using the Hill plot. For each data point, compute fractional saturation θ and the odds ratio θ/(1−θ).
- Hill relationship: log( θ/(1−θ) ) = nH · log(L) + b
- Hill coefficient: nH is the slope from linear regression
- Cooperativity index: CI = nH − 1
- Half-saturation: when θ = 0.5, then log(L50) = −b/nH
Interpretation: nH > 1 indicates positive cooperativity, nH ≈ 1 indicates no cooperativity, and nH < 1 indicates negative cooperativity.
How to use this calculator
- Choose an input mode: θ values, or bound and total values.
- Paste your dataset as one row per line, using commas or spaces.
- Click Calculate to see nH, CI, L50, and R².
- Use the CSV or PDF buttons to export the results table.
- If results look unstable, add points near θ ≈ 0.1 and 0.9.
Example data table
| L (µM) | θ | Notes |
|---|---|---|
| 0.5 | 0.12 | Low occupancy |
| 1 | 0.22 | Rising region |
| 2 | 0.36 | Mid transition |
| 5 | 0.58 | Near half-saturation |
| 10 | 0.72 | Approaching plateau |
| 20 | 0.83 | High occupancy |
Copy these rows into the dataset box to test quickly.
FAQs
1) What does the Hill coefficient represent?
It summarizes how sharply binding increases with ligand concentration. Values above one suggest positive cooperativity. Values below one suggest negative cooperativity. Near one implies independent binding behavior.
2) Why can’t θ be exactly 0 or 1?
The Hill plot uses a logarithm of θ/(1−θ). If θ is 0 or 1, that ratio becomes 0 or infinite, making the log undefined. Use values slightly inside the range.
3) Is CI a standard term?
Cooperativity is commonly reported as nH. This tool also reports CI = nH − 1 as a simple “distance from non-cooperative” indicator. Always cite nH in publications.
4) What is L50 in the results?
L50 is the ligand concentration where θ = 0.5 based on the fitted line. It is not always identical to Kd, especially under strong cooperativity or model mismatch.
5) How many points do I need?
Two points are the minimum, but more is better. Include low, mid, and high saturation data. Wider coverage usually improves the slope estimate and the reported R².
6) Should I use base 10 or natural logs?
Either works. The slope nH stays the same because both axes change by the same constant factor. Choose the base that matches your lab convention.
7) My R² is low. What should I check?
Confirm the data are properly normalized and monotonic. Remove obvious outliers, expand the concentration range, and avoid θ values near 0.5 only. Cooperativity can also be concentration-dependent.
8) Does this tool replace mechanistic modeling?
No. The Hill plot is a descriptive summary. For mechanistic insight, fit a binding model that matches your system, including stoichiometry and multiple states, then compare parameters across conditions.